Reliability Function of a Complex k-Out-of-n Model

This chapter considers the reliability function of a k-out-of-n model under conditions where the recovery of intermediate failures is either allowed or not. Various scenarios of the dependence of the system failure on the failure of its components are considered. Analytical expressions and algorithms are presented for calculating the reliability function and the mean system lifetime before the first failure. The results are accompanied by numerical examples. Section 2.1 considers the reliability function of a k-out-of-n model up to its first failure without intermediate recovery of the failing components. Section 2.2 deals with the model where the component-wise repair after their failures is allowed. A reliability analysis of a k-out-of-n model in a random environment with account for the increase in the functional load and the location of the failed components is considered in Sect. 2.3. The material of this chapter is based on papers [84, 119, 122, 132, 151].