The study of stress-strength reliability in a time-dependent context needs to model at least one of the stress or strength quantities as dynamic. We study the stress-strength reliability for the case in which the strength of the system is decreasing in time and the stress remains fixed over time; that is, the strength of the system is modeled as a stochastic process and the stress is considered to be a usual random variable. We present stochastic ordering results among the lifetimes of the systems which have the same strength but are subjected to different stresses. Multicomponent form of the aforementioned stress-strength interference is also considered. We illustrate the results for the special case when the strength is modeled by a Weibull process. 1. Introduction Stress-strength models are of special importance in reliability literature and engineering applications. A technical system or unit may be subjected to randomly occurring environmental stresses such as pressure, temperature, and humidity and the survival of the system heavily depends on its resistance. In the simplest form of the stress-strength model, a failure occurs when the strength (or resistance) of the unit drops below the stress. In this case the reliability is defined as the probability that the unit’s strength is greater than the stress, that is, , where is the random strength of the unit and is the random stress placed on it. This reliability has been widely studied under various distributional assumptions on and . (See, e.g., Johnson [1] and Kotz et al. [2] for an extensive and lucid review of the topic.) In the aforementioned simplest form, stress and strength quantities are considered to be both static. Dynamic modeling of stress-strength interference might offer more realistic applications to real-life reliability studies than static modeling and it enables us to investigate the time-dependent (dynamic) reliability properties of the system. Let and denote the stress that the system is experiencing and strength of the system at time , respectively. Then the lifetime of the system is represented as The most important characteristic in reliability analysis is the reliability function of a system which is defined as the probability of surviving at time , that is, This function is also known as the survival function in the reliability literature and its exact formulation is of special importance in engineering applications. The reliability function for the lifetime random variable given in (1) is The function given by (3) has been investigated in several papers. Whitmore [3]
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