Reliability Analysis of Some Consecutive-k-out-of-n Systems in a Stress-Strength Setup

Abstract

The aim of this thesis is to study the reliability of some linear consecutive k-out-of-n: F systems, with a stress-strength setup. Explicit expressions for the reliability of regular and relayed linear consecutive k-out-of-n: F systems, with one change point are obtained for any value of k, 1≤k≤n, by conditioning on the state of the component at the change point, working or failed. A change point in a system means that the reliabilities of the components before and at this point differ from those after it. The case of having more than one change point is also discussed, and explicit expressions of the reliability are obtained for regular and relayed linear consecutive k-out-of-n: F systems, when 2k≥n, by using the longest zeros’ run statistic. The components of the system are assumed to be independent. The change in reliabilities of the components may be due to change in the stress imposed on the components, change in the strength of the components, or change in both the stress and the strength. These three possibilities are studied, when there is one change point or when there are more than one change point. Formulas of the stress-strength reliabilities are derived generally for any continuous distributions for the stress and the strength. As application two cases are discussed: Case I, when the stress and the strength have distributions with the same exponential form, and Case II, when the stress and the strength have different distributions forms. In Case I explicit expressions for the stress-strength reliability of regular and relayed linear consecutive k-out-of-n: F systems are obtained under the three possibilities of a change point (one, or more). For Case II, as illustration the stress is assumed to have negative exponential distribution, while the strength is assumed