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MY WAY TO
RELIABILITY AND SAFETY
M.
Yastrebenetsky
I was born in Moscow
on September 10, 1934. I wrote about my family
and previous generations of Yastrebenetsky (a
soldier under Emperor Nicholas I, a businessman,
a doctor, a chemical engineer) in my book "Generations
of Yastrebenetsky” [1]. After finishing the
institute and postgraduate studies, 2/3 years of
my life were connected with activity in the
fields of reliability and safety of technical
systems. This activity is the subject of the
article.
Cite: M.
Yastrebenetsky MY WAY TO RELIABILITY AND SAFETY.
Reliability: Theory & Applications. 2024,
September 3(79): 27-40, DOI:
https://doi.org/10.24412/1932-2321-2024-379-27-40
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27-40
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ALGORITHMS FOR
APPROXIMATING A FUNCTION BASED ON INACCURATE
OBSERVATIONS
G.Sh. Tsitsiashvili, M.A. Osipova
This paper is
devoted to the approximation of a function by a
trigonometric polynomial based on its inaccurate
values at selected points. Two methods of
observation are considered. The first method is
to make observations at points evenly
distributed on the segment where the function is
specified. The second method is to take
observations at the points of division into a
finite number of equal parts of the
neighbourhoods of the selected points. Upper
estimates of the standard deviation of the
function from trigonometric polynomials are
constructed and the rate of their convergence is
estimated. Differences were found in the
computational complexity of these approximations
and in the number of observations of the
function values at the selected points. Thus,
the problem of approximating a function from
inaccurate observations of their values at
selected points is a multi-criteria one and its
solution depends on the choice of observation
points.
Cite: G.Sh.
Tsitsiashvili, M.A. Osipova ALGORITHMS FOR
APPROXIMATING A FUNCTION BASED ON INACCURATE
OBSERVATIONS. Reliability: Theory & Applications.
2024, September 3(79): 41-46, DOI:
https://doi.org/10.24412/1932-2321-2024-379-41-46
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41-46
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AVAILABILITY AND
PROFIT OPTIMIZATION OF CONTINUOUS CASTING SYSTEM
OF THE STEEL INDUSTRY USING ARTIFICIAL NEURAL
NETWORK TECHNIQUE
Shikha Bansal, Sohan
Lal Tyagi, Urvashi
The main purpose of
this study was to optimize the performance
parameters of the casting process using a neural
network approach. The casting process is molten
or liquefied metal is poured into the mould
cavity, after solidification it takes the near
net shape of the cavity. The entire
manufacturing process goes through six stations
viz Pouring turret "ladle", "Tundish", "Mould",
"Water spray chamber", "Support roller" and "Torch
cutter". The Artificial Neural Network (ANN)
technique is used in this paper to analyze the
casting system’s availability, profitability,
and state probability variation. An effort has
been made to identify the most critical
component of the system. The outcomes of the
analysis will help the practitioners in deciding
effective maintenance strategies.
Cite: Shikha
Bansal, Sohan Lal Tyagi, Urvashi AVAILABILITY
AND PROFIT OPTIMIZATION OF CONTINUOUS CASTING
SYSTEM OF THE STEEL INDUSTRY USING ARTIFICIAL
NEURAL NETWORK TECHNIQUE. Reliability: Theory &
Applications. 2024, September 3(79): 47-58, DOI:
https://doi.org/10.24412/1932-2321-2024-379-47-58
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47-58
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TOPP-LEONE
EXPONENTIATED GOMPERTZ INVERSE RAYLEIGH
DISTRIBUTION: PROPERTIES AND APPLICATIONS
Sule Omeiza Bashiru,
Alaa Abdulrahman Khalaf, Alhaji Modu Isa
This paper focused
on deriving a new lifetime distribution having
five parameters by compounding the Gompertz
inverse Rayleigh model and the Topp-Leone
exponentiated-G family of distributions. The new
model is called Topp-Leone exponentiated
Gompertz inverse Rayleigh (TLEGoIRa)
distribution. The new model is very flexible and
the shape of its pdf can be positively or
negatively skewed and symmetric. Some
statistical characteristics of the new model,
such as the moments, incomplete moments,
quantile function, rényi entropy and order
statistics are derived and investigated. The pdf
of the minimum and maximum order statistics of
the new model were derived and studied. The
model’s parameters are estimated using the
maximum likelihood approach. A simulation study
was conducted to investigate the consistency of
the newly proposed model, using the average bias
and root mean square error (RMSE) as metrics.
The outcome of the simulation suggested that as
sample sizes increase, both the average bias and
root mean square error (RMSE) decrease,
indicating that the distribution is consistent.
Finally, two real-life datasets were used to
explore the new model’s importance and
adaptability in comparison to other competing
models The results of the application revealed
that the new distribution out performs its
competitors.
Cite: Sule Omeiza Bashiru, Alaa Abdulrahman
Khalaf, Alhaji Modu Isa TOPP-LEONE EXPONENTIATED
GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION:
PROPERTIES AND APPLICATIONS. Reliability: Theory
& Applications. 2024, September 3(79): 59-77,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-59-77
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59-77
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A PROBABILITY MODEL
FOR SURVIVAL ANALYSIS OF CANCER PATIENTS
Mousumi Ray, Rama
Shanker
It has been observed
by statistician that to find a suitable model
for the survival analysis of cancer patients is
really challenging. The main reasons for that is
the highly positively skewed nature of datasets.
During recent decades several statistician tried
to propose one parameter, two-parameter,
three-parameter, four-parameter and
five-parameter probability models but due to
either theoretical or applied point of view the
goodness of fit provided by these distributions
are not very satisfactory. In this paper a
compound probability model called gamma-Sujatha
distribution, which is a compound of gamma and
Sujatha distribution, has been proposed for the
modeling of survival times of cancer patients.
dolor Many important properties of the suggested
distribution including its shape, moments (negative),
hazard function, reversed hazard function,
quantile function have been discussed. Method of
maximum likelihood has been used to estimate its
parameters. A simulation study has been
conducted to know the consistency of maximum
likelihood estimators. Two real datasets, one
relating to acute bone cancer and the other
relating to head and neck cancer, has been
considered to examine the applicability,
suitability and flexibility of the proposed
distribution. The goodness of fit of the
proposed distribution shows quite satisfactory
fit over other considered distributions.
Cite: Mousumi
Ray, Rama Shanker A PROBABILITY MODEL FOR
SURVIVAL ANALYSIS OF CANCER PATIENTS.
Reliability: Theory & Applications. 2024,
September 3(79): 78-94, DOI:
https://doi.org/10.24412/1932-2321-2024-379-78-94
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78-94
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ON A DISCRETE TIME
SHOCK MODEL IN CRITICAL SITUATION
Reza Farhadian,
Habib Jafari
In this paper, we
study a discrete time shock model which is
defined based on the length of the time between
successive shocks. For a system that is exposed
to a sequence of random shocks over time under
this model, if the interarrival time between two
successive shocks is equal to a prefixed
critical time point such as δ, the system fails,
and the system is not damaged otherwise. We have
considered two situations for the system, which
are regular situation and critical situation,
then we investigate the statistical behavior of
the systemŠs lifetime under these situations.
More precisely, we obtain the probability
generating function of the system’s lifetime,
the mean time to failure, the variance of the
system’s lifetime, the Laplace transform of the
system’s lifetime, and some other related
results. We end the paper with an example
including numerical comparisons of the results.
Cite: Reza
Farhadian, Habib Jafari ON A DISCRETE TIME SHOCK
MODEL IN CRITICAL SITUATION. Reliability: Theory
& Applications. 2024, September 3(79): 95-106,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-95-106
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95-106
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ENHANCED METHODS
UNDER EXPONENTIAL DISTRIBUTION CONCERN WITH EWMA
AND DEWMA METHODS
Dr. V. Kaviyarasu
and M. Inbarasi
Statistical Process
Control plays a crucial part in improving the
quality and lowering the fluctuation in the
production process environment. In SPC, the most
popularly used methods are Shewhart control
chart techniques and EWMA techniques which
distinguish itself for its quick identification
of minute process deviations, which makes it an
essential tool for guaranteeing product. EWMA
methods detect variances in quality of the
product as well as services, measure process
mean shifts with control charts, and track
manufacturing process parameters to find
deviations and make necessary adjustments. The
exponential distribution was employed in this
study because it may reflect vast and bulk
production in everyday life. Exponentially
distributed data, evaluate it alongside the EWMA
function. This paper’s objective is to study the
impact of EWMA & DEWMA parameters within the
EWMA control chart’s performance using
exponential distribution. Further, A few tables
are provided with suitable illustrations that
can be available with parameters with the help
of these findings. The study also examines how
the EWMA parameter affects the shape of the
distribution.
Cite: Dr. V. Kaviyarasu and M. Inbarasi
ENHANCED METHODS UNDER EXPONENTIAL DISTRIBUTION
CONCERN WITH EWMA AND DEWMA METHODS. Reliability:
Theory & Applications. 2024, September 3(79):
107-119, DOI:
https://doi.org/10.24412/1932-2321-2024-379-107-119
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107-119
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RELIABILITY SAMPLING
PLAN FOR GENERALIZED INVERTED EXPONENTIALLY
DISTRIBUTED UNDER PROGRESSIVE TYPE-II CENSORED
DATA
S. Singh, A. Kaushik
This article aims to
explore a sampling strategy designed to assess
the reliability of products that exhibit
lifetimes following a GIED. Considered sampling
approach has been specially constructed for a
Type-II progressive censoring scheme, which
includes binomial removals as part of its
methodology. Its core objectives is to find out
acceptance constant and the optimum sample size.
To facilitate practical implementation, the
article presents a tabulated form of the
sampling plan for the selected specification, as
per the considered censoring scheme. To validate
the dependability and precision of the suggested
sampling approach, we perform a Monte Carlo
experiment under various scenarios.
Cite: S.
Singh, A. Kaushik RELIABILITY SAMPLING PLAN FOR
GENERALIZED INVERTED EXPONENTIALLY DISTRIBUTED
UNDER PROGRESSIVE TYPE-II CENSORED DATA.
Reliability: Theory & Applications. 2024,
September 3(79): 120-131, DOI:
https://doi.org/10.24412/1932-2321-2024-379-120-131
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120-131
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ROLE OF AGEING
METRICS TO ANALYSE THE SURVIVAL DATA OF TONGUE
CANCER PATIENTS
B. Elina, Pulak
Swain, Satya Kr. Misra, Subarna Bhattacharjee
The paper vividly
describes the non-parametric estimation of basic
quantities for right censored data of times to
death for patients with tongue cancer. Here we
compare patients with two different sets of DNA
profile using several parameters like
reliability function, cumulative hazard rate
function, smoothed hazard rate function and
ageing intensity function. With the help of
graphical representations of these functions, we
analyse which DNA profile patients have better
prognosis.
Cite: B.
Elina, Pulak Swain, Satya Kr. Misra, Subarna
Bhattacharjee ROLE OF AGEING METRICS TO ANALYSE
THE SURVIVAL DATA OF TONGUE CANCER PATIENTS.
Reliability: Theory & Applications. 2024,
September 3(79): 132-143, DOI:
https://doi.org/10.24412/1932-2321-2024-379-132-143
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132-143
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STATISTICAL
PROPERTIES AND APPLICATIONS OF TRANSMUTED SKEW
STUDENT t DISTRIBUTION
David Ikwuoche John,
Mathew Stephen
In this study, a
modified 2-parameter skew t distribution called
the transmuted skew student t distribution (TSStD)
was presented. Some statistical and reliability
properties of TSStD such as the quantile
function, the raw moments, and the moment
generating function (among others), were derived.
