Cold Standby Components Research Articles

A novel evolutionary strategy optimization algorithm for reliability redundancy allocation problem with heterogeneous components

The reliability-redundancy allocation problem (RRAP) is an optimization problem that maximizes system reliability under some constraints. In most studies on the RRAP, either active redundant components or cold standby components are used in a subsystem. This paper presents a new model for the RRAP of a system with a mixed redundancy strategy, in which all components can be heterogeneous. This formulation leads to a more precise solution for the problem; however, RRAP is an np-hard problem, and the new mixed heterogeneous model will be more complicated to solve. After formulating the issue, a novel design of an evolutionary strategy optimization algorithm is proposed to solve that. The problem consists of discrete and continuous variables, and different mutation strategies are designed for each. The new formulation of the problem and the new method for solving it lead to better results than those reported in other recent papers. We implement the new suggested heterogeneous model with the PSO and SPSO algorithms to better compare the proposed algorithm. Results show improvement in both system reliability and fitness evaluation count.

A study on utilization of two cold standby components to increase reliability of a coherent system

. This article focuses on a specific type of coherent system in which, when the coherent system fails, either no active component remains or the remaining active components are connected in parallel. Roy and Gupta (2023) also considered the same type of coherent systems. We observe the restart of such a coherent system using two cold standby components. In our study, standbys are not placed into action simultaneously. They are put into action one by one. We compute the reliability function of the considered coherent system, which is equipped with two cold standby components. In addition, we show that when we use a stronger standby component (in the sense of failure rate order) at first, we get a longer system lifetime. Also, we compute three different mean residual life functions of the system. We have presented a few numerical results to illustrate the importance of our analysis.

A study on utilization of a cold standby component to enhance the mean residual life function of a coherent system

In this article, we consider a particular type of coherent systems, in which, when the coherent system fails, either no active component remains or the remaining active components are connected in parallel. This work studies two coherent systems of such type with two components, four coherent systems with three components, and seven coherent systems with four components as examples. Lifetime as well as system signature of each of these coherent systems is given. We investigate the restart of such a coherent system using a single cold standby component. The reliability of a system is studied through the (reliability) characteristics such as reliability function, mean time to failure, mean residual life functions of the system. We compute signature-based exact expression for the reliability function of the considered coherent system, which is equipped with a cold standby component. Also, we obtain three different mean residual life functions of the system. So far, no attempt has been made to study such coherent systems in cold standby sparing; therefore, we have provided some new results. We illustrate the theoretical results by considering three particular coherent systems as examples.

Analyzing the Impact of Repairable 1-out-of-3 Cold Standby Components on System Availability: A Capacity Analysis

Analyzing the Impact of Repairable 1-out-of-3 Cold Standby Components on System Availability: A Capacity Analysis

A hybrid Markov model–PSO algorithm for the exact solution of reliability optimization problems with cold standby components

A hybrid Markov model–PSO algorithm for the exact solution of reliability optimization problems with cold standby components

Research and Application of System Reliability Allocation based on Markov Chain

In order to maximize the reliability of a weapon system, a continuous time Markov method is used to allocate the system reliability redundancy. The choice of reliability redundancy strategy is considered as a decision variable, which strives to maximize the reliability of the system under the constraints of cost, weight and volume. In many model applications studied in the past, each system generally adopts a single active redundancy strategy or cold standby redundancy strategy. In the model cited in this paper, each subsystem can adopt the selective redundancy strategy of active or cold standby components, increasing the flexibility of the redundancy strategy, and establishing the precise reliability function for the system using the selective redundancy strategy through the continuous time Markov chain. Because reliability redundancy assignment is a nonlinear mixed integer programming problem, a pseudo-parallel genetic algorithm is designed to solve the model. Finally, the results show that the reliability of the weapon system is significantly improved.

Reliability analysis of heat exchanging system of deep-sea manned submersibles using Markov model

This study introduces reliability assessment models for heat exchanging systems in deep-sea manned submersibles based on the Markov analysis method. Three distinct design systems—a series solution and two series–parallel solutions, considering cold and hot standby components—were presented. In addition, the state transition models of the Markov random process were established with relation to common-cause failures. Moreover, the calculation methods were derived for the two reliability indices of the heat exchange system: steady state availability and mean time to failure. Thus, the reliability of various design solution cases was investigated by comparing the reliability indices with variations in the failure and repair rates. The influence of common-cause factors on the system reliability was discussed as well. Furthermore, design solutions were suggested based on the results of the quantitative calculations and analysis.

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

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.

