An improved methodology for evaluating availability of multistate series–parallel systems using the polynomial distribution function

Purpose: This paper employs new methods to evaluate the availability of multistate series–parallel systems, in which a number of similar components are available in each subsystem. Design/methodology/approach: In this paper, polynomial distribution function (PDF) is combined with universal generating function (UGF) and recursive algorithm (RA) methods to evaluate the availability of multistate series–parallel systems. To achieve this goal, the PDF is initially used to determine the performance rates and the probabilities corresponding to the performance states of the similar components in a subsystem. The obtained results are used to evaluate the system availability via the UGF and RA methods. Findings: It is shown that the combined UGF and PDF (UGF-PDF) and also the combined RA and PDF (RA-PDF) methods require less computational time than did the UGF and RA methods, respectively. Originality/value: In the UGF and RA methods, there is no difference in system availability evaluation time when considering similar or different components in each subsystem. But the proposed methods in this article do not have this restrictions; therefore, these methods can be used to evaluate system availability in optimal redundancy allocation problems. As a result, using these methods reduces the optimization time of those problems.