Time-Dependent Stress-Strength Reliability Models with Phase-Type Cycle Times

Abstract The estimation of stress-strength reliability in a time-dependent context deals with either the stress or strength or both dynamic. The repeated occurrence of stress in random intervals of time induces a change in the distribution of strength over time. In this paper, we study the stress-strength reliability of a system whose strength reduces by a constant over each run and the stress is considered as either fixed over time or as increasing by a constant over each run. The number of runs in any interval of time is assumed to be random. The stress-strength reliability of the system is obtained, assuming continuous phase-type distribution for the duration of time taken for completion of each run in any interval of time and Weibull or gamma distribution for initial stress and strength. We obtain matrix-based expressions for the stress-strength reliability and numerical illustrations are also discussed.