The mean remaining strength evaluation of a multi-state system under a stress-strength model

In this paper, the mean remaining strength (MRS) evaluation of a multi-state component and a multi-state k -out-of- n :G system based on a stress-strength model is studied. The MRS of a component (system) can be defined as the expected remaining strength of a component (system) surviving under random stress until its failure. According to the stress-strength model, any component of the system is affected by two random stresses found in the environment. Therefore, there exists two states for the components of the system. The MRS function of a component is obtained via order statistics for both state “1 or above†and state “2†referring the “partial performance or above†and †excellent performance†states, respectively. The MRS function of a three-state k -out-of- n :G system is also achieved. The MRS values are obtained by assuming Exponential and Weibull distributed strength and stress random variables. Pareto distributed stress and strength effects on the MRS are also discussed under dependency case. All the results are analyzed by considering different parameters, number of components and k values. In addition, all the theoretical results were supported by simulations, some numerical examples and graphical representations.