Dynamic reliability modeling for general standby systems

•Modeling general standby systems with heterogeneous multistate components.•Backup components can be in many levels of warmness from cold to hot.•Applicable to general standby systems with general lifetime distributions.•Numerical closed-form formulas for reliability, hazards, and MRL functions.•Optimal backup ordering based on hazard functions and warmness levels. 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.