Availability analysis of a generalized maintainable three‐state device parallel system with human error and common‐cause failures

Abstract

Purpose -The purpose of this paper is to study the combined effect of human error, common-cause failure, redundancy, and maintenance policies on the performance of a system composed of three-state devices. Design/methodology/approach -Generalized expressions for time-dependent and steady state availability of a generalized maintainable three-state device parallel system subjected to human errors and common-cause failures are developed in the paper under two maintenance policies: Type I repair policy (i.e. only the completely failed system is repaired); and Type II repair policy (i.e. both partially and completely failed system is repaired). The Markov method is used to develop general and special case expressions for state probabilities, and system time-dependent and steady state availabilities. Findings -In the case of three-state devices, it is demonstrated that by increasing the number of redundant devices in parallel do not necessarily lead to the improvement in the system availability. In fact, the availability of the system depends significantly on the dominant failure mode of the devices (i.e. short-mode or open-mode). When comparing the effect of maintenance policies on the system availability, it is observed that the Type II repair policy does not lead to an improvement in the system availability. Furthermore, it is observed that both human error and common-cause failure independently lead to lower system availability.Practical implications -This study will help maintenance engineers and reliability practitioners to become aware of the combined impact of redundancy, human error, common-cause failure, and maintenance policies on the performance of the three-state device systems. Consequently, they will make better maintenance related decisions in organizations such as oil refineries and power stations that use three state devices quite extensively. Originality/value -Most of the past models have independently studied the effects of redundancy, human error, and common-cause failure on maintainable system made up of three-state devices. This effort is one of the first attempts to study the combined effects of all these factors in a parallel system composed of three state devices.

A new reliability analysis method for software‐intensive systems with degradation accumulation effect based on goal oriented methodology

“…The list of operation rules for type 28 operator (4) Let the probability of the system being in state 𝑖 at time 𝑡 is 𝑃 (𝑖) (𝑡) = 𝑃{𝑋(𝑡) = 𝑖}, 𝑖 = 0, 1, 2. Based on Markov theory, 43 the instantaneous state probabilities of the component can be obtained by solving the differential equations Equation (1).…”

“…$$$$\begin{equation*}A = \left[ { \def\eqcellsep{&}\begin{array}{@{}*{3}{c}@{}} { - {\lambda _1} - {\lambda _3}}&\quad {{\lambda _1}}&\quad {{\lambda _3}}\\[5pt] {{\mu _1}}&\quad { - {\lambda _2} - {\mu _1}}&\quad {{\lambda _2}}\\[5pt] {{\mu _2}}&\quad 0&\quad { - {\mu _2}} \end{array} } \right]\end{equation*}$$$$(4) Let the probability of the system being in state i at time t is $${P_{( i )}}(t) = P\{ {X(t) = i} \},i = 0,1,2$$. Based on Markov theory, 43 the instantaneous state probabilities of the component can be obtained by solving the differential equations Equation (). …”

Reliability technology using GO methodology: A review

“…Yi et al 105 deduced the CCF probability formulas of a two-unit parallel structure considering maintenance correlation based on Markov theory. Dhillon et al [106][107][108][109] studied the related problem for various configurations, considering the CCF and human errors. The latter studies can be applied to the GO method.…”