Through the method of maximum likelihood, the
two parameters of the model were estimated. The
stability of the model was studied via
Montecarlo simulations utilizing bias, mean
square error, and root mean square error as
metrics. The results from the stability study
revealed that the TSStD was well-behaved. Four
datasets were modeled with the transmuted skewed
student t distribution and four other
probability density models. On the basis of
information criteria, the results revealed that
the transmuted skew student t distribution
provides a better fit for all the datasets
compared to the other competing models.
Cite: David
Ikwuoche John, Mathew Stephen STATISTICAL
PROPERTIES AND APPLICATIONS OF TRANSMUTED SKEW
STUDENT t DISTRIBUTION. Reliability: Theory &
Applications. 2024, September 3(79): 144-156,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-144-156
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144-156
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SINE-TOPP-LEONE
EXPONENTIATED G FAMILY OF DISTRIBUTIONS:
PROPERTIES, SURVIVAL REGRESSION AND APPLICATION
A. M. Isa, S. I.
Doguwa, B. B. Alhaji, H. G. Dikko
In this research
article, we have introduced a new class of
continuous probability distributions known as
the Sine Topp-Leone Exponentiated-G family of
distributions. This newly proposed family
exhibits a higher degree of flexibility compared
to some of the established distribution families.
The various models within this family find
wide-ranging applications in fields such as
physics, engineering, and medicine. Some
statistical properties of the Sine Topp-Leone
Exponentiated-G family of distributions such as
moments, moment generating function, quantile
function and order statistics are derived. Two
special models were also presented and studies.
Maximum likelihood estimation method was used to
estimate parameters of the models. The
consistency of the proposed family was determine
using simulation studies. Two real life datasets
were analyzed to show the flexibility of the
proposed model and the results of the analysis
showed that, the proposed model was more
efficient and best fit the data sets than its
competitors.
Cite: A. M.
Isa, S. I. Doguwa, B. B. Alhaji, H. G. Dikko
SINE-TOPP-LEONE EXPONENTIATED G FAMILY OF
DISTRIBUTIONS: PROPERTIES, SURVIVAL REGRESSION
AND APPLICATION. Reliability: Theory &
Applications. 2024, September 3(79): 157-172,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-157-172
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157-172
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ANALYSIS OF
RELIABILITY OF TYPICAL POWER SUPPLY CIRCUITS
S.V. Rzayeva, N.M.
Piriyeva, I.A. Guseynova
This article is
devoted to the analysis of the reliability of
typical power supply circuits. The question of
what factors have the greatest impact on the
reliability of power supply circuits, as well as
what methods and tools are used to analyze and
improve their reliability is considered.
Particular attention is paid to the comparative
analysis of various types of power supply
schemes and the determination of their
advantages and disadvantages in terms of
reliability. The article also discusses current
trends and developments in the field of
increasing the reliability of power supply and
possible ways to optimize existing circuits. The
results obtained can be useful for specialists
in the field of power engineering and electrical
engineering in the design, maintenance and
modernization of power supply systems.
Cite: S.V.
Rzayeva, N.M. Piriyeva, I.A. Guseynova ANALYSIS
OF RELIABILITY OF TYPICAL POWER SUPPLY CIRCUITS.
Reliability: Theory & Applications. 2024,
September 3(79): 173-178, DOI:
https://doi.org/10.24412/1932-2321-2024-379-173-178
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173-178
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FUZZY LOGIC
RELIABILITY BLOCK DIAGRAM APPROACH FOR PATIENT
HEALTH MONITORING USING R PROGRAMMING
Liji Sebastian, Rita
S, Vennila J
In this research, a
new approach using fuzzy logic and reliability
block diagram (RBD) techniques is used to ensure
the reliability of patient health monitoring
systems. This technique handles uncertainties in
health information, while RBD assesses system
reliability by displaying factor relations. The
RBD model construct for system components and
measure reliability using probabilistic models.
Fuzzy logic identifies the effect of
uncertainties on overall reliability. Using this
approach in a simulated health monitoring
scenario, using R, we demonstrate its
effectiveness and potential to increase reliable
health monitoring for improved patient outcomes
and healthcare efficiency. Furthermore, the
awareness gained from this study can be directed
beyond healthcare such as modern process control
and environmental sensing.
Cite: Liji
Sebastian, Rita S, Vennila J FUZZY LOGIC
RELIABILITY BLOCK DIAGRAM APPROACH FOR PATIENT
HEALTH MONITORING USING R PROGRAMMING .
Reliability: Theory & Applications. 2024,
September 3(79): 179-185, DOI:
https://doi.org/10.24412/1932-2321-2024-379-179-185
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179-185
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RELIABILITY ANALYSIS
OF AN ANTI-DRONE SYSTEM BY CONSIDERING RANDOM
ENVIRONMENTAL FACTORS
Dharmaraja
Selvamuthua, Harshita Badiyasara, Smrati
Tripathia, Priyanka Kalitab, Raina Rajc
In today’s security
landscape, the proliferation of unauthorized
drones in restricted airspace has emerged as a
significant threat. These drones pose various
risks, from potential surveillance and espionage
to more sinister possibilities such as physical
attacks. Consequently, the development of
effective anti-drone laser systems has become
increasingly vital. Our study focuses on three
main objectives: modeling internal reliability,
identifying critical components, and studying
the factors affecting the reliability of
anti-drone systems. We aim to enhance the
overall performance and effectiveness of
anti-drone laser systems by analyzing the
reliability of critical components and
understanding how system parameters influence
system reliability. To this end, reliability
block diagram (RBD) methodology has been
employed to compute the reliability of the laser
subsystem in the anti-drone system. Additionally,
we conduct a comprehensive review of
component-wise reliability to identify
vulnerable points within the system, thus
enabling targeted improvements and optimizations.
To capture the realistic scenario of system
failure behavior, different distributions have
been used to compute the reliability of the
system, ensuring a thorough understanding of its
operational reliability in diverse conditions.
Finally, the energy values and probability of
hitting are obtained for the anti-drone laser
system to effectively mitigate environmental
challenges.
Cite:
Dharmaraja Selvamuthua, Harshita Badiyasara,
Smrati Tripathia, Priyanka Kalitab, Raina Rajc
RELIABILITY ANALYSIS OF AN ANTI-DRONE SYSTEM BY
CONSIDERING RANDOM ENVIRONMENTAL FACTORS.
Reliability: Theory & Applications. 2024,
September 3(79): 186-205, DOI:
https://doi.org/10.24412/1932-2321-2024-379-186-205
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186-205
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STRATEGIES FOR
REPLACEMENT IN WORKFORCE SCHEDULING RELIABILITY
MODELS
Iyappan. M, Balaji.
M, R. Saranraj, G. Sathya Priyanka
It is a typical
occurrence to replace some industrial equipment
or components, such as electronic chips, bulbs,
etc. It deals with the ideas of dependability
theory, in which the likelihood of an equipment
malfunctioning instantly is calculated assuming
that it has operated normally for a given amount
of time, 't'. In reliability, it's known as the
hazard rate. The rate of hazard may be rising,
falling, or staying the same. However,
replacement tactics are employed to maintain
output. Basically, two distinct approaches are
employed. 1. Replacing a broken item; 2.
Replacing items on a regular basis. Since it is
a preventive measure to maintain production, the
effective administration of maintaining system
functionality depends on the application of both
reliability concepts in addition to replacement
theory. One may envision a similar issue with
the personnel system as well. To determine the
best manpower policies in this situation,
replacement methods and dependability theory can
also be coupled. This theory's application to
labor systems is examined, and appropriate
methods for employee replacement and advancement
are covered in order to ensure the system's
successful upkeep. In order to obtain the best
fit, manpower planning is a dynamic process that
controls the movement of workers into, through,
and out of the organization. In order to
determine appropriate manpower replacement
policies for promotion and replacement of
personnel for the successful maintenance of the
system, this study discusses the application of
dependability theory and the renewal process.
Cite: Iyappan.
M, Balaji. M, R. Saranraj, G. Sathya Priyanka
STRATEGIES FOR REPLACEMENT IN WORKFORCE
SCHEDULING RELIABILITY MODELS. Reliability:
Theory & Applications. 2024, September 3(79):
206-214, DOI:
https://doi.org/10.24412/1932-2321-2024-379-206-214
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206-214
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PERFORMANCE ANALYSIS
OF M[X]/GB/1 FEEDBACK RETRIAL QUEUE WITH
VARIABLE SERVER MODEL
N. Micheal
Mathavavisakan, K. Indhira
In this article, a
working vacation policy-based on bulk arrival
feedback retrial queueing system with variable
server capacity has been analyzed. The server
can serve a minimum of one customer and a
maximum of B customers in a batch in accordance
with the variable server capacity bulk service
rule. As soon as the orbit becomes empty at the
time of service completion, the server goes for
a working vacation. The server works at a lower
speed during a working vacation period. In
addition, the steady state probability
generating function for system size and orbit
size is generated by incorporating the
supplementary variables technique (SVT). Further,
the conditional decomposition law is shown for
this retrial queueing system. Moreover, system
performance metrics, and significant special
instances are discussed. Finally, the effects of
various parameters on the system performance are
analyzed numerically.
Cite: N.
Micheal Mathavavisakan, K. Indhira PERFORMANCE
ANALYSIS OF M[X]/GB/1 FEEDBACK RETRIAL QUEUE
WITH VARIABLE SERVER MODEL. Reliability: Theory
& Applications. 2024, September 3(79): 215-229,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-215-229
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215-229
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STOCHASTIC MODELING
AND PERFORMABILITY ANALYSIS OF REPAIRABLE SYSTEM
OF A PLYWOOD INDUSTRY
Mr. Amit Kumar Singh,
Dr. P. C. Tewari
The current paper
analyzes the performance behavior concerning the
performability of the Veneer layup system in a
plywood industry. A Markovian Approach is
utilized to develop a process model for the
system and enhance to evaluate system
performability i.e. the function of system
availability. The study investigates the impact
of varying failure and repair rates on the
availability of system, variation in the
availability is also determined by varying
available repair facilities, using a licensed
software package. Particle Swarm Optimization (PSO)
method has been employed to optimize the results.
Additionally, a Decision Support System (DSS)
has been proposed for making strategic decisions
regarding financial investments and maintenance
order priorities. The findings of the paper will
aid the practitioners in deciding the
maintenance order priorities among various
subsystems.
Cite: Mr. Amit Kumar Singh, Dr. P. C. Tewari
STOCHASTIC MODELING AND PERFORMABILITY ANALYSIS
OF REPAIRABLE SYSTEM OF A PLYWOOD INDUSTRY.
Reliability: Theory & Applications. 2024,
September 3(79): 230-241, DOI:
https://doi.org/10.24412/1932-2321-2024-379-230-241
|
230-241
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E-BAYESIAN
ESTIMATION FOR BATHTUB-SHAPED LIFETIME
DISTRIBUTION BASED ON UPPER RECORD VALUES
Sana, M. Faizan
In this research
paper, we presents the expected Bayesian (E-Bayesian)
estimation of bathtub-shaped lifetime (BSL)
distribution for scale parameter based on upper
record values (URV) using a conjugate prior
distribution. Also, we are considered different
prior distributions for the E-Bayesian
estimators. Some properties of the E-Bayesian
estimators are discussed. A simulation study is
given to compare the performance of the
E-Bayesian estimators with Bayesian estimator.
we notice that the E-Bayesian estimators are
perform better than the Bayesian estimators.
Moreover, the performance of the Bayesian
estimators and E-Bayesian estimators for Prior
II are better than Prior I. Also, we observe
that if we increase the sample size n then the
estimators are showing lesser mean square error
(MSE).
