Reliability optimization for non-repairable series-parallel systems with a choice of redundancy strategies and heterogeneous components: Erlang time-to-failure distribution

Abstract

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

Optimization of Reliability–Redundancy Allocation Problems: A Review of the Evolutionary Algorithms

“…Cold standby redundancy includes failure detection switches and redundant unit activation. When active or coldstandby redundancies can be selectively selected for individual subsystems, researchers prefer to optimize reliability [90][91][92][93][94][95]. Another weakness of the idealization reliability assessment is the certainty approach considering the input parameter values.…”

Optimal reliability allocation of heterogeneous components in pharmaceutical production plant

“…The redundant components can be active [ 7 – 10 ] or standby [ 11 – 14 ] modes and homogeneous [ 3 , 15 ] or heterogeneous [ 16 – 18 ]. It has been proven that the use of heterogeneous redundant components leads to better system reliability than the homogeneous one [ 16 , 17 , 19 ]. Most of the solution approaches proposed to solve the reliability optimization problems (ROPs) were based on nature-inspired optimization algorithms, this kind of algorithms belongs to artificial intelligence (AI), such as ant colony optimization with an adaptive penalty function (ASACO) [ 20 ], genetic algorithms with dynamic adaptive penalty strategy (GAs) [ 21 ], novel modified differential evolution (NMDE) [ 22 ], bidirectional butterfly optimization algorithm (BBOA) [ 15 ], and particle swarm optimization with stochastic perturbation nature (SPPSO) [ 23 ].…”

The Exploration of Wild Horse Optimization in Reliability Redundancy Allocation Problems

“…The optimization of system reliability is an important type of optimization problems, it covers a vital topic in real-life applications such as systems of telecommunication, transformation, space exploration, textile manufacturing, and airport security systems [1]. Many researchers considered the improvement of the reliability for systems or products to compete in business enterprises.…”