Reliability and availability analysis of a retrial system with mixed standbys and an unreliable repair facility

We study a K-out-of-M+W+C: G mixed standby system with an unreliable repair facility, in which there are M primary operating components, W warm standby components and C cold standby components. The life times of primary components and warm components are assumed to be exponentially distributed random variables. The repair facility is performed preventive maintenance (PM) when it is idle, and it is subject to breakdowns when it repairs a failed component (called as active breakdowns). Upon arrival, a failed component is repaired immediately if the repair facility is found free, and the failed component enters a retrial orbit for seeking repair service after some time later if the repair facility is found busy, under PM, or under repair. By adopting a Markov process approach and solving equations of statistical equilibrium in matrix form, we obtain the system steady-state availability of the machine system, the steady-state availability and the expected busy cycle of the repair facility. Furthermore, we obtain the reliability function and the mean time to the failure (MTTF) of the system by using Laplace transform method. Numerical examples are presented to show the effects of system parameters on the reliability function, steady-state availability and MTTF and to analyze the optimization problem of the cost-effectiveness ratio.

Redundancy allocation of mixed warm and cold standby components in repairable K-out-of-N systems

In system design process, standby redundancy is a widely used technique to improve system reliability and availability. Typical standby techniques involve cold standby, hot standby, and warm standby. In this article, we investigate the repairable K-out-of- N system with mixed standby strategy containing both warm and cold standby. In the proposed system, each component can be in failure, cold, warm, and active states and the components are assumed to be repairable. The systems are modeled by continuous time Markov chain and the system long-run availability is derived. Furthermore, the optimal configuration of standby components in the system is studied considering both system availability and system running cost. Illustrative examples are presented to show the applications of the proposed model.

Reliability function of k-out-of-n system equipped with two cold standby components

In this article, we focus on reliability properties of a k-out-of-n system equipped with two cold standby components. We describe the lifetime of the system and compute the reliability function of the system, which will allow us to investigate the risk of system failure. Further, three different mean residual life functions of the system are derived. We also provide some stochastic ordering results. The theoretical results established in this article addresses a problem proposed by Eryilmaz and Wang. We have presented a few numerical results to illustrate the importance of our analysis.

Redundancy allocation problem of phased-mission system with non-exponential components and mixed redundancy strategy

The redundancy allocation problem (RAP) has been widely studied, which aims to identify the optimal design to achieve the best system indicators, such as system reliability or availability, under certain constraints. This problem has been studied well in the single phased mission systems. But many practical systems, like the manmade satellites or spacecraft, perform a series of tasks in multiple, consecutive, non-overlapping time durations (phases). For these multi-phased systems, dependencies among the phases need to be fully considered. To address this problem, the RAP of the phased mission systems (PMSs) is studied in this paper. Moreover, in order to improve system reliability as much as possible, the mixed redundancy strategy where both active and cold standby components can be simultaneously used in a subsystem is applied. The non-exponential components, which are more practical, are also considered. The Semi-Markov process (SMP) as well as a numerical approximation method are used to deal with the dynamic non-exponential components. Then, an improved Genetic algorithm (GA) is used to determine the types and quantities of active and cold-standby components in each subsystem to optimize the whole system. At last, the propulsion system in a spacecraft is optimized to illustrate the proposed method.

Reliability of a coherent system equipped with two cold standby components

In this paper, we focus on a particular type of coherent system which may fail either on the failure of its first component or on the failure of its second component. We investigate the renewal of such a coherent system using two cold standby components. We obtain the reliability function of the considered coherent system which is equipped with two cold standby components. We study the problem to optimize the reliability of the system. Some stochastic ordering results are also presented. Examples are provided to illustrate the theoretical results presented in this study. Our results subsume some of the earlier results in the literature.

An improved particle swarm optimization algorithm for reliability-redundancy allocation problem with mixed redundancy strategy and heterogeneous components

The reliability–redundancy allocation problem (RRAP) has been intensively studied to identify the optimal system design under several constraints, so as to maximize the system reliability as much as possible. Recently, the mixed redundancy strategy where both active redundant components and cold standby components can be simultaneously used by a subsystem has been introduced into the RRAP, leading to a more superior result than that of a subsystem with either active redundancy strategy or cold standby strategy. Nevertheless, in the existing studies, all the components deployed in a subsystem have to be homogeneous even if the mixed redundancy strategy is chosen. The strong premise is released in this paper by introducing heterogeneous components into the RRAP. The resulting optimization problem is resolved by proposing an improved particle swarm optimization (PSO) algorithm with stochastic perturbation nature. The efficiency of the proposed algorithm has been demonstrated by conducting a set of comparative studies on three benchmark problems. As observed in our study, the design flexibility introduced by our method can always yield a greater system reliability than that of the state-of-the-art methods. Most importantly, we also reveal that the switching reliability has significant influence on the optimal system configuration.

