Weibull-Lindley Distribution: A Bathtub Shaped Failure Rate
Model
V.M.Chacko, Deepthi K S, Beenu Thomas,
Rajitha C
The Lindley and Weibull are the two
most commonly used distributions for analyzing lifetime
data. These distributions have several desirable properties
and nice physical interpretations. This paper introduces a
new distribution, which generalizes the well-known Lindley
and Weibull distribution, having Bathtub shaped failure
rate. The Statistical properties of this distribution are
discussed in this paper. Applications in reliability study
are discussed. A real data set is analyzed and it is
observed that the present distribution can provide a better
than some other very well known distributions.
Keywords: Reliability, Bathtub shaped failure rate,
Weibull distribution, Lindley distribution
DOI:
https://doi.org/10.24411/1932-2321-2018-14001
A Practical Approach
for Performing Multi-response Optimization for Advanced
Process Control
Prasath Ganesan, Sachin Patil, Vikas
Pandey, Tony M Shaju, Srinivas Pothula
In account of the statistical methods
used in advanced manufacturing process optimization,
multi-response optimization is one of the key areas of
focus. Previously multi-response optimization problems were
solved by past experiences and engineering judgment by many
industries which lead to uncertainty in the decision making
and less confidence in getting optimized process parameters
to produce robust products. For identifying the optimal
process parameters for a manufacturing a robust product in
which multiple CTQ (Critical-to-Quality) characteristics
need to be achieved, a systematic statistical optimization
approach is required. This paper presents one of the
practical systematic approaches for multi-response
optimization of advanced manufacturing processes. This
statistical methodology uses Taguchi DoE (Design of
Experiment) based approach to optimize the process
parameters for individual CTQ followed by a multi-response
optimization using composite desirability functions to
achieve multiple CTQs.
Keywords: Multi-response optimization, Design of
Experiments, Critical-to-Quality, Taguchi, Regression
DOI:
https://doi.org/10.24411/1932-2321-2018-14002
Om
Distribution With Properties And Applications
Rama Shanker, Kamlesh Kumar Shukla
A new one parameter lifetime
distribution named, ‘Om distribution’ has been proposed and
studied. Its various statistical properties including shapes
for probability density, moments based measures, hazard rate
function, mean residual life function, stochastic ordering,
mean deviations, Bonferroni and Lorenz curves, distribution
of order statistics, and stress-strength reliability have
been discussed. Estimation of parameter has been discussed
with the method of maximum likelihood. Applications of the
distribution have been explained through two examples of
real lifetime data from engineering and the goodness of fit
found to be quite satisfactory over several one parameter
lifetime distributions.
Keywords: Lifetime distributions, Statistical
Properties, Maximum likelihood estimation, Applications
DOI:
https://doi.org/10.24411/1932-2321-2018-14003
Imperfect Production
Model for Sensitive Demand with Shortage
Uttam Kumar Khedlekar and Ram Kumar
Tiwari
In this paper, we have presented
economic production inventory model considering non-linear
demand depanding on selling price. Here, all imperfect
quality items are reworked after the regular production
process and the reworked items are considered as similar as
good quality items. Rework is important in those businesses
where last product is expensive and raw materials are
insuficient. Now, our objective is to find out the optimal
ordering lot size, optimal selling price and shortage for
which the profit of the model is maximum. A numerical
example is presented to illustrate the validity of the
model. Manageral implications has been presented in terms of
the production and pricing of imperfect items.
Keywords: Dynamic pricing, Non linear price sensitive
demand, Optimal price settings, Imperfect item, Rework,
Partial backlogging
DOI:
https://doi.org/10.24411/1932-2321-2018-14004
A Bayes Analysis and
Comparison of Weibull and Lognormal Based Accelerated Test
Models with Actual Lifetimes Unknown
S.K. Upadhyay, Reema Sharma
The paper considers an accelerated test
situation where the actual lifetimes of the items are not
directly observable rather their status are known in the
form of binary outcomes. By assuming two widely entertained
models, namely the Weibull and the lognormal distributions,
for the actual lifetimes, the paper provides full Bayesian
analysis of the entertained models when both scale and shape
parameters of the models are allowed to vary over the
covariates involved in the study, thus giving rise to
corresponding accelerated test models. The Bayes
implementation is based on sample based approaches, namely
the Metropolis algorithm and the Gibbs sampler using proper
priors of the parameters where the prior elicitation is
based on the expert testimonies. The situation involving
missing items where actual status is also unknown is
additionally entertained using the same modelling
assumption. A comparison between the two entertained models
is carried out using some standard Bayesian model comparison
tools. Finally, numerical illustration is provided based on
a given set of current status data and some relevant
findings are reported.
Keywords: Binary outcomes, Missing items, Accelerated
testing, Weibull distribution, Lognormal distribution,
Log-linear link function, Metropolis algorithm, Gibbs
sampler, Model comparison
DOI:
https://doi.org/10.24411/1932-2321-2018-14005
Continuous
Multistate System Universal Generating Function
V. M. Chacko
Usually, systems and components are
described as being in one of two modes, “on” or “off.” Such
systems are described using binary structure functions. In
multistate systems (MSS), components can be in more than two
states—for example, there can be partially failed or
partially operating modes. The system state can be
described by continuously many values. A system that can
have different task performance levels is named multi-state
system (MSS). In this paper, we present a technique for
solving a family of Continuous MSS reliability problems. A
universal generating function (UGF) method is proposed for
fast reliability estimation of continuous MSSs. The UGF
method provides the ability to estimate relatively quickly
different MSS reliability indices for series-parallel,
parallel-series and bridge structures. It can be applied to
MSS with different physical nature of system performance
measure.
Keywords: multi-state system, universal generating
function, reliability
DOI:
https://doi.org/10.24411/1932-2321-2018-14006
Mission-Based System
Reliability Modeling for Establishing Testable Performance
Requirements of a Distributed Network Monitoring System
Arthur Fries, Garfield Jones
Mission-based subsystem reliability requirements are derived
for a parent distributed network monitoring system operating
under circumstances that differ from standard analytical
constructs in a number of ways. First, the system comprises
a hierarchy of elements of different functionalities
individually adhering to distinct operational profiles.
Second, some constituent elements only need to perform
during relatively small and nonpredetermined portions of the
overall system mission accomplishment window. Third, failed
elements can be restored or replaced in time to enable
additional opportunities for satisfying mission needs.
Keywords: Distributed Network Monitoring System,
Subsystem reliability, Operational profile, Mean time
between operational mission failures
DOI:
https://doi.org/10.24411/1932-2321-2018-14007