Cite: Sana,
M. Faizan E-BAYESIAN ESTIMATION FOR
BATHTUB-SHAPED LIFETIME DISTRIBUTION BASED ON
UPPER RECORD VALUES. Reliability: Theory &
Applications. 2024, September 3(79): 242-247,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-242-247
|
242-247
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A CLASS OF
LOGARITHMIC-CUM-EXPONENTIAL ESTIMATORS FOR
POPULATION MEAN WITH RISK ANALYSIS USING DOUBLE
SAMPLING
Diwakar Shukla,
Astha Jain
In order to improve
upon the efficiency of an estimate in double
sampling for estimating population mean of
character under study using an auxiliary
variable, a part of survey resources are used to
collect the information on auxiliary variable.
Some authors have suggested exponential-type
estimators and some others advocated for
log-type estimators. But combination of such is
required for specific situation. This paper
presents a class of logarithmic-cum-exponential
ratio estimators in double sampling setup. The
expressions for the mean squared error and bias
of the proposed class of estimators are derived
for two different cases(sub-sample and
independent sample). Sometimes the persons
involved in the sample survey have to undergo
for risk on life. For example, data collection
in naxalites area, working in intense forest,
interview during spread of epidemic or data
collection in politically disturbed region. Such
risk may affect the accuracy, efficiency of
estimation. A linear Risk function is used for
the proposed class of estimators. Two cases of
double sampling are compared in terms of
relative efficiency in view to risk aspect.It is
found that the proposed class of estimators has
a lower mean squared error than the simple mean
estimator, usual ratio, usual exponential, usual
log estimators in the double sampling setup. In
addition, these theoretical results are
supported by a numerical example. Risk function
based simulated study is performed for the
support of findings of the content. Optimal
sample sizes under risk are derived and compared
under two cases.
Cite: Diwakar
Shukla, Astha Jain A CLASS OF
LOGARITHMIC-CUM-EXPONENTIAL ESTIMATORS FOR
POPULATION MEAN WITH RISK ANALYSIS USING DOUBLE
SAMPLING. Reliability: Theory & Applications.
2024, September 3(79): 248-262, DOI:
https://doi.org/10.24412/1932-2321-2024-379-248-262
|
248-262
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STOCHASTIC ANALYSIS
OF A GAS TURBINE SYSTEM WITH PRIORITY AND RANDOM
INSPECTION BY SINGLE SERVER UNDER DIFFERENT
HUMID CONDITIONS
Pinki, Vijeta Kumari,
Dalip Singh
In this study, we
investigated the impact of two different humid
levels on the reliability measures of a
stochastic model for a gas turbine system
composed of a gas turbine and a steam turbine.
To enhance the system’s overall performance, we
prioritize gas turbine repair over steam turbine
repair in addition to a combined inspection and
preventative maintenance approach. To find some
reliability measures, such as the mean time to
system failure, availability, etc., semi-Markov
process and regenerating point technique are
utilized. These measures are analysed
graphically based on the data obtained from a
gas turbine power plant in Delhi, India.
Cite: Pinki,
Vijeta Kumari, Dalip Singh STOCHASTIC ANALYSIS
OF A GAS TURBINE SYSTEM WITH PRIORITY AND RANDOM
INSPECTION BY SINGLE SERVER UNDER DIFFERENT
HUMID CONDITIONS. Reliability: Theory &
Applications. 2024, September 3(79): 263-274,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-263-274
|
263-274
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PYTHON
IMPLEMENTATION OF FUZZY LOGIC FOR ZERO-INFLATED
POISSON SINGLE SAMPLING PLANS
Kavithanjali S,
Sheik Abdullah A
Acceptance sampling
is used in Statistical Quality Control (SQC) to
conduct lot quality evaluations through sample
inspections which involve probability theory and
fuzzy sets. It aims to optimize quality, costs,
and productivity, frequently applying linguistic
variables when accurate parameter values are not
good enough which is handled using fuzzy set
theory. This research analyses single sampling
plans (SSP) in the presence of fuzzy number
non-conformities, modelling them with the
Zero-inflated Poisson (ZIP) distribution
structure. This study presents a unique method
to single sampling plans (SSP) inside the
Zero-inflated Poisson (ZIP) distribution
framework that makes use of fuzzy logic
approaches. In addition, we show how to apply
this method using a Python programme, providing
practical suggestions for real-world quality
control complications.
Cite:
Kavithanjali S, Sheik Abdullah A PYTHON
IMPLEMENTATION OF FUZZY LOGIC FOR ZERO-INFLATED
POISSON SINGLE SAMPLING PLANS. Reliability:
Theory & Applications. 2024, September 3(79):
275-281, DOI:
https://doi.org/10.24412/1932-2321-2024-379-275-281
|
275-281
|
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ANALYSIS OF
NON-MARKOVIAN BATCH ARRIVAL RETRIAL QUEUE WITH
PRIORITY SERVICES, IMMEDIATE FEEDBACK, PUSH OUT,
DIFFERENTIATED BREAKDOWNS, DELAYED REPAIR,
RANDOMIZED VACATION
G. Ayyappan, S.
Nithya
Priority and
ordinary customers arrive according to Poisson
processes, and their service time based on the
general distribution. The server constantly
offers a single service for both priority and
ordinary customers. We compute the Laplace
transforms of the time-dependent probabilities
of system states using the probability
generating function and supplementary variable
technique. Numerical results are obtained which
are also examined to facilitate the sensitivity
analysis of system descriptions.
Cite: G.
Ayyappan, S. Nithya ANALYSIS OF NON-MARKOVIAN
BATCH ARRIVAL RETRIAL QUEUE WITH PRIORITY
SERVICES, IMMEDIATE FEEDBACK, PUSH OUT,
DIFFERENTIATED BREAKDOWNS, DELAYED REPAIR,
RANDOMIZED VACATION. Reliability: Theory &
Applications. 2024, September 3(79): 282-297,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-282-297
|
282-297
|
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PERSONALIZED
FEATURES-BASED STRESS DETECTION WITH
HYPERPARAMETER TUNING USING GENETIC ALGORITHM
Jigna Jadav, Uttam
Chauhan
In recent years,
there have been considerable improvements in how
we keep track of mental health, especially with
devices you can wear, which give us a better
chance of spotting and dealing with problems
like stress before they become serious. This
research paper presents an innovative approach.
Experimental validation uses a comprehensive
dataset of 15 subjects working as multinational
company employees. Heart Rate Variability(HRV)
was obtained from wearable sensors using Apple
Watch during working hours. We have calculated
time, frequency and non-linear domains as well
and added personalized features like a person's
age, height, weight, etc. Recurrent Neural
Network( RNN )and Long Short-Term Memory ( LSTM
)models are applied and get an accuracy of 87%
and 90%, respectively. To enhance stress
detection accuracy by optimizing hyperparameters
using a genetic algorithm (GA) explicitly
targeting the configuration of LSTM models. Key
hyperparameters, including the number of units
in the LSTM layer and the number of training
epochs, are optimized to maximize stress
detection accuracy. Model Through 5 generations
of evolution, the GA identifies optimal
hyperparameter settings of 45 units in the LSTM
layer 49 epochs, significantly improving stress
detection accuracy compared to baseline
configurations. It gives 92 % accuracy with
optimized hyperparameters. Analyzing recorded
data, we observe that the time per training step
decreases gradually, indicating efficient
convergence during optimization. Simultaneously,
stress detection accuracy steadily improves over
epochs, showcasing the model's effectiveness in
learning patterns from physiological data. So,
This study provides insights into the practical
application of genetic algorithms for
hyperparameter optimization in healthcare
contexts, contributing to advancements in
personalized monitoring and intervention
strategies for mental well-being.
Cite: Jigna
Jadav, Uttam Chauhan PERSONALIZED FEATURES-BASED
STRESS DETECTION WITH HYPERPARAMETER TUNING
USING GENETIC ALGORITHM. Reliability: Theory &
Applications. 2024, September 3(79): 298-309,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-298-309
|
298-309
|
|
ANALYSIS OF SINGLE
SERVER FEEDBACK RETRIAL QUEUE WITH BERNOULLI
WORKING VACATION AND STARTING FAILURE
Keerthiga S, Indhira
K
The suggested
queueing model describes a single-server
feedback retrial queueing system with starting
failure, Bernoulli working vacation and vacation
interruptions. The server departs on a working
vacation as soon as orbit is empty. During the
working vacation period, the server provides a
slower level of service. The supplementary
variable method was utilized to determine the
steady-state probability-generating functions
for the system and its orbit. If there are
consumers in the system at the end of each
vacation, the server becomes idle and ready to
serve new customers. The average busy time and
the average busy cycle are presented as
important system performance indicators.
Additionally, the adaptive neuro-fuzzy interface
system has compared the numerical results with
the neuro-fuzzy results. Finally, particle swarm
optimization (PSO) were utilized to obtain the
best (optimal) cost for the system in this study.
We have examined the convergence of these
optimization strategies.
Cite:
Keerthiga S, Indhira K ANALYSIS OF SINGLE SERVER
FEEDBACK RETRIAL QUEUE WITH BERNOULLI WORKING
VACATION AND STARTING FAILURE. Reliability:
Theory & Applications. 2024, September 3(79):
310-326, DOI:
https://doi.org/10.24412/1932-2321-2024-379-310-326
|
310-326
|
|
IMPROVING THE
SPECTRAL EFFICIENCY IN DOWNLINK MULTIPLE USER
MULTIPLE INPUT MULTIPLE OUTPUT TRANSMISSION FOR
FIFTH GENERATION AND BEYOND WIRELESS
COMMUNICATIONS
Abdulmujeeb
Akajewole Masud, Donatus Uchechukwu Onyishi
This research
presents a solution in Multiple Input Multiple
Output (MIMO) wireless systems to meet the
growing demand for high data rates in cellular
networks. Although MIMO systems offer greater
capacity, the higher frequencies used have
caused interference problems, especially for
mobile User Equipment (UE). This research aims
to reduce interference problems in the downlink
of Multi-user MIMO (MU-MIMO) systems, with a
specific focus on improving Quality of Service (QoS)
metrics, such as outage probability and
Signal-to-Interference plus Noise Ratio (SINR).
Existing solutions to these challenges are
complex due to the dynamic nature of the factors
involved in modelling real-world scenarios. As
such, an Improved Downlink MU-MIMO (ID-MU-MIMO)
algorithm is developed as a solution to these
problems. The ID-MU-MIMO method employs both
single antenna users and multiple transmitter
antennas. The performance of the suggested
algorithm is compared to the IEEE 802.11ax
standard specification and a previous research
work for validation and evaluation. Performance
measures considered to aid validation included
outage probability, spectrum efficiency, and
communication connection reliability. On this
premise, the outcomes showed that the proposed
ID-MU-MIMO scheme outperforms both the IEEE
802.11ax standard and current MD-MU-MIMO systems.
In particular, compared to IEEE 802.11ax, the ID-
MU-MIMO technique achieved a 7.71% reduction in
interference. When compared to the performance
of the random and uniform MD-MU-MIMO algorithms,
the proposed ID-MU- MIMO scheme showed a
reduction in interference in percentages of
8.90% and 2.28%, respectively. The ID-MU-MIMO
scheme outpermed the random and uniform
MD-MU-MIMO algorithms in terms of
Signal-to-Interference Noise Ratio (SINR),
outperforming them by 4.27% and 2.75%,
respectively, and resource block use,
outperforming them by 20.05% and 3.89%,
respectively.
