RT&A
2017,
# 3(46) Vol.12
Ahmadur Rahman, Showkat Ahmad Lone,
Arif Ul Islam
Statistical Analysis
for Type-I Progressive Hybrid Censored Data from Burr Type
XII Distribution under Step-Stress Partially Accelerated
Life Test Model
Progressive hybrid censoring scheme is
now quite common in the experiment of life testing and
reliability analysis. In this article the data, failure life
times of units, is obtained by using type-I progressive
hybrid censoring scheme. It is assumed that data follows
Burr Type XII distribution. The point and interval
estimation of the Burr Type XII distribution parameters and
acceleration factor are performed using maximum likelihood
estimator under stress partially accelerated life test
model. Monte Carlo simulation study is used to obtain the
biases and mean square errors of the estimators.
Keywords: Reliability, type I progressive hybrid
censoring scheme, Burr Type XII distribution, maximum
likelihood function, Monte Carlo simulation, Step-Stress
partially accelerated life test model.
Baffa Sani, Ramatu Idris Gatawa, Ibrahim
Yusuf
Reliability
Assessment of Deteriorating System
Industrial equipment and technical
systems are exposed various degree of deterioration ranging
from minor deterioration, medium to major deterioration and
subsequently failed thereafter and are replaced at failure.
Such deteriorations can slightly reduce system performance
and will ultimately lead to random failure. This paper
presents modelling and evaluation of reliability
characteristics such as availability, profit and mean time
to failure (MTTF) of a system subjected to three consecutive
stages of deterioration (minor, medium and major) before
failure. Markov models of the system are derived through the
system state transition probabilities and differential
equations which are further used to evaluate the system
availability, busy period, profit and mean time to failure (MTTF).
Based on assumed numerical values given to system
parameters, graphical illustrations are given to highlight
important results.
Keywords:
Deterioration, Reliability, Availability, profit
Paolo Rocchi
How Entropy
Infiltrates the Reliability Domain: Two Theoretical
Inquiries
The reliability theory includes an
enormous amount of works but does not yet become a mature
discipline. Many factors account for this fail; as first the
reliability domain is lacking the comprehensive and unifying
frame. The entropy concept demonstrates to be capable of
offering unified views and providing integrated mathematical
tools in various scientific sectors. The present paper
presents a concise review of two recent theoretical studies
that introduce the entropy in the reliability domain in
order to treat broad issues. The first of these applies
thermodynamic entropy to degradation mechanisms and provides
a model for a wide range of degradation processes. The
second employs the Boltzmann-like entropy to describe the
spontaneous decay of systems during the entire lifespan.
Keywords:
The present state of the reliability theory, thermodynamic
degradation, entropy generation theorem, Boltzmann-like
entropy, bathtub curve, reparability function
V.M.Chacko, Beenu Thomas, Deepthi K S
A ‘One Parameter’
Bathtub Shaped Failure Rate Distribution
Most real life system exhibit bathtub
shapes for their failure rate functions. Generalized
Lindley, Generalized Gamma, Exponentiated Weibull and
x-Exponential distributions are proposed for modeling
lifetime data having bathtub shaped failure rate model. This
paper considered a simple model but exhibiting bathtub
shaped failure rate and discuss the failure rate behavior.
The proposed distribution has only one parameter. A Little
works are available in literature with one parameter.
Computation of moments requires software. Applications in
reliability study is discussed.
Keywords:
Bathtub failure rate, Reliability
Alexander Bochkov
Special Issue.
Preface
On the cover of this issue there is a
"special issue". What is its difference from the usual
numbers issued earlier? The fact is that with this number,
we wanted to pay tribute to the memory of our friend and
colleague Igor Ushakov. It is he who owes his origin and
existence to the Gnedenko Forum and our journal, it is with
his name that all our initiatives of the last 11 years are
connected. We decided to post three articles by Igor,
printed in our magazine in different years. They very
clearly demonstrate its versatility. The first article is a
philosophical reflection on the ways of developing the
theory of reliability and its recent "golden age". These
arguments are all the more valuable because their author is
one of those who stood at the roots of what is now called
the theory of reliability. The second article is an example
of the scientific work of Igor Ushakov, in which he
discusses the interesting practical application of
generating functions. The third is his recollections about
the teacher - about Boris Vladimirovich Gnedenko, with whom
he was associated by kind friendship.
Igor Ushakov
Is Reliability
Theory Still Alive?
At the banquet held during closing of the MMR-2004
Conference (Santa Fe, USA), one of the most prominent
specialists on Reliability Theory, Professor of The George
Washington University Nozer Singpurwalla was a host of the
discussion during the dinner. The
topic he chose was a bit provocative: “IS RELIABILITY THEORY
STILL ALIVE ?” Even the question itself led to a furious
reaction of the conference participant: ”Yes! It is alive!
It is flourishing!” What is going now if even such a
question was suggested to the audience by such a serious
mathematician who dedicated all his talent to developing
Reliability Theory? It seems to me that Professor
Singpurwalla is right asking such a question. Though an
answer to this question is not so simple. Being in a
position a “mammoth” (if not a dinosaur J) in Reliability
Theory, I take a brevity to discuss this difficult question.
Keywords: History, Reliability
Theory
Igor Ushakov , Sumantra Chakravarty
Object Oriented
Commonalities in Universal Generating Function for
Reliability and in C++
The main idea of Universal Generating
Function is exposed in reliability applications. Some
commonalities in this approach and the C++ language are
discussed. In Chakravarty and Ushakov implementation for
Globalstar, C++ objects are in one-to-one correspondence
with reliability objects. An object is specified by mean
time between failures (MTBF), mean time to repair/replace (MTTR)
and an effectiveness weight (partial effectiveness index:
PEI). By definition, PEI=1 for binary atomic units. All
failure distributions are implicitly assumed to be
Exponential. If failed units were to be automatically
swapped, a switching time was also assigned by Chakravarty
and Ushakov (2000). Even small switching time is important
because it changes a parallel system “on paper” to a series
system with small MTTR. This may have dramatic effect
overall on system reliability.
Keywords:
Universal Generating Function,
C++ language, reliability
objects, system reliability
Igor Ushakov
Thurst of Life: Two
Gnedenko’s Visits to the United States
It won’t be an exaggeration to say that
I never met a man with a stronger thirst for life, creating
good around him, and being a courageous man who also faced
life’s test and terrible illness… I was really lucky: I had
been working with Boris Vladimirovich for many years
shoulder-to-shoulder, traveled with him many business trips,
spent many evenings with his hospitable family, he was my
guest as well many times… It was my great privilege:
Gnedenko visited me twice in the United States when I was
working at The George Washington University: in spring of
1991 and in summer of 1993. I will try to present a “photo
report” of these events using only few words for comments.
Keywords: Gnedenko, USA, photo
report, memory
