Two Approximation Algorithms for Reliability Assessment of Multi-State Systems under A Markovian Environment  
Author Tao Jiang


Co-Author(s) Yu Liu


Abstract Multi-state system (MSS) reliability theory has received considerable popularity in the last few decades. However, only a few studies have considered the effect of stochastic dynamic environments on the deterioration processes of MSSs. We propose two approximation algorithms for the reliability assessment of MSSs working under a Markovian dynamic environment. The deterioration process of an MSS and the stochasticity of the environment are characterized by a progressive Markov chain and a non-progressive Markov chain, respectively. The cumulative effect of the Markovian environment is formulated by a stochastic time scale (STS) model. Two approximation algorithms, namely the distribution approximation algorithm (DAA) and moment approximation algorithm (MAA), are developed to evaluate the reliability of an MSS. In the DAA, the approximation distribution of the STS is obtained via the Laplace and inverse Laplace transforms, whereas the raw moments of the STS are approximately deduced in the MAA. An illustrative example, along with a set of comparative experimental studies, is given to demonstrate the effectiveness of the proposed algorithms. The results show that both the approximation algorithms are effective in terms of reliability assessment for MSSs operating under a Markovian environment, and the MAA is superior to the DAA.


Keywords multi-state system, Markovian environment, stochastic time scale, reliability evaluation, parameter estimation
    Article #:  RQD27-144

Proceedings of 27th ISSAT International Conference on Reliability & Quality in Design
Virtual Event

August 4-6, 2022