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.

中文翻译：

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基于相类型分布的时变应力强度可靠性模型

在许多现实生活中，系统的强度和所施加的压力会随着时间的变化而变化。在本文中，我们考虑随时间变化的应力-强度可靠性模型，这些模型在随机的时间周期内受到随机的应力。系统的每次运行都会导致系统强度随时间变化。当系统的初始应力和初始强度遵循连续相类型分布并且完成运行所花费的时间（称为循环时间）是一个随机变量时，我们可以在时间t获得系统的应力-强度可靠性。具有指数分布，伽玛分布或威布尔分布。使用模拟数据集，我们研究了对应于模型参数集的不同时间点的应力-强度可靠性的变化。