Stress-strength reliability analysis of multi-state system based on generalized survival signature

The stress-strength model has been widely used in reliability design of system. In the traditional stress-strength reliability theory, the system and each component are assumed to be only in one of two possible states being either working or failed, and the notion of stress-strength reliability is the probability that the strength is larger than the stress. In this paper, we study the stress-strength reliability of multi-state system based on generalized survival signature. It is supposed that the state of multi-state system is defined by using the ratio between strength and stress random variables. The definitions of generalized survival signature for a certain class of multi state systems with multi-state components in both discrete and continuous cases are given. In addition, the expressions of stress-strength reliability in both discrete and continuous situations are derived. In the case of continuous multi-state system, it is assumed that the random strength and stress are both from the Weibull distributions with different scale parameters, and the two different continuous kernel functions are Pareto and generalized half logistic distribution functions, respectively. Based on the assumptions, the stress-strength reliability is estimated by using both classical and Bayesian statistical theories. The uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress-strength reliability of the continuous multi-state system are derived. Under the squared error loss function, the exact expression of Bayes estimator for the stress-strength reliability of the continuous multi-state system is developed by using Gauss hypergeometric function. Finally, the Monte Carlo simulations are performed to compare the performances of the proposed stress-strength reliability estimators, and a real data set is also analyzed for an illustration of the findings.