Cite:
Abdulmujeeb Akajewole Masud, Donatus Uchechukwu
Onyishi IMPROVING THE SPECTRAL EFFICIENCY IN
DOWNLINK MULTIPLE USER MULTIPLE INPUT MULTIPLE
OUTPUT TRANSMISSION FOR FIFTH GENERATION AND
BEYOND WIRELESS COMMUNICATIONS. Reliability:
Theory & Applications. 2024, September 3(79):
327-342, DOI:
https://doi.org/10.24412/1932-2321-2024-379-327-342
|
327-342
|
|
ENHANCING PROCESS
CAPABILITY ANALYSIS FOR LOGNORMAL DATA UTILIZING
BOX COX TRANSFORMATION AND GOODNESS OF FIT TESTS
J. Krishnan, R.
Vijayaraghavan
Process capability
analysis is a valuable tool in quality assurance,
but deviations from normal distribution
necessitate adjustments to basic process
capability indices. Process control literature
offers solutions for non-normality, with data
transformation being a common approach. The Box-
Cox transformation (BCT) is often used to
normalize non-normal data, relying on maximum
likelihood estimation (MLE) to determine the
transformation parameter, lambda. Alternative
methods exist for estimating the single
transformation parameter lamda, employing
goodness-of-fit tests instead of the MLE method.
This study explores two expressions within the
Box-Cox transformation (BCT), encompassing both
optimal and rounded values of lambda. The
primary goal is to identify an effective method
for transforming non-normal data into a
distribution closer to normality through
goodness-of-fit tests, aiming to obtain accurate
estimates for process capability analysis in
alignment with six sigma standards. Furthermore,
this study focuses on the influence of utilizing
both optimal and rounded values of lambda when
transforming non-normal data to normal, and how
these lambda values impact the estimates of
process capability analysis. The findings reveal
that methods such as Shapiro-Wilk's (SW) and
Artificial Covariate (AC) outperform the MLE
method. Moreover, employing the optimal lambda
value during data transformation leads to
improved estimates of process capability. Data
simulation and analysis were conducted using
Minitab software and the R programming language.
Cite: J.
Krishnan, R. Vijayaraghavan ENHANCING PROCESS
CAPABILITY ANALYSIS FOR LOGNORMAL DATA UTILIZING
BOX COX TRANSFORMATION AND GOODNESS OF FIT TESTS.
Reliability: Theory & Applications. 2024,
September 3(79): 343-355, DOI:
https://doi.org/10.24412/1932-2321-2024-379-343-355
|
343-355
|
|
INFERENCE ON THE
INVERSE POWER BURR-HATKE DISTRIBUTION UNDER TYPE
II CENSORING
Pavitra Kumari,
Vinay Kumar
There are many
real-life situations, where data require
probability distribution function which have
decreasing or upside-down bathtub (UBT) shaped
failure rate function. The inverse power burr
hatke distribution consists both decreasing and
UBT shaped failure rate functions. Here, we
address the different estimation methods of the
parameter and reliability characteristics of the
inverse Pareto distribution from both classical
and Bayesian approaches. We consider classical
estimation procedures to estimate the unknown
parameter of inverse power burr-hatke
distribution, such as maximum likelihood. Also,
we consider Bayesian estimation using squared
error loss function based joint priors. The
Monte Carlo simulations are performed to compare
the performances of the obtained estimators in
mean square error sense. Finally, the
flexibility of the proposed distribution is
illustrated empirically using one real-life
datasets. The analyzed data shows that the
introduced distribution provides a superior fit
than some important competing distributions such
as the Weibull, inverse Pareto and Burr-Hatke
distributions.
Cite: Pavitra
Kumari, Vinay Kumar INFERENCE ON THE INVERSE
POWER BURR-HATKE DISTRIBUTION UNDER TYPE II
CENSORING. Reliability: Theory & Applications.
2024, September 3(79): 356-363, DOI:
https://doi.org/10.24412/1932-2321-2024-379-356-363
|
356-363
|
|
ANALYSIS OF TWO
NON-IDENTICAL UNIT SYSTEM HAVING SAFE AND UNSAFE
FAILURES WITH REBOOTING AND PARAMETRIC
ESTIMATION IN CLASSICAL AND BAYESIAN PARADIGMS
Poonam Sharma, Pawan
Kumar
The present paper
aims at the study of a two non-identical system
model having safe and unsafe failures and
rebooting. The focus centers on the analysis
w.r.t important reliability measures and
estimation of parameters in Classical and
Bayesian paradigms. At first one of the units is
operational whereas other one is confined to
standby mode. Any unit may suffer safe or unsafe
failure. A safe failure is immediately taken up
for remedial action by a repairman available
with the system all the time, while the case of
unsafe failure cannot be dealt directly but
first rebooting is performed to convert the
unsafe failure to safe failure mode so as to
start repair normally. A switching device is
used to make the repaired and standby units
operational. The lifetime of both the units and
switching device are taken to be exponentially
distributed random variables whereas the
distribution of repair times are assumed to be
general. Regenerative point technique is
employed to derive assosciated measures of
effectiveness. To make the study more
elaborative and visually attractive, some of the
derived characteristics have been studied
graphically too. A simulation study has also
been undertaken to exhibit the behaviour of
obtained characteristics in Classical and
Bayesian setup. Valuable inferences about MLE
and Bayes estimates have been drawn from the
tables and graphs for varying values of failure
and repair parameters.
Cite: Poonam
Sharma, Pawan Kumar ANALYSIS OF TWO
NON-IDENTICAL UNIT SYSTEM HAVING SAFE AND UNSAFE
FAILURES WITH REBOOTING AND PARAMETRIC
ESTIMATION IN CLASSICAL AND BAYESIAN PARADIGMS.
Reliability: Theory & Applications. 2024,
September 3(79): 364-379, DOI:
https://doi.org/10.24412/1932-2321-2024-379-364-379
|
364-379
|
|
RELIABILITY
ESTIMATION OF STRESS-STRENGTH MODEL USING FUZZY
DISTORTION FUNCTION UNDER UNCERTAINTY IN
ENVIRONMENTAL FACTORS
K Sruthi, M Kumar
In the reliability
estimation of stress-strength models, external
factors such as temperature, humidity, etc. may
influence the distribution of stress and
strength random variables. In traditional
reliability analysis, these external factors are
accounted for by introducing a real-valued
distortion function, which replaces the original
distribution with a distorted one. However, it’s
important to note that the effect of these
external factors is not always adequately
represented by a single real-valued function. To
address this issue, we propose the use of fuzzy
numbers within the distortion function. In this
paper, we introduce the concept of a "fuzzy
distortion function" to incorporate the
uncertainty stemming from external factors when
estimating the reliability of stress-strength
relationships. We present a methodology for
estimating fuzzy reliability by employing this
fuzzy distortion function. Through an
illustrative example, we demonstrate how this
approach to estimating fuzzy reliability offers
a wider range of possibilities for system
reliability and provides more comprehensive
insights into the system’s behaviour. Throughout
our exploration, we have delved into the diverse
properties inherent in fuzzy distortion
functions. These properties highlight the
versatility and adaptability of such functions
in capturing uncertainty within data sets.
Moreover, we have scrutinized several methods
for constructing fuzzy distortion functions from
pre-existing ones. By examining these methods,
we gain valuable insights into how fuzzy
distortion functions can be tailored to specific
contexts and applications, thereby enhancing the
accuracy and robustness of reliability analysis
in complex systems. Additionally, in the
conventional stress-strength model, reliability
is determined without considering the
uncertainty in the parameters of the
distribution function. The drawback of existing
methods in the literature is that they do not
consider the uncertainty or fuzziness in the
parameters of the distribution. Therefore, we
estimate the system reliability in the presence
of fuzzy parameters in the distribution function
of corresponding random variables. The method we
discuss in this paper provides a reliability
estimate of the given system under realistic
situations. A sensitivity analysis study is
carried out to examine the behaviour of mean
square errors (MSE) of estimated system
reliability under various scenarios. It is
observed that MSE can be significantly reduced
by a suitable choice of parameters in the
membership function of fuzzy parameters.
Cite: K
Sruthi, M Kumar RELIABILITY ESTIMATION OF
STRESS-STRENGTH MODEL USING FUZZY DISTORTION
FUNCTION UNDER UNCERTAINTY IN ENVIRONMENTAL
FACTORS. Reliability: Theory & Applications.
2024, September 3(79): 380-392, DOI:
https://doi.org/10.24412/1932-2321-2024-379-380-392
|
380-392
|
|
ANALYTICAL AND
COMPUTATIONAL ASPECTS OF A MULTI-SERVER QUEUE
WITH IMPATIENCE UNDER DIFFERENTIATED WORKING
VACATIONS POLICY
Aimen Dehimi,
Mohamed Boualem, Amina Angelika Bouchentouf,
Sofiane Ziani, Louiza Berdjoudj
A multi-server
queueing system with synchronous differentiated
working vacation policy, Bernoulli schedule
vacation interruption, and customer impatience (balking
and reneging) is studied. The system consists of
c servers and a finite capacity N, where
customers arrive according to a Poisson process
and are served in the chronological order of
their arrival. When the system becomes empty,
servers wait for a random duration before
entering a type-1 working vacation, during which
service is provided at a reduced rate. If
customers are present in the system at the
moment of service achievement during this period,
the vacation is interrupted. With a certain
probability, servers return to the regular busy
period; otherwise, they continue the working
vacation. Upon completion of the working
vacation, if the system is still empty, servers
can take another working vacation of shorter
duration, named type-2 working vacation;
otherwise, they switch to the regular busy
period. Customer impatience is considered during
both the normal busy period and working
vacations. A recursive analysis method is used
to find the steady-state probabilities of the
system. Then, some important performance
measures are obtained. Furthermore, an optimal
operational policy for the model is developed to
minimize the total expected cost. The Grey Wolf
Optimization (GWO) meta-heuristic approach is
employed to determine the optimal service rates
for both working vacations and normal busy
periods. Finally, several numerical examples are
provided to validate and support the theoretical
findings.
Cite: Aimen
Dehimi, Mohamed Boualem, Amina Angelika
Bouchentouf, Sofiane Ziani, Louiza Berdjoudj
ANALYTICAL AND COMPUTATIONAL ASPECTS OF A
MULTI-SERVER QUEUE WITH IMPATIENCE UNDER
DIFFERENTIATED WORKING VACATIONS POLICY.
Reliability: Theory & Applications. 2024,
September 3(79): 393-407, DOI:
https://doi.org/10.24412/1932-2321-2024-379-393-407
|
393-407
|
|
COSINE
MARSHAL-OLKIN-G FAMILY OF DISTRIBUTION:
PROPERTIES AND APPLICATIONS
Akeem Ajibola
Adepoju, Alhaji Modu Isa, Olalekan Akanji Bello
Trigonometric
distributions have recently been emphasized due
to it applicability and relevance for modeling
different phenomena. This article contributes to
the existing literature on trigonometric family
by introducing and investigating new
trigonometric family of distribution which is
developed by compounding the cosine family of
distribution with Marshall-olkin family of
distribution to form a new Cosine Marshall-Olkin
family of distribution (CMO). Graphical,
numerical and analytical approach was explored
to study the properties and applicability of the
new CMO family of distribution. Special
representations and important reliability
properties and other statistical properties were
defined. Simulation study was conducted in order
to have an insight on the estimates of the three
parameters model using maximum products of
spacing (MPS). Emphases on the greater
flexibility of the new CMO family of
distribution beyond the cosine-G family and
other top models of the Cosine related family
was made through Weibull distribution. The
results revealed the superiority of the Cosine
Marshall-Olkin Weibull model (CMO-W) over others
via two data sets.
Cite: Akeem
Ajibola Adepoju, Alhaji Modu Isa, Olalekan
Akanji Bello COSINE MARSHAL-OLKIN-G FAMILY OF
DISTRIBUTION: PROPERTIES AND APPLICATIONS.
