Reliability properties of k-out-of-n systems with one cold standby unit

In this paper, we study reliability properties of a k-out-of-n system with a single cold standby unit. We mainly focus on the case when the system operates in discrete time. In order to describe its aging behavior we consider three different mean residual life functions. By using some properties of order statistics we present several monotonicity results associated with these reliability characteristics. Since the calculation of the described quantities requires finding sums of infinite series, we provide a procedure to approximate them with an error not greater than a desired value. As an illustration we consider three special cases when the component lifetimes have geometric, negative binomial and discrete Weibull distributions. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study examines the reliability properties of a k-out-of-n system with a single cold standby unit, operating in discrete time. Three different mean residual life functions are considered to describe aging behavior, leading to monotonicity results related to reliability characteristics. A method to approximate quantities requiring sums of infinite series with a specified error is provided for accurate calculation.