Time-Dependent Stress-Strength Reliability Model with Phase-Type Cycle Time Based on Finite Mixture Models

Abstract This paper deals with the estimation of the stress-strength reliability of time-dependent models. Suppose that a system is allowed to run continuously and is subjected to random stress at random time points. Then we can assume a decrease in the strength of the system during the completion of each run. Let the strength of the system decreases by a constant and the stress on the system increases by a constant over each run. Time taken for completion of a run is assumed to have continuous phase-type distribution, the initial strength of the system, as well as, initial stress on the system are assumed to have a finite mixture of either Weibull distributions or power transformed half logistic distributions. A detailed numerical illustration of the results is also carried out.