Time-dependent system reliability under stress-strength setup

In engineering applications, stress-strength models are of special importance. A technical system may be subjected to several stresses such as pressure, temperature and corrosion and the survival of the system heavily depends on its strength. In the simplest terms, stressstrength model can be described as an assessment of the reliability of the component in terms of X and Y random variables where X is the random “stress” experienced by the component and Y is the random “strength” of the component available to overcome the stress. From this simplified explanation, the reliability of the component is the probability that the component is strong enough to overcome the stress applied on it. Extensive works have been done for the reliability of the component and its estimation under different choices for stress and strength distributions [4, 8, 10, 12]. Traditionally, stress and strength random variables are considered to be both static when available data on X and Y are considered not to involve the time of system operation. But in real-life reliability studies, the status of a stress-strength system clearly changes dynamically with time. This problem may be achieved by modeling at least one of the stress or strength quantities as time-dependent [2, 3, 5, 6, 7, 9, 13]. In some cases, the reliabilities of the components in the system depend on the effect of several stresses which cause degradation. Structurally, the reliability of the system depends on the reliability of its components. Thus, degradation in components reliabilities in the system can lead to the degradation of the entire system reliability. In this paper, we aim to propose a new method for computing the timedependent reliability of the system using its time-dependent components reliabilities under stress-strength setup. A method is presented for the case in which the system consists of n independent components whose time-dependent strengths are independent identically distributed random processes and these components are subjected to m common multiple random stresses over time. We also note that the research concerns only non-renewable systems. The rest of this paper is organized as follows. Section 2 gives