Reliability of the two-unit priority standby system revisited

This paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system’s lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential distributions.

Solving Cold-Standby Reliability-Redundancy Allocation Problems with Particle-Based Simplified Swarm Optimization

Particle swarm optimization (PSO) and simplified swarm optimization (SSO) are two of the state-of-the-art swarm intelligence technique that is widely utilized for optimization purposes. This paper describes a particle-based simplified swarm optimization (PSSO) procedure which combines the update mechanisms (UMs) of PSO and SSO to determine optimal system reliability for reliability-redundancy allocation problems (RRAPs) with cold-standby strategy while aimed at maximizing the system reliability. With comprehensive experimental test on the typical and famous four benchmarks of RRAP, PSSO is compared with other recently introduced algorithms in four different widely used systems, i.e., a series system, a series-parallel system, a complex (bridge) system, and an overspeed protection system for a gas turbine. Finally, the results of the experiments demonstrate that the PSSO can effectively solve the system of RRAP with cold-standby strategy and has good performance in the system reliability obtained although the best system reliability is not obtained in all four benchmarks.

The Optimal System for Complex Series-Parallel Systems with Cold Standby Units: A Comparative Analysis Approach

The purpose of this research is to propose three reliability models (configurations) with standby units and to study the optimum configuration between configurations analytically and numerically. The chapter considered the need for 60 MW generators in three different configurations. Configuration 1 has four 15 MW primary units, two 15 MW cold standby units and one 30 MW cold standby unit; Configuration 2 has three 20 MW primary units, three 20 cold standby units; Configuration 3 has two 30 MW primary units and three 30 MW cold standby units. Some reliability features of series–parallel systems under minor and complete failure were studied and contrasted by the current. Failure and repair time of all units is assumed to be exponentially distributed. Explanatory expressions for system characteristics such as system availability, mean time to failure (MTTF), profit function and cost benefits for all configurations have been obtained and validated by performing numerical experiments. Analysis of the effect of different system parameters on the function of profit and availability has been carried out. Analytical comparisons presented in terms of availability, mean time to failure, profit function and cost benefits have shown that configuration 3 is the optimal configuration. This is supported by numerical examples in contrast to some studies where the optimal configuration of the system is not uniform as it depends on some system parameters. Graphs and sensitivity analysis presented reveal the analytical results and accomplish that Configuration 3 is the optimal in terms of design, reliability physiognomies such as availability of the system, mean time to failure, profit and cost benefit. The study is beneficial to engineers, system designers, reliability personnel, maintenance managers, etc.

Stochastic Analysis of a Priority Standby System under Preventive Maintenance

In this paper, we propose a system of two dissimilar units: one unit prioritizes operation (priority unit), and the other unit is kept as a cold standby (ordinary unit). In this system, we assume that the failures, repairs, and preventive maintenance (PM) times follow arbitrary distributions for both units, except for the fact that the repair time of the ordinary unit follows an exponential distribution. The priority unit has normal, partial failure or total failure modes, while the ordinary unit has normal or total failure modes. The PM of the system can be started after time t when (i) the priority unit is in the normal or partial failure modes up to time t and (ii) the standby unit is available up to time t. PM can be achieved in two types: the costlier type with probability p and the cheaper type with probability (1−p). Under these assumptions, we investigate the reliability measures of the system using the regenerative point technique. Finally, we show a numerical example to illustrate the theoretical findings and show the effect of preventive maintenance in the reliability measures of the proposed system.