Analysis of series–parallel system’s sensitivity in context of components failures

¹ Department of Mathematics, Graphic Era Deemed to be University, Dehradun, India
² Department of Mathematics, Computer Science and Engineering, Graphic Era Deemed to be University, Dehradun, India
³ Department of Mathematics, Graphic Era Hill University, Dehradun, India

^* Corresponding author: nupurgoyal.math@geu.ac.in

Received: 24 August 2022
Accepted: 18 May 2023

Abstract

This research examines the reliability characteristics of a broad series–parallel system. Complex system, having elements in series and parallel configuration is considered here to compute the reliability. Due to the failure of component, the system can either breakdown or can work with reduced frequency. To analyze the effect of component failure, sensitivity of the system with respect to reliability parameters is analyzed. In this study, generally distributed and exponentially distributed repair rates are taken into consideration from failed state to the working state of the system. The mathematical model of the designed structure is developed using Markov process and supplementary variable technique. The comparative study of the system availability and its sensitivity with respect to general distribution and general as well as exponential distribution has been examined. The Gumbel–Hougaard family of copula is used to analyze the effect of both the distributions together. For a better explanation of this work, a numerical example has been provided and shown the results graphically.