Reliability: Theory & Applications. 2024,
September 3(79): 408-422, DOI:
https://doi.org/10.24412/1932-2321-2024-379-408-422
|
408-422
|
|
ANALYSIS OF MMAP/PH1,PH2/1
PREEMPTIVE PRIORITY INVENTORY RETRIAL QUEUEING
SYSTEM WITH SINGLE VACATION, WORKING BREAKDOWN,
REPAIR AND CLOSEDOWN
G. Ayyappan, S.
Meena
This paper analyzes
preemptive priority inventory retrial queueing
system with a single vacation, working breakdown,
repair, and closedown. We assume that an arrival
follows the Marked Markovian arrival process and
that the server will provide them with
phase-type services. The (s, S) policy to
replenish the items and the replenishing
duration follow an exponential distribution. In
this paper, we consider two types of customers:
high-priority(HP) customers and low-priority(LP)
customers. Arriving HP customers should get the
service if the server is idle and has a positive
inventory level; otherwise, they should wait in
front of the service station. Arriving LP
customers get service only if there is a
positive inventory level and there are no
high-priority customers in the system; otherwise,
go for the finite capacity size of the orbit.
After the completion of service, if no one is
present in the high-priority queue and orbit,
the server will close down the system and then
go on a single vacation. The server is idle when
the vacation period ends. When the server breaks
down, it only serves the present customer and
operates in slow mode while it is being repaired.
The number of high-priority customers in the
system, the number of low-priority customers in
the orbit, the inventory level, and server
status may all be determined in a steady state.
Numerous key performance indicators are defined,
and a cost analysis is obtained. To make our
mathematical concept clearer, a few numerical
examples are provided.
Cite: G.
Ayyappan, S. Meena ANALYSIS OF MMAP/PH1,PH2/1
PREEMPTIVE PRIORITY INVENTORY RETRIAL QUEUEING
SYSTEM WITH SINGLE VACATION, WORKING BREAKDOWN,
REPAIR AND CLOSEDOWN. Reliability: Theory &
Applications. 2024, September 3(79): 423-441,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-423-441
|
423-441
|
|
OPTIMIZATION OF AN
INVENTORY MODEL FOR DETERIORATING ITEMS ASSUMING
DETERIORATION DURING CARRYING WITH TWO-WAREHOUSE
FACILITY
Krishan Kumar Yadav,
Ajay Singh Yadav, Shikha Bansal
A common topic in
the context of its application in today’s
business contexts is inventory modelling and
management. It is well-known that deterioration
has a big impact on inventory management. One of
the most frequent supply chain concerns is the
deterioration of items during transit from a
supplier’s storehouse to a retailer’s storehouse.
In light of this, a two-level supply chain
inventory model for decaying goods is developed
with two warehouse (storehouse) facilities for
retailers, namely Owned Warehouse (OW) and
Rented Warehouse (RW), assuming deterioration
both during carrying from a supplier’s
storehouse to a retailer’s storehouses and in
the retailer’s storehouses themselves. Also, we
are assuming the selling price and time
sensitive demand. We are developed this model
under inflation. Shortages are not allowed. The
main objective of this study is to determine the
optimal ordering policy in order to maximizes
the retailer’s profit per unit of time. The
applicability of our suggested model is
investigated using a numerical example and with
the support of MATLAB programming software (version:
R2021b). Sensitivity analysis is used to examine
the effects of changing the values of system
parameters. Graphical representations are also
shown in this paper.
Cite: Krishan
Kumar Yadav, Ajay Singh Yadav, Shikha Bansal
OPTIMIZATION OF AN INVENTORY MODEL FOR
DETERIORATING ITEMS ASSUMING DETERIORATION
DURING CARRYING WITH TWO-WAREHOUSE FACILITY.
Reliability: Theory & Applications. 2024,
September 3(79): 442-459, DOI:
https://doi.org/10.24412/1932-2321-2024-379-442-459
|
442-459
|
|
ON MODELING OF
BIOMEDICAL DATA WITH EXPONENTIATED GOMPERTZ
INVERSE RAYLEIGH DISTRIBUTION
Sule Omeiza Bashiru,
Alaa Abdulrahman Khalaf, Alhaji Modu Isa,
Aishatu Kaigama
This paper
introduces and thoroughly examines the
Exponentiated Gompertz Inverse Rayleigh (EtGoIr)
Distribution, a four-parameter extension of the
Gompertz Inverse Rayleigh distribution. The
primary focus is on its application to
biomedical datasets, shedding light on its
mathematical and statistical properties. Some
properties of the distribution that were derived
include the quantile function, median, moments,
incomplete moments, Rényi entropy, and
probability weighted moments. The model
parameters were estimated using the method of
maximum likelihood. A simulation study was
conducted to investigate the consistency of the
proposed model. The outcome of the investigation
revealed that the model demonstrates consistency,
as evidenced by the reduction in both root mean
square error (RMSE) and bias as sample sizes
increase. To showcase the practical relevance of
the EtGoIr distribution, the paper applies the
model to three distinct biomedical datasets. The
results highlight its enhanced flexibility,
demonstrating superior fit compared to its
counterpart.
Cite: Sule
Omeiza Bashiru, Alaa Abdulrahman Khalaf, Alhaji
Modu Isa, Aishatu Kaigama ON MODELING OF
BIOMEDICAL DATA WITH EXPONENTIATED GOMPERTZ
INVERSE RAYLEIGH DISTRIBUTION. Reliability:
Theory & Applications. 2024, September 3(79):
460-475, DOI:
https://doi.org/10.24412/1932-2321-2024-379-460-475
|
460-475
|
|
BEHAVIOR ANALYSIS
PRESENTED SYSYEM WITH FAILURE AND MAINTENANCE
RATE WITH USING DEEP LEARNING ALGORITHMS
Shakuntla Singla,
Shilpa Rani, Diksha Mangla, Umar Muhammad
Modibbo
The paper discusses
the behavioral analysis and dependability of a
three-unit system utilizing RPGT for system
parameters. Since all three units P, Q and R
include parallel subcomponents, in the event
that one of them fails, the system continues to
operate although at a reduced capacity, but it
is not profitable to run the system when two
units are in reduced state hence considered
failed state. The rates of failures are
exponentially distributed, but the rates of
repair are generalized, independent, and differ
based on the operational unit. Fuzzy concept is
used to declare/ determine whether the system is
in failed/ reduced/ failed state. Graphs and
tables are drawn to compare failure/repair
effect on the parameters values. The system
parameters are modelled using Regenerative Point
graphical Technique (RPGT) and optimized using
Deep learning methods such as Adam, SGD, RMS
prop. The results of the optimization may be
used to validate and challenge existing models
and assumptions about the systems.
Cite:
Shakuntla Singla, Shilpa Rani, Diksha Mangla,
Umar Muhammad Modibbo BEHAVIOR ANALYSIS
PRESENTED SYSYEM WITH FAILURE AND MAINTENANCE
RATE WITH USING DEEP LEARNING ALGORITHMS .
Reliability: Theory & Applications. 2024,
September 3(79): 476-485, DOI:
https://doi.org/10.24412/1932-2321-2024-379-476-485
|
476-485
|
|
OPTIMIZING INVENTORY
CONTROL THROUGH A GRADIENT-BASED MULTILEVEL
APPROACH IN THE FACE OF DEMAND AND LEAD TIME
UNCERTAINTIES
Muragesh Math,
D.Gopinath, B. S.Biradar
Systems of two-level
assembly with unknown timing of leads are taken
into consideration while arranging supplies.
Probably, the final product's demand and its
deadline are known. When all required parts are
on hand, each level's assembly process gets
underway. To address these problems, we have
developed a model for the control of inventories
for an uncapitatedwarehousing space in a
manufacturing plant with unpredictable demand
and lead times. The goal is to choose orders in
a way that minimizes the overall system's cost.
We present a multilevel optimization model
including a rotating horizon that utilizes
gradients to handle unknown lead time and demand,
irrespective of the distributions at the core of
them. Furthermore, a precise algorithm is
created to solve the model. In a case study, we
compare our approach with the current model. Our
computational results indicate that while the
new gradient-based multi-level optimization
model nearly continuously yields the least
expensive overall across all parameter settings.
These models' performances are either
systematically worse or extremely sensitive to
cost parameters (holding cost, shortfall cost,
etc.).
Cite:
Muragesh Math, D.Gopinath, B. S.Biradar
OPTIMIZING INVENTORY CONTROL THROUGH A
GRADIENT-BASED MULTILEVEL APPROACH IN THE FACE
OF DEMAND AND LEAD TIME UNCERTAINTIES.
Reliability: Theory & Applications. 2024,
September 3(79): 486-496, DOI:
https://doi.org/10.24412/1932-2321-2024-379-486-496
|
486-496
|
|
THE EXPONENTIATED
SKEW LAPLACE DISTRIBUTION: PROPERTIES AND
APPLICATIONS
Timothy Kayode
Samson, Christian Elendu Onwukwe, Ekaette Inyang
Enang
In this paper, a
4-parameter Exponentiated Skew Laplace
distribution is defined and studied. Various
statistical properties including its moment
generating function, characteristics function,
hazard function, and reliability function of the
proposed ESLD were derived. The estimation of
its parameters was carried out using the maximum
likelihood method of estimation. The performance
of the proposed ESLD compared with other similar
distributions was demonstrated empirically with
daily returns of S & P 500 between 2/02/24 and
28/03/2024 and daily returns of Bitcoin between
2/02/24 and 1/04/24 as obtained from Yahoo
Finance. The fitness performance of the proposed
distribution was evaluated based on
log-likelihood, AIC, and BIC. Results obtained
show that the proposed ESLD reported the highest
log likelihood as well as the lowest AIC and BIC
in the two data sets. This study therefore
underscores the superiority of the proposed
distribution over the some of the similar
existing distributions.
Cite: Timothy
Kayode Samson, Christian Elendu Onwukwe, Ekaette
Inyang Enang THE EXPONENTIATED SKEW LAPLACE
DISTRIBUTION: PROPERTIES AND APPLICATIONS.
Reliability: Theory & Applications. 2024,
September 3(79): 497-509, DOI:
https://doi.org/10.24412/1932-2321-2024-379-497-509
|
497-509
|
|
A NOVEL ASYMMETRIC
COMPOUND CLASS OF DISTRIBUTIONS WITH ESTIMATION
AND APPLICATION
A.G. Al-Kilany, Amal
S. Hassan, L.S. Diab, E.S. El-Atfy
This paper
introduces and discusses the novel asymmetric
class of distributions that have the name
inverse power Lomax power series (IPLPS). This
class of distributions is produced by combining
the inverse power Lomax with the power series
distributions. This combined approach provides
an opportunity for the creation of flexible
distributions with significant physical
implications in many fields, like biology and
engineering. The IPLPS distributions encompass
several new compound distributions as sub-models
along with a new class of compound distributions.
Many statistical features, including moments,
quantile function, conditional moments, inverse
moments, uncertainty measures, and
probability-weighted moments, are obtained. As a
special model of the generated class, the
parameters of the inverse power Lomax Poisson
distribution are estimated by different methods,
including least squares, Cramér von Mises,
maximum likelihood, and weighted least squares.
Through an extensive simulation analysis, the
execution of different parameter estimation
techniques for the inverse power Lomax Poisson
model is performed to show its validity based on
its mean squared error and absolute bias. Two
real datasets are utilized to show the
practicality of the newly generated model.
Results show that the inverse power Lomax
Poisson distribution provides the most fitted
model for these datasets in comparison to other
distributions such as power Lomax, Marshall-
Olkin power Lomax, power Lomax Poisson, and
Topp-Leone Lomax distributions.
Cite: A.G.
Al-Kilany, Amal S. Hassan, L.S. Diab, E.S.
El-Atfy A NOVEL ASYMMETRIC COMPOUND CLASS OF
DISTRIBUTIONS WITH ESTIMATION AND APPLICATION.