Redundancy optimization of cold-standby systems under periodic inspection and maintenance

In this paper, a redundancy allocation problem for cold-standby systems with degrading components is studied. We consider performing a policy of periodic inspection and preventive maintenance on the cold-standby components. Components in cold-standby mode are assumed to suffer from performance degradation when exposed in extreme standby environments for a long-term storage. Except the online working components, other cold-standby components are periodically inspected and preventively maintained to retain them in or restore them to an acceptable condition. The situation, that the cold-standby components are restored like new but their failure rates increase, is considered. In this paper, we develop a model to determine an optimal combination of the component choices, the number of redundant components, and the length of periodic inspection interval, so as to maximize the system reliability while meeting the resource limits, such as cost and weight. As it is difficult to obtain a closed-form expression of the objective function for the optimization problem, an approximated objective function is proposed. The approximation is also used for evaluating the expected cost of periodic inspection and maintenance. We then develop a modified genetic algorithm to solve the optimization problem. Finally, a numerical example is presented to illustrate the effectiveness of the proposed model and the solution methodology.

Reliability analysis of a cold-standby system considering the development stages and accumulations of failure mechanisms

In this paper we classify failure mechanisms (FMs) into three types based on the triggering loads, including environmental load-triggered (E-type), operating load-triggered (O-type), and combined load-triggered (C-type) FMs. In a cold-standby component, E-type FMs develop when the component does not operate and may develop with different speeds due to changes in the environmental conditions at different stages. O-type FMs are triggered by operational loads. Environmental loads and operating loads are necessary for triggering C-type FMs. Previous studies have often assumed that cold-standby components are not subject to failures or degradation in the standby stage. However, E-type FMs can develop in cold-standby components at the standby stage and contribute to the degradation of the components. In this paper, we propose a hierarchical method based on the sequential binary decision diagram (SBDD) to analyze the reliability of a non-repairable cold-standby system while considering the correlation and development of FMs. In the case study, a reliability analysis is conducted for an example power supply subsystem equipped with an electronic control device, which comprises one primary unit and one cold-standby unit. The results show that the reliability of the cold-standby system is quite different when considering the development of E-type FMs in the cold-standby unit. In addition, the lifetime of the system will decrease when E-type FMs are considered in the simulation.

On Reliability Analysis of <inline-formula> <tex-math notation="LaTeX">$k$</tex-math> </inline-formula> -Out-of-<inline-formula> <tex-math notation="LaTeX">$n$</tex-math> </inline-formula>:<inline-formula> <tex-math notation="LaTeX">$F$</tex-math> </inline-formula> Systems Equipped With a Single Cold Standby Component Under Degradation Performance

A $k$ -out-of- $n$ : $F$ system is considered, and its reliability is studied under degradation performance. The effect of the presence of a cold standby component is investigated on likelihood and reliability functions. A Gamma process is assumed for degradation of active and standby components, and the effect of varying the shape and scale parameters is studied on system reliability. The maximum likelihood estimator and also the asymptotic confidence interval for reliability of the system are investigated. Finally, the results are illustrated via a real degradation dataset.

Coherent system with standby components

A coherent system that consists of n independent components and equipped with r cold standby components is considered. A generalized mixture representation for the survival function of such a system is obtained, and it is used to examine reliability properties of the system. In particular, the effect of adding r standby components to a given set of original components is measured by computing mean time to failure of the system. The limiting behavior of the failure rate of the system is also examined using the mixture representation. The results are illustrated for a bridge system. A case study that is concerned with an oil pipeline system is also presented.

Estimation of stress-strength reliability of a parallel system with active, warm and cold standby components

In this paper we estimate the stress–strength reliability of a parallel system with l active components, s warm standby components, and k cold standby components. We assume perfect switching among the components from warm standby mode to active mode and from cold standby mode to warm standby mode. A reduced stress for the warm standby components is introduced and the components may fail in the warm standby mode. The reliability of the parallel system is evaluated by assuming the stress and strength of the components to be independent random variables. We derive the expression of reliability of the system by assuming both the stress and strength of the components having Exponential, Weibull, and Lomax distributions, respectively. The method of maximum likelihood estimation is used to obtain the reliability estimators. Illustrations are provided through an example using MATLAB programming.

Reliability of weighted k-out-of-n: G systems consisting of two types of components and a cold standby component

ABSTRACTIn this article, the influence of a cold standby component to the reliability of weighted k-out-of-n: G systems consisting of two different types of components is studied. Weighted k-out-of-n: G systems are generalization of k-out-of-n systems that has attracted substantial interest in reliability theory because of their various applications in engineering. A method based on residual lifetimes of mixed components is presented for computing reliability of weighted k-out-of-n: G systems with two types of components and a cold standby component. Reliability and mean time to failure of different structured systems have been computed. Moreover, obtained results are used for defining optimal system configurations that can minimize the overall system costs.