Reliability variation of multi-state components with inertial effect of deteriorating output performances

Abstract For the repairable multi-state component (MSC), we introduce a continuous-time Markov process to analyze the availability of the element in this paper. When output performance of the MSC is lower than demand but higher than zero, the component will not fail to work immediately under some circumstances. Based on the concept of inertia in physics, the inertial effect of deteriorating output performances is considered. The influence of inertial effect makes the component operate longer than ever before, resulting in failure delay. To measure the probability influence of inertial effect on availability quantitatively, a critical threshold is set for each deteriorating output state. Both non-negative constants and random variables of the critical thresholds are modeled respectively. Comparing with the original system described with a Markov process, the new situation with inertial effect is recorded as the new system and described with a generic stochastic process. Availability variations of the original system and the new system show the influence of inertial effect on the reliability. A numerical example of a power supply system, which is a typical multi-state system (MSS), is presented to illustrate the results obtained. Relevant studies may be extended in many fields such as queuing theory and quality management.

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