Reliability: Theory & Applications. 2024,
September 3(79): 510-529, DOI:
https://doi.org/10.24412/1932-2321-2024-379-510-529
|
510-529
|
|
EXPLORING LENGTH
BIASED QUASI SUJA DISTRIBUTION: PROPERTIES AND
APPLICATIONS
Vidya Yerneni, Aafaq
A. Rather
This paper
introduces a new statistical distribution called
length biased quasi suja distribution (LBQS). It
explores its properties, including moments,
moment generating function(MGF), characteristic
function(CF), harmonic mean, reliability, hazard
rate and reverse hazard rate. Order statistics
of the above distribution is obtained.
Furthermore, the paper also examines various
entropy which measures the randomness of system,
like Renyi entropy and Tsalli’s entropy. It also
evaluates Bonferroni and Lorenz curves which are
useful in measuring the inequality. It also
discusses parameter estimation techniques
specifically maximum likelihood estimation and
likelihood ratio testing. Moreover, a simulation
study has been conducted to demonstrate how well
the distribution would perform in real-life
situation. The validity of the distribution is
also demonstrated with real-world data example
of failure data, highlighting its potential for
practical applications in data analysis.
Cite: Vidya
Yerneni, Aafaq A. Rather EXPLORING LENGTH BIASED
QUASI SUJA DISTRIBUTION: PROPERTIES AND
APPLICATIONS. Reliability: Theory & Applications.
2024, September 3(79): 530-544, DOI:
https://doi.org/10.24412/1932-2321-2024-379-530-544
|
530-544
|
|
A NEW GENERALIZATION
OF SABUR DISTRIBUTION
Suvarna Ranade,
Aafaq A. Rather
When the weight
function depends on the lengths of the units of
interest, the resulting distribution is called
length biased. Length biased distribution is
thus a special case of the more general form,
known as weighted distribution. In this study,
we introduce a novel probability distribution
named the Length- Biased Sabur distribution (LBSD).
This new distribution enhances the traditional
Sabur distribution by incorporating a weighted
transformation approach. The paper investigates
the probability density function (pdf) and the
cumulative distribution function (cdf)
associated with the LBSD. A thorough examination
of the distinctive structural properties of the
proposed model is conducted, covering the
survival function, conditional survival function,
hazard function, cumulative hazard function,
mean residual life, moments, moment generating
function, characteristic function, likelihood
ratio test, ordered statistics, entropy measures,
and Bonferroni and Lorenz curve.
Cite: Suvarna
Ranade, Aafaq A. Rather A NEW GENERALIZATION OF
SABUR DISTRIBUTION. Reliability: Theory &
Applications. 2024, September 3(79): 545-553,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-545-553
|
545-553
|
|
MODELING THE
INTERCONNECTED OPERATION OF ENERGY SYSTEMS FOR
ENERGY SECURITY STUDY IN TODAY’S CONTEXT
Dmitry Krupenev,
Natalia Pyatkova
The paper shows the
need for comprehensive research into energy
security problems to assess the possibilities of
interconnected operation of all energy
industries with the view to identifying the
implications for consumers of energy resources
in the event of emergencies in one or several
industries at the same time. The paper presents
a methodological framework and features of
modeling the interrelated operation of the
industries in current context and a model
developed for these studies. The results of
experimental studies using the developed
methodology are shown through the analysis of
several critical situations (threats to energy
security) of various nature.
Cite: Dmitry
Krupenev, Natalia Pyatkova MODELING THE
INTERCONNECTED OPERATION OF ENERGY SYSTEMS FOR
ENERGY SECURITY STUDY IN TODAY’S CONTEXT.
Reliability: Theory & Applications. 2024,
September 3(79): 554-566, DOI:
https://doi.org/10.24412/1932-2321-2024-379-554-566
|
554-566
|
|
ESTIMATION OF
PARAMETERS FOR KUMARASWAMY EXPONENTIAL
DISTRIBUTION BASED ON PROGRESSIVE TYPE-I
INTERVAL CENSORED SAMPLE
Manoj Chacko, Shilpa
S Dev
In this paper, we
consider the problem of estimation of parameters
of the Kumaraswamy exponential distribution
using progressive type-I interval censored data.
The maximum likelihood estimators (MLEs) of the
parameters are obtained. As it is observed that
there is no closed-form solutions for the MLEs,
we implement the Expectation-Maximization (EM)
algorithm for the computation of MLEs. Bayes
estimators are also obtained using different
loss functions such as the squared error loss
function and the LINEX loss function. For the
Bayesian estimation, Lindley’s approximation
method has been applied. To evaluate the
performance of the various estimators developed,
we conduct an extensive simulation study. The
different estimators and censoring schemes are
compared based on average bias and mean squared
error. A real data set is also taken into
consideration for illustration.
Cite: Manoj
Chacko, Shilpa S Dev ESTIMATION OF PARAMETERS
FOR KUMARASWAMY EXPONENTIAL DISTRIBUTION BASED
ON PROGRESSIVE TYPE-I INTERVAL CENSORED SAMPLE.
Reliability: Theory & Applications. 2024,
September 3(79): 567-582, DOI:
https://doi.org/10.24412/1932-2321-2024-379-567-582
|
567-582
|
|
ANALYSIS OF MX/G/1
QUEUE WITH OPTIONAL SECOND SERVICE, FEEDBACK AND
BERNOULLI VACATION
S. Karpagam, B.
Somasundaram, A. Kavin Sagana Mary, R. Lokesh,
In this article the
single-server queue situation described with
batch arrivals, a mandatory first service and a
choice of second service are provided to the
customers. A general distribution governs the
service times, whereas a compound Poisson
distribution follows customer arrivals. Although
each new customer requests the first mandatory
service, only some of them choose the optional
second service. Customers who are dissatisfied
with mandatory service are more likely to get
the required services later on. After every
service is finished, the server might choose to
go on Bernoulli vacation. Time dependent
probability generating functions are constructed
in terms of Laplace transforms using the
supplementary variable approach, and explicit
results are obtained for the steady state.
Additionally, mean waiting time and mean queue
length expressions are examined. The graphical
and numerical representations improve
comprehension of the results even further.
Cite: S.
Karpagam, B. Somasundaram, A. Kavin Sagana Mary,
R. Lokesh, ANALYSIS OF MX/G/1 QUEUE WITH
OPTIONAL SECOND SERVICE, FEEDBACK AND BERNOULLI
VACATION. Reliability: Theory & Applications.
2024, September 3(79): 583-594, DOI:
https://doi.org/10.24412/1932-2321-2024-379-583-594
|
583-594
|
|
INVERTED DAGUM
DISTRIBUTION: PROPERTIES AND APPLICATION TO
LIFETIME DATASET
Abdulhameed A. Osi,
Shamsuddeen A. Sabo, Ibrahim Z. Musa
This article
presents the introduction of a novel univariate
probability distribution termed the inverted
Dagum distribution. Extensive analysis of the
statistical properties of this distribution,
including the hazard function, survival function,
Renyi’s entropy, quantile function, and the
distribution of the order statistics, was
conducted. Parameter estimation of the model was
performed utilizing the maximum likelihood
method, with the consistency of the estimates
validated through Monte Carlo simulation.
Furthermore, the applicability of the proposed
distribution was demonstrated through the
analysis of two real datasets.
Cite:
Abdulhameed A. Osi, Shamsuddeen A. Sabo, Ibrahim
Z. Musa INVERTED DAGUM DISTRIBUTION: PROPERTIES
AND APPLICATION TO LIFETIME DATASET. Reliability:
Theory & Applications. 2024, September 3(79):
595-604, DOI:
https://doi.org/10.24412/1932-2321-2024-379-595-604
|
595-604
|
|
A NOVEL HYBRID
DISTRIBUTED INNOVATION EGARCH MODEL FOR
INVESTIGATING THE VOLATILITY OF THE STOCK MARKET
Mubarak M.T.,
Adubisi O.D., Abbas U.F.
When calculating
risk and making decisions, investors and
financial institutions heavily rely on the
modeling of asset return volatility. For the
exponentiated generalized autoregressive
conditional heteroscedasticity (EGARCH) model,
we created a unique innovation distribution in
this study called the
type-II-Topp-Leone-exponentiated-Gumbel (TIITLEGU)
distribution. The key mathematical
characteristics of the distribution were
determined, and Monte Carlo experiments were
used to estimate the parameters of the novel
distribution using maximum likelihood estimation
(MLE) procedure. The performance of the EGARCH
(1,1) model with TIITLEGU distributed innovation
density in relation to other innovation
densities in terms of volatility modeling is
examined through applications using two Nigerian
shock returns. The results of the diagnostic
tests indicated that, with the exception of the
EGARCH (1,1)-Johnson (SU) reparametrized (JSU)
innovation density, the fitted models have been
sufficiently specified. The parameters for the
EGARCH (1,1) model with different innovation
densities are significant at various levels.
Furthermore, in out-of-sample prediction, the
fitted EGARCH (1,1)-TIITLEGU innovation density
performed better than the EGARCH (1,1)- existing
innovation densities. As a result, it is decided
that the EGARCH-TIITLEGU model is the most
effective for analyzing Nigerian stock market
volatility.
Cite: Mubarak
M.T., Adubisi O.D., Abbas U.F. A NOVEL HYBRID
DISTRIBUTED INNOVATION EGARCH MODEL FOR
INVESTIGATING THE VOLATILITY OF THE STOCK MARKET.
Reliability: Theory & Applications. 2024,
September 3(79): 605-618, DOI:
https://doi.org/10.24412/1932-2321-2024-379-605-618
|
605-618
|
|
SINGLE AND DOUBLE
ACCEPTANCE SAMPLING PLAN FOR TRUNCATED LIFE
TESTS BASED ON GAMMA LINDLEY DISTRIBUTION
Sriramachandran G.
V.
For time-truncated
life tests, this work defines single
acceptance and double acceptance sampling
plans assuming that the product's lifespan
follows the Gamma Lindley distribution. The
minimum sample size needed in a single
acceptance sampling plan for lot approval is
calculated for a range of parameter combinations
and a fixed test termination time. This ensures
the given average product life and the
corresponding number of failures. Operational
characteristic and producer risk values are also
tabulated for these parameter values. Using a
double acceptance sampling plan, the best
first and second samples are obtained to
ensure that the products specified average
with a certain level of customer trust.
Finally, under the same conditions, the
minimum sample size obtained using these
strategies are compared with other acceptance
sampling plans.
Cite:
Sriramachandran G. V. SINGLE AND DOUBLE
ACCEPTANCE SAMPLING PLAN FOR TRUNCATED LIFE
TESTS BASED ON GAMMA LINDLEY DISTRIBUTION.
Reliability: Theory & Applications. 2024,
September 3(79): 619-629, DOI:
https://doi.org/10.24412/1932-2321-2024-379-619-629
|
619-629
|
|
FUZZY VARIABLE
LINEAR PROGRAMMING PROBLEMS USING A FUZZY DUAL
SIMPLEX ALGORITHM
Srinivasa Rao Kolli,
U.V. Adinarayana Rao, Taviti Naidu Gongada
In modern research,
several brilliant minds investigate linear
programming problems involving fuzzy variable
quantities. Many researchers have turned to
linear programming by fuzzy variables to address
this problem. Various fuzzy simplex approaches
have been developed, using ranking functions to
handle fuzzy numbers. Results from this research
suggest that linear ranking functions can
provide a straightforward interpretation of
problems involving linear programming by fuzzy
variable quantities. To solve these types of
problems, the Fuzzy Dual Simplex Tableau method
is often applied, which proves useful for
sensitivity analysis when modifications are made
to the activity vectors of the fundamental
columns. In this study, a numerical case is
presented to demonstrate the potential benefits
of this approach for future technologies.
Cite:
Srinivasa Rao Kolli, U.V. Adinarayana Rao,
Taviti Naidu Gongada FUZZY VARIABLE LINEAR
PROGRAMMING PROBLEMS USING A FUZZY DUAL SIMPLEX
ALGORITHM. Reliability: Theory & Applications.
