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Time-dependent stress-strength reliability models based on phase type distribution. (English) Zbl 1505.62206

Summary: In many of the real-life situations, the strength of a system and stress applied to it changes as time changes. In this paper, we consider time-dependent stress-strength reliability models subjected to random stresses at random cycles of time. Each run of the system causes a change in the strength of the system over time. We obtain the stress-strength reliability of the system at time \(t\) when the initial stress and initial strength of the system follow continuous phase type distribution and the time taken for completing a run, called the cycle time, is a random variable which is assumed to have exponential, gamma or Weibull distribution. Using simulated data sets we have studied the variation in stress-strength reliability at different time points corresponding to different sets of parameters of the model.

MSC:

62-08 Computational methods for problems pertaining to statistics
62N05 Reliability and life testing

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