Title: Mean time to failure modelling and sensitivity analysis of mixed standby serial systems

Authors: Ibrahim Yusuf; Muhammad Sagir Aliyu; Mus'abu Musa

Addresses: Department of Mathematical Sciences, Bayero University, Kano, Nigeria ' Department of Mathematics, Jigawa State College of Education, Gumel, Nigeria ' Department of Mathematics, Faculty of Physical Sciences, Kebbi State University of Science and Technology, Aliero, Kebbi State, Nigeria

Abstract: In this article, we investigate and compare the mean time to failure (MTTF) of series-parallel systems. This paper considers four different configurations with each having exponential failure and repair time. Each configuration consisting of the main, warm and cold standby units. A cold standby unit is included in Configuration 1 together with two warm standby units. Two cold standby units and one warm standby unit make up Configuration 2. In Configuration 3, there are four primary units, two warm standby units, and one cold standby unit. The Configuration 4 consists of six primary units, one warm standby unit, and two cold standby units. First order linear differential difference equations are used to produce a mathematical formula for MTTF for each configuration, which is then verified through analytical and numerical testing. Through the analytical and ranking experiment, Configuration 1 is found to be optimal.

Keywords: mean time to failure; MTTF; mixed standby; redundancy; series-parallel.

DOI: 10.1504/IJMOR.2024.137043

International Journal of Mathematics in Operational Research, 2024 Vol.27 No.2, pp.267 - 289

Received: 16 Nov 2022
Accepted: 07 Jan 2023
Published online: 01 Mar 2024 *

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