2024, September 3(79): 630-637, DOI:
https://doi.org/10.24412/1932-2321-2024-379-630-637
|
630-637
|
|
A MODIFIED AILAMUJIA
DISTRIBUTION: PROPERTIES AND APPLICATION
David Ikwuoche John,
Okeke Evelyn Nkiru, Franklin Lilian
This study presents
a modified one-parameter Ailamujia distribution
called the Entropy Transformed Ailamujia
distribution (ETAD) is introduced to handle both
symmetric and asymmetric lifetime data sets. The
ETAD properties like order and reliability
statistics, entropy, moment and moment
generating function, quantile function, and its
variability measures were derived. The maximum
likelihood estimation (MLE) method was used in
estimating the parameter of ETAD and through
simulation at different sample sizes, the MLE
was found to be consistent, efficient, and
unbiased for estimating the ETAD parameter. The
flexibility of ETAD was shown by fitting it to
six different real lifetime data sets and
compared it alongside seven competing one-
parameter distributions. The goodness of fit (GOF)
results from Akaike information criteria,
Bayesian information criteria, corrected Akaike
information criteria, and Hannan-Quinn
information criteria show that the ETAD was the
best fit amongst all the seven competing
distributions across all the six data sets.
Cite: David
Ikwuoche John, Okeke Evelyn Nkiru, Franklin
Lilian A MODIFIED AILAMUJIA DISTRIBUTION:
PROPERTIES AND APPLICATION. Reliability: Theory
& Applications. 2024, September 3(79): 638-652,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-638-652
|
638-652
|
|
MODIFIED GROUP RUNS
CONTROL CHART FOR MONITORING PROCESS DISPERSION
Chandrakant G. Gardi,
Vikas B. Ghute
Due to a rise in
competitiveness, it has become an intense
concern to the manufacturers to monitor process
dispersion to avoid low quality production. To
ensure quality production, the control chart
that gives early detection of change in the
dispersion is always encouraged. Researchers
have suggested various control charts based on
different estimators of process dispersion.
Recently, many synthetic control charts based on
such estimators are put forth by researchers to
effectively monitor the dispersion in the
process. Modified Group Runs (MGR) control chart
is an extension of synthetic charts with further
enhancement in the detection ability. In this
paper, we propose a MGR control chart based on
Downton’s estimator (D). Comparison of MGR
control chart with synthetic chart based on
estimator D reveals the enhanced performance of
MGR-D chart.
Cite:
Chandrakant G. Gardi, Vikas B. Ghute MODIFIED
GROUP RUNS CONTROL CHART FOR MONITORING PROCESS
DISPERSION. Reliability: Theory & Applications.
2024, September 3(79): 653-659, DOI:
https://doi.org/10.24412/1932-2321-2024-379-653-659
|
653-659
|
|
ON THE FLEXIBILITY
OF TYPE I HALF LOGISTIC EXPONENTIATED FRECHET
DISTRIBUTION
Olalekan Akanji
Bello, Sani Ibrahim Doguwa, Abukakar Yahaya,
Haruna Mohammed Jibril,
In this article, we
delve into the modeling and analysis of
lifetimes, which hold substantial importance
across various scientific and industrial fields.
Our focus is on introducing a novel distribution
termed the Type I Half-Logistic Exponentiated
Frechet (TIHLEtF) Distribution, which is an
extension of the Frechet distribution. We have
derived a crucial representation of the density
function for this distribution. Furthermore, we
explore several statistical properties
associated with the TIHLEtF distribution. These
properties encompass explicit expressions for
the quantile function, probability-weighted
moments, moments, moments generating function,
reliability function, hazard function, and order
statistics. To estimate the model parameters, we
employ the maximum likelihood estimation
technique and present the results of a
simulation study. To emphasize the superiority
of our newly introduced distribution, we apply
it to two real datasets. The outcomes of our
analysis reveal that the TIHLEtF distribution
outperforms the other considered distributions
in terms of fitting the data in these real-world
cases.
Cite:
Olalekan Akanji Bello, Sani Ibrahim Doguwa,
Abukakar Yahaya, Haruna Mohammed Jibril, ON THE
FLEXIBILITY OF TYPE I HALF LOGISTIC
EXPONENTIATED FRECHET DISTRIBUTION. Reliability:
Theory & Applications. 2024, September 3(79):
660-674, DOI:
https://doi.org/10.24412/1932-2321-2024-379-660-674
|
660-674
|
|
BAYESIAN ANALYSIS OF
EXTENDED MAXWELL-BOLTZMANN DISTRIBUTION USING
SIMULATED AND REAL-LIFE DATA SETS
Nuzhat Ahad,
S.P.Ahmad, J.A.R eshi
The objective of the
study is to use Bayesian techniques to estimate
the scale parameter of the 2Kth order weighted
Maxwell-Boltzmann distribution(KWMBD). This
involved using various prior assumptions such as
extended Jeffrey’s, Hartigan’s , Inverse-gamma
and Inverse-exponential, as well as different
loss functions including squared error loss
function (SELF), precautionary loss function (PLF),
Al Bayyati’s loss function (ALBF), and Stein’s
Loss Function (SLF).The maximum likelihood
estimation (MLE) is also obtained. We compared
the performances of MLE and bayesian estimation
under each prior and its associated loss
functions. And demonstrated the effectiveness of
Bayesian estimation through simulation studies
and analyzing real-life datasets.
Cite: Nuzhat
Ahad, S.P.Ahmad, J.A.R eshi BAYESIAN ANALYSIS OF
EXTENDED MAXWELL-BOLTZMANN DISTRIBUTION USING
SIMULATED AND REAL-LIFE DATA SETS. Reliability:
Theory & Applications. 2024, September 3(79):
675-688, DOI:
https://doi.org/10.24412/1932-2321-2024-379-675-688
|
675-688
|
|
BAYESIAN
NON-INFERIORITY TEST BETWEEN TWO BINOMIAL
PROPORTIONS
W. B. Yahya, C. P.
Ezenweke, O. R. Olaniran, I. A. Adeniyi, K.
Jimoh, R. B. Afolayan, M. K. Garba, I. Ahmed
The paper aimed to
propose a new Bayesian test method for
establishing a non-inferiority measure between
an active treatment (drug) and a new (cheaper)
treatment using two independent binomial samples.
A Bayesian test statistic was developed for
testing non-inferiority between two independent
binomial proportions. Conjugate Beta prior was
assumed for the binomial proportions to elicit
posterior from the same Beta family of
distributions. The efficiency of this test
method was established via power analysis and
its ability to yield the nominal Type I error
rate (alpha) in a detailed Monte-Carlo study.
Results from this study showed that the proposed
test method yielded higher powers and good
estimates of the Type I error rate at the chosen
sample sizes and varying non-inferiority margins
(effect sizes). Thus, the new Bayesian test
method is very efficient at detecting the
significance of the non-inferiority margin
between two independent binomial proportions
when such is not negligible at all sample sizes.
Further results showed that the size of the two
population proportions being tested influences
the power and the estimated nominal Type I error
rate with an increase in power and a good
estimate of Type I error rate achieved when both
population proportions being tested are less
than 0.5. It is therefore concluded that the new
Bayesian test method can be employed whenever it
is desirable to establish the existence of non-
inferiority or otherwise between a pair of (clinical)
treatments (drugs). All the simulations and
analyses were performed with the R statistical
package.
Cite: W. B.
Yahya, C. P. Ezenweke, O. R. Olaniran, I. A.
Adeniyi, K. Jimoh, R. B. Afolayan, M. K. Garba,
I. Ahmed BAYESIAN NON-INFERIORITY TEST BETWEEN
TWO BINOMIAL PROPORTIONS. Reliability: Theory &
Applications. 2024, September 3(79): 689-703,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-689-703
|
689-703
|
|
BAYESIAN AND
E-BAYESIAN ESTIMATION OF EXPONENTIATED INVERSE
RAYLEIGH DISTRIBUTION USING CONJUGATE PRIOR
Ramesh Kumar, Hemani
Sharma, Rahul Gupta, Ableen Kaur
This study explores
the application of Bayesian and E-Bayesian
techniques to estimate the scale parameter of
the Exponentiated Inverse Rayleigh distribution.
Bayesian estimates for the parameter are derived
using an informative Gamma prior and evaluated
under three distinct loss functions: De- Groot,
Squared Error, and Al-Bayyati loss functions.
Various Properties of the E-Bayesian estimators
under different loss functions have also been
studied. To compare the effectiveness of
E-Bayesian estimates against the Bayesian
counterpart, a simulation study is conducted
using MatLab. The various derived estimators
were compared in terms of their Mean Squared
Error. The results of a simulation study reveal
that E-Bayesian estimates exhibit a smaller Mean
Squared Error in comparison to Bayesian
estimates, thereby demonstrating their enhanced
efficiency. Among the E- Bayesian estimates, the
third one stands out as the most effective.
Moreover, the analysis highlights that the
Squared Error loss function outperforms the
Al-Bayyati and De-Groot loss functions,
exhibiting a smaller MSE. Furthermore, the
efficacy of these estimators is demonstrated
through an analysis of a real-life dataset.
Cite: Ramesh
Kumar, Hemani Sharma, Rahul Gupta, Ableen Kaur
BAYESIAN AND E-BAYESIAN ESTIMATION OF
EXPONENTIATED INVERSE RAYLEIGH DISTRIBUTION
USING CONJUGATE PRIOR . Reliability: Theory &
Applications. 2024, September 3(79): 704-716,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-704-716
|
704-716
|
|
AVAILABILITY
ANALYSIS FOR IDENTIFICATION OF CRITICAL FACTOR
OF A THERMAL POWER PLANT
Pardeep Kumar, Vipin
Kumar Sharma, Dinesh Kumar
In the present
stimulated business environment, power sector is
playing a major role in the economic growth of
India. During the last 20 years, the country had
been facing a poor supply of energy and this
supply-demand gap is increasing continuously. So,
it is important for power plants to improve its
power generation capacity drastically by
reducing the failure rate. In the present paper,
to analyze the causes of poor availability,
thermal power plant has divided into six
different systems and a system comprising of
waste gases heating system has been considered.
With the help of transition diagram,
mathematical equations have been used to find
out the availability. After analyzing, it was
found that the value of availability is very low
and boiler tube failure is one of the most
critical factors for this low availability of
system. Economizer zone has identified having
long existence time of failures and frequency of
occurrence is very high. So, minimizing the
failure rate with the help of a proper
maintenance schedule will result in decreasing
the shutdown period of the plant and increasing
the system availability.
Cite: Pardeep
Kumar, Vipin Kumar Sharma, Dinesh Kumar
AVAILABILITY ANALYSIS FOR IDENTIFICATION OF
CRITICAL FACTOR OF A THERMAL POWER PLANT.
Reliability: Theory & Applications. 2024,
September 3(79): 717-724, DOI:
https://doi.org/10.24412/1932-2321-2024-379-717-724
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717-724
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WEIGHTED R-NORM
ENTROPY FOR LIFETIME DISTRIBUTIONS: PROPERTIES
AND APPLICATION
Bilal Ahmad Bhat,
M.A.K Baig
In the field of
information theory, different uncertainty
measures have been introduced by various
researchers. These measures are widely used in
reliability and survival studies. In this
article, we introduce two new weighted
uncertainty measures which are known as weighted
R-Norm entropy (WRNE) and weighted R-Norm
residual entropy (WRNRE). WRNE and WRNRE are
“length- biased” shift-dependent uncertainty
measures in which higher weight is assigned to
large values of the observed random variable.
