Supply chain management has received considerable attention in the literature and it is meaningful and important to be able to measure the reliability of supply chains. In the article, the suppliers in the supply chain systems are not independent of each other and the dependency relation may be either linear or nonlinear correlation. From the view of the distribution service process, a copula-based method is proposed for analyzing the reliability of supply chains. In this article, by introducing the model of k-out-of-n: G system into the studies of supply chains, an evaluation method is suggested and the reliability indexes are obtained. Finally, a numerical example is presented to illustrate the results obtained in this article.

A model for two-unit series multistate Markov repairable systems with repair time omission is developed based on a model for single-unit multistate Markov repairable systems. In the model, each component has three states: perfect operation, minor failure, and complete failure. Repair time for a complete failure, if it is sufficiently short (no longer than a critical value), does not affect the system operation. The critical value is first supposed to be a constant, and then to be a nonnegative random variable. Some reliability indexes, such as the instantaneous availability, the steady-state availability, and the mean time to first failure, are given. Finally, some numerical examples are presented to illustrate the results obtained in the paper.

The computation of reliability characteristics of a system that consists of dependent components is sometimes difficult especially when the type of dependence is not known. This article introduces the copula method to calculate the reliability of dependent consecutive k-out-of-n: G systems. The components in these systems are dependent on each other and the dependency may be either linear or nonlinear. The copula is a popular tool for modeling the dependence structure of data. It contains the information about the dependency structure of a vector of random variables and can capture nonlinear dependence. Based on the copula theory, the article analyzes the consecutive k-out-of-n: G systems and gets the reliability indexes. Finally, some numerical examples are presented to illustrate the results obtained in this article.