Download Executive Summary of the research work done by CHACKO V M for

Executive Summary of the research work done by CHACKO V M
for the period of 10-02-2011 to 31-03-2014
MRP (S)-835/10-11/KLCA019/UGC-SWRO dated 10-02-2011 Sanction Letter
Title: Total time on test transform ordering of semi-Markov process with application
to multistate system reliability theory
Reliability is a critical measure of performance of engineering systems such as power
generators, space crafts, telecommunication networks, control systems, nuclear reactors, oil and
gas pipelines etc. Conventional reliability theory is built on a framework in which both the
systems and its components can be in one of only two possible states: ‘working ‘ or ‘failed’.
Consequently, the system structure function is a binary function of binary variables. However the
binary feature of these reliability models places serious limitations on its utility, because most of
the engineering systems and their components exhibit many levels of performance between two
extremes of ‘working’ and ‘failed’. Multistate system reliability models allow both system and
components to assume more than two levels of performance.
First passage times of appropriate stochastic process have often been used to represent times
to failure of devices or systems which are subject to shocks and wear, random repair time and
random interruptions during their operations. The life distribution properties of these processes
have therefore been widely investigated in Multistate system reliability and maintenance
literature. The life distributions involved in devices or systems have several interesting properties
such as increasing mean residual life (IMRL), decreasing mean residual life (DMRL), etc. The
total time on test (TTT) transform is used as a tool for identification of failure distribution model
in binary system. Marshell and Shaked (1983), (1986) and Shantikumar (1984) considered
processes with new better than used (NBU) first passage times. Belzunce et al. (2002) derived,
for the uniformizible, continuous time Markov process, conditions in terms of discrete
uniformized Markov chain for the second order NBU and NBU based on laplace transformation
classes.
Lam (1992) studied NBUE and new worse than used in expectation (NWUE) properties of
increasing Markov processes and Markov Chains and
properties of Markov renewal processes.
considered the NBUE and NWUE
Use of TTT transform for the identification of failure rate models is discussed by Barlow
and Campo (1975). Later, Klefsjo (1982) presented some relationship between the TTT
transform and other ageing properties (with their duals) of random variable, eg. decreasing mean
residual life (DMRL), NBU, NBUE, harmonically new better than used in expectation (HNBUE)
and heavy tailedness. It further discussed properties of scaled TTT transform for some criteria of
the mean residual life such as decreasing mean residual life average (DMRLA), decreasing
harmonic mean residual life average (DHMRLA), new better than used harmonic mean residual
life average (NBUHMRLA), and new better than used mean residual life average (NBUMRLA).
But when we consider a complex system whose performance process is Markov or semiMarkov, we need the knowledge of DMRLA properties or other relevant ageing properties for
applying suitable maintenance and repair/replacement policies. The identification of failure rate
model of a system whose performance process is Markov/semi-Markov will be helpful to the
engineers and designers for applying suitable maintenance and repair or replacement policies,
since identification of failure rate model using TTT describes new methods for analyzing
nonnegative observations. Chacko et.al (2010) discussed use of TTT transform in identifying
failure rate model of semi-Markov reliability system.
I consider a semi-Markov process whose first passage time distribution is IFR or IFRA or
NBU or NBUE or DMRL (with their duals) or DMRL or DMRLA or NBUHMRL or NBUMRL
(with their duals). We consider the reliability function based on the transition probability
function in the upstates. The conditions of identification using transition probability function
provide equivalent information drawn from failure rate function of first passage time variable.
I introduced some sufficient conditions for the TTT ordering of the semi-Markov process
based on MRL criteria built from transition probability function. This result has been presented
at Annual Conference of Kerala Statistical Association held at University of Calicut during 1517 March 2012 and published in an International journal Reliability: Theory and Application, 01
(28) (vol.8) 53-64, 2013, march
The identification of the failure rate model of first passage time distribution of a semiMarkov process is important. The results are applicable to systems like power generation system
whose performance is measured in terms of productivity or capacity and having more than two
levels of performance. Preventive or corrective maintenance can be applied to the MSS if we
have the knowledge regarding its failure behavior, since type of the failure rate is an important
parameter for the maintenance and replacement policies.
Total time on test transform orders based on transition probability function of semimarkov system are studied. Connections among the new orders and other common stochastic
orders are examined and investigated. To establish the implication between other ordering of two
processes with TTT ordering. The advantage of the proposed ordering over the others in case of
censored data is analyzed. The application to engineering areas are given. This results are
published in Reliability: Theory And Applications, Title of the publication is-Total Time on
Test Transforms ordering of semi-Markov system, 03 (34) (vol.9) 57-63, 2014, September
. A survey has been conducted. It shows that the many engineering systems like
computers, electric power generation systems, flight engine system, oil transportation systems,
signal transmission and communication systems etc can be effectively modeled as Multistate
systems. So that reliability calculation and importance and joint importance measure of
components can be computed easily using MSS techniques. Using exponential assumption for
life in a state, we could model the computers as MSS, being the failure occur only because of
virus, voltage variation, jerking, overload etc but not because of ageing, and obtained the
reliability as 0.98 for one year of mission time in the branded items ACER, SONY, LENEVO
and COMPAQ. SONY is found to be stochastically better than other items, based on TTT
ordering.
We have developed a theory on Large multistate semi-Markov system and it is
communicated for the publication. We have data from oil transportation companies and applied
our results to the transportation network system. A wide area for the application comes under this
results. Reliability analysis of more complex systems with large number of components and
configuration make the system as multistate. As soon as a single component fails from a system
of large components, the load is shared by other components and a reliability diminishing occur.
It calls for MSS modeling and TTT ordering for the comparison.
Research
publication:
papers
published/
Accepted
for
publication/
Communicated
for
1. Mean residual life criteria of first passage time of semi-markov process based
on total time on test transforms, Reliability; Theory and Applications, 01 (28)
(vol.8) 53-64, 2013, march
2. Presented at Annual Conference and National Seminar of Kerala Statistical
Association, University of Calicut, Kerala.
3. Total Time on Test Transforms ordering of semi-markov system, Reliability:
Theory And Applications (International Journal of World Reliability GroupGnedenko E-forum), 03 (34) (vol.9) 57-63, 2014, September
4. Total Time on Test Transform ordering in Large Multistate semi-Markov
System (Communicated)
5. P-Birnbaum Distributions: Applications to Reliability and Banking Habits (To
Appear) Reliability: Theory And Applications, March 2015 Presented at
National Level Conference on Interdisciplinary Realms of Statistics, Sree
Kerala Varma College, Thrissur, Jan 9-10, 2015
6. A Generalization of Birnbaum Saunders Distribution, Presented at National
Seminar on Recent Advances in Statistical Theory and its Applications, 2526 Feb, 2015, St.Thomas College, Thrissur
7. Association in Time of Markov Process, Presented at National Conference on
Applied Mathematics, 27-27, Feb, 2015, St.Thomas College, Thrissur
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