Mathematical Techniques for Computing the Reliability of a Parallel-series System of Order (2,3,1) under Rayleigh Failure Laws

Abstract

Some well-known mathematical techniques have been used to compute the reliability of a parallel-series system of order (2,3,1). The system is composed of four units labelled as A, B, C and D. The configuration involves two parallel subsystems: the first containing units A, B and C arranged in series and the second comprising a single unit D. The failure rate of units is assumed to follow the Rayleigh distribution. With the use of the decomposition method, cut set method and event space method, expressions for both reliability and Mean Time to System Failure (MTSF) have been derived. By considering all units to be identical, the reliability measures have been obtained numerically for specific parameter values. The trends of these measures have been represented graphically to understand the effect of parameters. The study has its practical significance in assessing the reliability of solar panel system. . KEYWORDS :Parallel-series System, Rayleigh failure laws, Decomposition method, Cut set method, Event space method.