4.7 Article

Dynamic reliability modeling for general standby systems

Journal

COMPUTERS & INDUSTRIAL ENGINEERING
Volume 161, Issue -, Pages -

Publisher

PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.cie.2021.107615

Keywords

Exact analysis; K-out-of-N general standby structure; Phase-type distribution; System reliability function; System hazard function; Mean residual life function

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This study presents a general standby system model applicable to various types of standby structures, and uses matrix algebra to derive reliability indicators, which are useful for determining optimal component ordering.
General standby systems with component lifetimes following independent and nonidentical phase-type (PH) distributions are presented in a state-space model using state transition block matrices. The model is constructed by identifying a block matrix representing each system state and a block matrix that causes a transition from one system state to another. This general model is applicable to hot, warm, or cold standby and any combination of them in K-out-of-N general standby structures. The resulting model becomes a PH representation of the system lifetime distribution and is thus useful for exact dynamic system reliability analysis. The advantage is that many functional system reliability measures, such as the reliability, hazard, and mean residual life functions, can be obtained by simple matrix algebra. These functions are shown to be useful for determining optimal component ordering. Comparisons with other methods from previous publications are presented.

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