Several important properties of these measures
are studied. Some significant characterization
results and the relationships of WRNRE with
other reliability measures are presented. We
also show that the survival function is uniquely
determined by the WRNRE. Finally, based on a
real life data set of bladder cancer patients,
we illustrate the importance of WRNE and WRNRE.
Cite: Bilal
Ahmad Bhat, M.A.K Baig WEIGHTED R-NORM ENTROPY
FOR LIFETIME DISTRIBUTIONS: PROPERTIES AND
APPLICATION. Reliability: Theory & Applications.
2024, September 3(79): 725-735, DOI:
https://doi.org/10.24412/1932-2321-2024-379-725-735
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725-735
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AN IMPROVED
ESTIMATOR OF FINITE POPULATION MEAN UNDER RANKED
SET SAMPLING
Francis Delali Baeta,
Dioggban Jakperik, Michael Jackson Adjabui
To obtain reliable
estimates of population parameters, data that is
sampled for estimation must accurately represent
the underlying population. Sampled data that is
representative of the underlying population
depends also on the sampling technique that was
used in obtaining them. This is very important
since sampling bias could lead to over or under
estimation of parameters. Ranked Set Sampling is
considered to be a better alternative to the
classical sampling designs in obtaining such
data. Ranked Set Sampling is designed to
minimize the number of measured observations
required to achieve a desired precision in
making inferences, and thus it is more
economical to use for the purposes of estimation,
compared to the classical sampling designs. This
is also an added advantage in cases where it is
difficult to obtain data. Many estimators have
been developed recently for the estimation of
finite population mean under ranked set sampling.
This paper aims to improve estimation by
modifying an existing estimator using a simple
linear combination of the known population mean,
square root of the known coefficient of
variation, and the known median of an auxiliary
variable. The theoretical properties of the
proposed estimator, such as the bias and mean
squared error were derived up to the first order
of approximation, using Taylor’s expansion. The
bias, mean squared error, absolute relative bias,
and the relative efficiency were used as means
of evaluation and comparison between the
proposed modified estimator and its competitors.
The R software was used to aid computations.
Empirical applications to real data showed that
the proposed modified estimator is superior to
the competing estimators that were compared
since it has least bias, the least mean squared
error, the least absolute relative bias, and the
highest relative efficiency in all sample sizes
that were considered. The bias and mean squared
error of the modified estimator under Ranked Set
Sampling was found to be smaller than those of
the existing estimators that were compared.
Hence it is more efficient and capable of
providing reliable estimates than the existing
estimators that were compared and so we
recommend that it should be used in survey
estimations.
Cite: Francis
Delali Baeta, Dioggban Jakperik, Michael Jackson
Adjabui AN IMPROVED ESTIMATOR OF FINITE
POPULATION MEAN UNDER RANKED SET SAMPLING.
Reliability: Theory & Applications. 2024,
September 3(79): 736-743, DOI:
https://doi.org/10.24412/1932-2321-2024-379-736-743
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736-743
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BAYESIAN ESTIMATION
OF PARAMETERS AND RELIABILITY CHARACTERISTICS IN
THE INVERSE GOMPERTZ DISTRIBUTION
Taiwo. M. Adegoke,
Latifat A. Abimbola, Oladapo M. Oladoja,
Oyindamola. R. Oyebanjo, K.O. Obisesan
In this study, we
derive Bayes’ estimators for the unknown
parameters of the Inverse Gompertz Distribution
(IGD) using three alternative loss functions:
the Squared Error Loss Function (SELF), the
Entropy Loss Function (ELF), and the Linex Loss
Function. Closed-form formulas for Bayes
estimators are not possible when both parameters
are unknown, hence Lindley’s approximation (L-Approximation)
is used for computation. We examine the
performance of these estimators using their
simulated hazards and assess their effectiveness
in parameter estimation. It was discovered that
as the sample size increases, parameter
estimations became more precise and accurate
across all functions. However, ELF consistently
has lower MSE values than SELF and LINEX,
indicating better parameter estimation. This
pattern was also seen in the estimation of the
hazard function, where ELF regularly beat SELF
and LINEX, implying more efficient parameter
estimation overall.
Cite: Taiwo.
M. Adegoke, Latifat A. Abimbola, Oladapo M.
Oladoja, Oyindamola. R. Oyebanjo, K.O. Obisesan
BAYESIAN ESTIMATION OF PARAMETERS AND
RELIABILITY CHARACTERISTICS IN THE INVERSE
GOMPERTZ DISTRIBUTION. Reliability: Theory &
Applications. 2024, September 3(79): 744-756,
DOI:
https://doi.org/10.24412/1932-2321-2024-379-744-756
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744-756
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A TWO-PARAMETER
ARADHANA DISTRIBUTION WITH APPLICATIONS TO
RELIABILITY ENGINEERING
Ravi Shanker, Nitesh
Kumar Soni, Rama Shanker, Mousumi Ray, Hosenur
Rahman Prodhani
The search for a
statistical distribution for modelling the
reliability data from reliability engineering is
challenging and the main cause is the stochastic
nature of the data and the presence of skewness,
kurtosis and over-dispersion. During recent
decades several one and two-parameter
statistical distributions have been proposed in
statistics literature, but all these
distributions were unable to capture the nature
of data due to the presence of skewness,
kurtosis and over-dispersion in the data. In the
present paper, two-parameter Aradhana
distribution, which includes one parameter
Aradhana distribution as a particular case, has
been proposed. Using convex combination approach
of deriving a new statistical distribution, a
two- parameter Aradhana distribution has been
proposed. Various interesting and useful
statistical properties including survival
function, hazard function, reverse hazard
function, mean residual life function,
stochastic ordering, deviation from mean and
median, stress-strength reliability, Bonferroni
and Lorenz curve and their indices have been
discussed. The raw moments, central moments and
descriptive measures based on moments of the
proposed distribution have been obtained. The
estimation of parameters using the maximum
likelihood method has been explained. The
simulation study has been presented to know the
performance in terms of consistency of maximum
likelihood estimators as the sample size
increases and. The goodness of test of the
proposed distributions has been tested using the
values of Akaike Information criterion and
Kolmogorov-Smirnov statistics. Finally, two
examples of real lifetime datasets from
reliability engineering have been presented to
demonstrate its applications and the goodness of
fit, and it shows a better fit over
two-parameter generalized Aradhana distribution,
quasi Aradhana distribution, new quasi Aradhana
distribution, Power Aradhana distribution,
weighted Aradhana distribution, gamma
distribution and Weibull distribution. The
flexibility, tractability and usefulness of the
proposed distribution show that it is very much
useful for modelling reliability data from
reliability engineering. As this is a new
distribution and it has wide applications, it
will draw the attention of researchers in
reliability engineering and biomedical sciences
to search many more applications in the future.
Cite: Ravi
Shanker, Nitesh Kumar Soni, Rama Shanker,
Mousumi Ray, Hosenur Rahman Prodhani A
TWO-PARAMETER ARADHANA DISTRIBUTION WITH
APPLICATIONS TO RELIABILITY ENGINEERING.
Reliability: Theory & Applications. 2024,
September 3(79): 757-774, DOI:
https://doi.org/10.24412/1932-2321-2024-379-757-774
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757-774
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STATISTICAL DESIGN
OF CONDITIONAL REPETITIVE GROUP SAMPLING PLAN
BASED ON TRUNCATED LIFE TEST FOR PERCENTILE
LIFETIME USING EXPONENTIATED GENERALIZED FRECHET
DISTRIBUTION
S. Jayalakshmi, S.
Vijilamery
Reliability
Acceptance sampling plan is used to assess
whether to accept or reject a product depending
on its lifetime. An inspection carried out for
the purpose of determining if lifetime
inspections are performing properly can be
tested by submitting a truncated lifetime test.
In this paper describes a new approach on
Conditional Repetitive Group Sampling Plan based
on Truncated life test is proposed and the
lifetime follows an Exponentiated Generalized
Frechet Distribution. For each consumer risk, it
is determined whether minimum sample sizes are
required to assert a percentile life. It is
calculated that the operating characteristic
function values of the sampling plans as well as
the producer’s risk ratio corresponding to the
sampling plans. The results are illustrated with
numerical examples and a real-world data set is
used to demonstrate the impact and performance
of the suggested acceptance sampling plans.
Cite: S.
Jayalakshmi, S. Vijilamery STATISTICAL DESIGN OF
CONDITIONAL REPETITIVE GROUP SAMPLING PLAN BASED
ON TRUNCATED LIFE TEST FOR PERCENTILE LIFETIME
USING EXPONENTIATED GENERALIZED FRECHET
DISTRIBUTION. Reliability: Theory & Applications.
2024, September 3(79): 775-787, DOI:
https://doi.org/10.24412/1932-2321-2024-379-775-787
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775-787
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NEW EXTENSION OF
INVERTED MODIFIED LINDLEY DISTRIBUTION WITH
APPLICATIONS
Devendra Kumara,
Anju Goyalb, P. Pareekc, M. Sahaa
In this article we,
proposed a new two parameter distribution called
inverted power modified Lindley distribution.
The main objective is to introduce an extension
to inverted modified Lindley distribution as an
alternative to the inverted exponential,
inverted gamma and inverted modified Lindley
distributions, respectively. The proposed
distribution is more flexible than the above
mentioned distributions in terms of its hazard
rate function. In the part of estimation of the
proposed model, we first utilize the maximum
likelihood (ML) estimator and parametric
bootstrap confidence intervals, viz., standard
bootstrap, percentile bootstrap, bias-corrected
percentile (BCPB), bias-corrected accelerated
bootstrap (BCAB) from the classical point of
view as well the Bayesian estimation under
different loss functions, squared error loss
function, modified squared error loss function,
and Bayes credible interval as to obtain the
model parameter based on order statistics. A
simulation study is carried out to check the
efficiency of the classical and the Bayes
estimators in terms of mean squared errors and
posterior risks, respectively. Two real life
data sets, have been analyzed for order
statistics to demonstrate how the proposed
methods may work in practice.
Cite:
Devendra Kumara, Anju Goyalb, P. Pareekc, M.
Sahaa NEW EXTENSION OF INVERTED MODIFIED LINDLEY
DISTRIBUTION WITH APPLICATIONS. Reliability:
Theory & Applications. 2024, September 3(79):
788-804, DOI:
https://doi.org/10.24412/1932-2321-2024-379-788-804
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788-804
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A MAP/PH1, PH2/2
INVENTORY QUEUEING SYSTEM WITH TWO COMMODITY,
MULTIPLE VACATION, SERVER FEEDBACK, WORKING
BREAKDOWN, REPAIR AND EMERGENCY REPLENISHMENT
G. Ayyappan, N.
Arulmozhi
We investigate a
continuous review inventory queuing system in
the present study that has two heterogeneous
servers: Server-2, which is reliable, and
Server-1, which is unreliable. An exponentially
distributed random time is used to describe the
repair process when server-1 has an interruption.
On the other hand, server-2 is completely
dependable, but it goes on vacation when the
system is empty. These two goods can be
reordered under ordering regulations. To ensure
customer satisfaction, an emergency
replenishment of one item with no lead time
occurs when the on-hand inventory level falls to
zero. We use the matrix analytic approach for
the QBD process under a steady-state probability
vector. We also take into account the overall
cost and the busy time. Furthermore, numerical
data shows the benefits of the suggested
approach in a range of random circumstances.
Cite: G.
Ayyappan, N. Arulmozhi A MAP/PH1, PH2/2
INVENTORY QUEUEING SYSTEM WITH TWO COMMODITY,
MULTIPLE VACATION, SERVER FEEDBACK, WORKING
BREAKDOWN, REPAIR AND EMERGENCY REPLENISHMENT.
Reliability: Theory & Applications. 2024,
September 3(79): 805-823, DOI:
https://doi.org/10.24412/1932-2321-2024-379-805-823
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805-823
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