New approach to evaluate the failure probability of a k-out-of-n system under harmful shocks

Abstract

This paper introduces a novel approach to calculating the failure probability of k-out-of-n systems under harmful shocks, which occur randomly and affect at least one component. Traditional methods for this calculation face challenges such as high computational costs and complexity, especially for large systems. The new approach simplifies the computation by developing an easily executable algorithm, saving time and resources. The proposed formula has been shown to be equivalent to existing ones. Additionally, it has been demonstrated that the failure probability under certain conditions follows a binomial distribution, with system design influencing the failure probability for each shock.