Pawan Kumar, Rakesh Kumar (Guest
Editors)
Editorial. Special
issue on Queuing and Reliability Models with their
Applications
This special issue is the outcome of the selected papers
presented in the twenty-seventh international conference of
Forum for Interdisciplinary Mathematics (FIM) in conjunction
with third convention of IARS on Interdisciplinary
Mathematics, Statistics and Computational Techniques (IMSCT
2018–FIM XXVII) which is held in the Department of
Statistics, University of Jammu, Jammu & Kashmir, India
during November 02-04, 2018. At last, the guest editors
would like to acknowledge the contributions of all those
professors who helped them to bring this special issue in
current form. The guest editors would also like to thank the
Editor-in-Chief, and also the Managing Editor, Prof.
Alexander Bochkov of the journal Reliability: Theory and
Applications for providing a platform for publishing the
research papers in special issue.
DOI:
https://doi.org/10.24411/1932-2321-2019-11001
Rakesh Gupta, Parul Bhardwaj
A Discrete
Parametric Markov-Chain Model Of A Two Unit Cold Standby
System With Appearance And Disappearance Of Repairman
The paper deals with the stochastic
analysis of a two-identical unit cold standby system model
assuming two modes- normal and total failure. A single
repair facility appears in and disappears from the system
randomly. The random variables denoting the failure time,
repair time, time to appearance and time to disappearance of
repairman are independent of discrete nature having
geometric distributions with different parameters. The
various measures of system effectiveness are obtained by
using regenerative point technique.
DOI:
https://doi.org/10.24411/1932-2321-2019-11002
Rakesh Gupta, Arti Tyagi
A Discrete
Parametric Markov-Chain Model Of A Two-Unit Cold Standby
System With Repair Efficiency Depending On Environment
The paper deals with stochastic
analysis of a two identical unit cold standby system model
with two modes of the units-normal (N) and total failure
(F). A single repairman is always available with the system
to repair a failed unit. Two physical conditions-good and
poor of repairman depending upon the perfect and imperfect
environment are considered. The system transits from perfect
to imperfect environment and vice-versa after random periods
of time. The failure and repair times of a unit are taken as
independent random variables of discrete nature having
geometric distributions with different parameters.
DOI:
https://doi.org/10.24411/1932-2321-2019-11003
Pradeep Chaudhary, Rashmi Tomar
A Two Identical Unit
Cold Standby System Subject To Two Types Of Failures
The paper deals with a system model
composed of a two identical unit standby system in which
initially one is operative and other is kept as cold
standby. Each unit of the system has two possible modes –
Normal (N) and Total Failure (F). An operating unit may fail
either due to normal or due to chance causes. A single
repairman is always available with the system to repair a
unit failed due to any of the above causes. The system
failure occurs when both the units are in total failure
mode. The failure time distributions of a unit failed due to
both the causes are taken as exponentials with different
parameters whereas the repair time distributions of a failed
unit in both types of failure are taken as general with
different CDFs. Using regenerative point technique, the
various important measures of system effectiveness have been
obtained
DOI:
https://doi.org/10.24411/1932-2321-2019-11004
Akshita Sharma, Pawan Kumar
Analysis of
Reliability Measures of Two Identical Unit System with One
Switching Device and Imperfect Coverage
The present paper deals with the
reliability analysis of a two identical unit system model
with safe and unsafe failures, switching device and
rebooting. Initially one of the units is in operative state
and other is kept in standby mode. A single repairman is
always available with the system for repairing and rebooting
the failed units. In case of unsafe failure, repair cannot
be started immediately but first rebooting is done which
transforms the unsafe failure to safe failure and thereafter
repair is carried out as usual. Switching device is used to
put the repaired and standby units to operation. The failure
time distributions of both the units and switch are also
assumed to be exponential while the repair time
distributions are taken general in nature. Reboot delay time
is assumed to be exponentially distributed. Using
regenerative point techniques, various measures of system
effectiveness such as transition probabilities,
availability, busy period, expected numbers of repairs etc.
have been obtained, to make the study more informative some
of them have been studied graphically.
DOI:
https://doi.org/10.24411/1932-2321-2019-11005
Urvashi Gupta, Pawan Kumar
Performance Measures
Of A Two Non-Identical Unit System Model With Repair And
Replacement Policies
The present paper deals with two
non-identical units A and B, both are in operative mode. If
the unit A fails then it is taken up for preparation of
repair before entering into repair mode and the unit-B
gives a signal for repair before going into failure mode.
If the unit gets repaired then it becomes operative
otherwise it is replaced by the new one. A single repairman
is always available with the system to repair the failed
units and the priority in repair is always given to the
unit-A. The failure time distributions of both the units are
taken as exponential and the repair time distributions are
taken as general. Using regenerative point technique the
various characteristics of the system effectiveness have
been obtained such as Transition Probabilities and Mean
Sojourn times, Mean time to system failure (MTSF),
Availability of the system, Busy Period of repairman,
Expected number of Replacement, Expected profit incurred.
DOI:
https://doi.org/10.24411/1932-2321-2019-11006
Tahsina Aziz, M. Rezaul Karim
Assessment And
Prediction Of Reliability Of An Automobile Component Using
Warranty Claims Data
This paper presents an analysis of
warranty claims data of a component of an automobile. The
objectives of the analysis are to assess and predict the
reliability of the component. To do these the paper present
nonparametric and parametric analyses for the lifetime
variable, age in month, based on warranty claims data. It
also investigates on the variation of reliability of the
component with respect to month of production and dominant
failure modes. The paper will be useful to the manufacturer
for assessing and predicting reliability and warranty costs
and for assuring customer satisfaction and product
reputation.
DOI:
https://doi.org/10.24411/1932-2321-2019-11007
Gulab Singh Bura and Shilpi Gupta
Time Dependent
Analysis of an Queue With Catastrophes
We consider a Markovian queueing system
with two identical servers subjected to catastrophes. When
the system is not empty, catastrophes may occur and destroy
all present customers in the system. Simultaneously the
system is ready for new arrivals. The time dependent and the
steady state solution are obtained explicitly. Further we
have obtained some important performance measures of the
studied queueing model.
DOI:
https://doi.org/10.24411/1932-2321-2019-11008
Bhupender Kumar Som
Cost-profit Anslysis
of Stochastic Heterogeneous Queue with Reverse Balking,
Feedback and Retention of Impatient Customers
Consider a system operating as an
M/M/2/N queue. Increasing system size influences newly
arriving customers to join the system (reverse balking). As
the system size increases, the customers’ waiting in the
queue become impatient. After a threshold value of time, the
waiting customer abandons the queue (reneging). These
reneging customers can be retained with some probability
(retention). Few customers depart dissatisfied with the
service and rejoin the system as feedback customers. In this
paper a feedback queuing system with heterogeneous service,
reverse balking, reneging and retention is developed. The
model is solved in steady-state recursively. Necessary
measures of performance are drawn. Numerical interpretation
of the model is presented. Cost-profit analysis of the
system is performed by developing a cost model. Sensitivity
analysis of the model is also presented arbitrarily.
DOI:
https://doi.org/10.24411/1932-2321-2019-11009
Rakesh Kumar, Bhavneet Singh Soodan
Transient Analysis
of a Single-Server Queuing System with Correlated Inputs and
Reneging
In this paper, we study a continuous
time single-server queuing system, wherein the arrivals at
two consecutive transition marks are correlated. The service
times and the reneging times are exponential distributed.
The time-dependent behavior of the model is studied using
Runge-Kutta method.
DOI:
https://doi.org/10.24411/1932-2321-2019-11010
