Cold Standby System Research Articles

Profit analysis of a two-unit similar cold standby system with endurance time and preventive maintenance

Profit analysis of a two-unit similar cold standby system with endurance time and preventive maintenance

A two Identical Unit Cold Standby System with two Repairmen and Correlated Failure and Repair Times

The paper deals with the stochastic analysis of a two identical unit cold standby system model. As soon as a unit fails it is attended first by assistant repairman, who completes its repair to make it as good as new with fixed known probability p. Otherwise, with probability q( =1-p), the unit repaired by assistant repairman goes to expert repairman so as to make it as good as new. Both the repairmen are always available with the system and they work their jobs simultaneously. The failure time and repair time by assistant repairman are correlated random variables having their joint distribution as Bivariate exponential. Various measures of system effectiveness useful to system designers and operation managers are obtained by using regenerative point technique. The MTSF and steady state profit have also been studied through graphs in respect of parameter alpha for three different values of repair rate by expert repairman and two different values of correlation coefficient between failure and repair times and important conclusions are drawn.. KEYWORDS :Bivariate exponential distribution, Mean time to system failure (MTSF), Regenerative point, Laplace transform.

Reliability and Residual Life of Cold Standby Systems

In this study, we conduct a reliability characterisation study of cold standby systems. Utilising synthetic rectangular formulas and cold preparedness equivalent models for cold standby systems, we analyse the lifetimes of several typical configurations, including series, parallel, and k/n:m voting systems. This study proposes system equivalent models for various types of cold standby systems, all composed of components that follow the same exponential distribution. We use the equivalent model to determine the optimal timing for the use of cold spares and derive the reliability function and residual lifetime function for each type of system. To demonstrate the validity of our model, the Monte Carlo simulation is strategically designed based on the system failure rate function. The experimental results are then compared with those obtained from the numerical model, highlighting that the numerical method incurs a lower time cost.

Role of individual component failure in the performance of a 1-out-of-3 cold standby system: A Markov model approach

Abstract The current work assesses the availability and reliability of repairable 1-out-of-3 cold standby systems, undergoing switching failure, by the Markov models, where a finite set of differential equations govern the repairable system. A numerical approach based on KAOS programming in MATLAB is employed to solve the differential equations. Thus, numerical solutions for the time-dependent availability can then be obtained. The Laplace transform method is used for the reliability model to find the explicit form of the reliability function and the mean time to failure (MTTF) of the system. An availability estimation model for a 1-out-of-3 cold standby system is developed and the main electrical power network, local electricity generator, and domestic electricity generator are studied. Finally, the model is analyzed to illustrate the effect of both failures and repair rates as well as component capacity partitioning on system availability and MTTF.

Time-domain computation of the reliability of standby systems with and without priority under general repair

In this paper, we consider a two-unit, non-identical cold standby system under general repair with or without priority. In the prioritized case, one unit in the system is designated to serve as standby only, that is, the standby unit is only utilized when the main unit has failed and is being repaired, whereas in the non-prioritized case, both units serve alternately as standby with each unit being put to standby mode when its repair is complete. The effect of each repair is modelled by a degree θ, 0≤θ≤1, where θ=0 means full repair (or full replacement) and θ=1 means minimal repair. For these cases, and for arbitrary distributions of the lifetimes and repair times of the units in the system, we obtain the reliability function in the time domain as opposed to the Laplace domain. Our functions utilize results from classical and generalized renewal theory results. We validated our formulas on various in-house standby configurations, as well as standby configurations occurring in coolant systems of nuclear power plants.

A subset simulation analysis framework for rapid reliability evaluation of series-parallel cold standby systems

A subset simulation analysis framework for rapid reliability evaluation of series-parallel cold standby systems

Efficient reliability approximation for large k-out-of-n cold standby systems with position-dependent component lifetime distributions

Efficient reliability approximation for large k-out-of-n cold standby systems with position-dependent component lifetime distributions

Cost-Benefit Analysis of a Two-Unit Cold Standby System with Imperfect Repair Man and Abnormal Weather Conditions

Cost-Benefit Analysis of a Two-Unit Cold Standby System with Imperfect Repair Man and Abnormal Weather Conditions

Stochastic Comparisons of Lifetimes of Used Standby Systems

In this paper, we first establish upper stochastic bounds on the lifetime of a used cold standby system with arbitrary age, using the likelihood ratio order and the usual stochastic order. Then, stochastic comparisons are made between the lifetime of a used cold standby system with age t and the lifetime of a cold standby system consisting of used components with age t using the likelihood ratio order and the usual stochastic order. We use illustrative examples to explore the results presented.

Optimal switching and condition-based maintenance of cold standby systems subject to competitive failure and imperfect switchover

Cold standby redundant structures can improve system reliability and availability but are subjected to internal degradation and external shocks during operation. Thus, the switching process in a standby system is prone to failures. This study investigates the optimal switching and condition-based maintenance (CBM) decision of a two-unit cold standby system subject to mutually dependent competitive failure processes with an imperfect switchover. First, periodic switching and offline CBM policies under imperfect switchover are proposed; second, the reliability models of competitive failure—between soft failure caused by system degradation subject to nonfatal shock and hard failure caused by fatal shock—are established. An iterative model of the system state probability distribution is subsequently derived by analysing the characteristics of state transitions in alternate use and maintenance of the active and standby units. An analytical decision model is also established to minimise the average cost rate in a finite horizon to obtain the optimal switching period and maintenance threshold. Finally, a case study of a coal mine main ventilator system validates the proposed model.

Reliability Analysis of Cold-standby Systems with Subsystems Using Conditional Binary Decision Diagrams

<p>Cold-standby systems have been widely used for conditions with limited power, which achieve fault tolerance and high-reliability systems. The cold spare (CSP) gate is a common dynamic gate in the dynamic fault tree (DFT). DFT with CSP gates is typically used to model a cold-standby system for reliability analysis. In general, inputs of the CSP gate are considered to be basic events. However, with the requirement of the current system design, the inputs of the CSP gate may be either basic events or top events of subtrees. Hence, the sequence-dependency among basic events in CSP gates becomes much more complex. However, the early conditional binary decision diagram (CBDD) used for the reliability analysis of spare gates does not consider it well. To address this problem, the conditioning event rep is improved to describe the replacement behavior in CSP gates with subtrees inputs, and the related formulae are derived. Further, a combinatorial method based on the CBDD is demonstrated to evaluate the reliability of cold-standby systems modeled by CSP gates with subtrees inputs. The case study is presented to show the advantage of using our method.</p> <p> </p>

Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand

Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit’s failure rate exceeding a predetermined threshold. The cold standby system’s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ.

A new generalized δ-shock model and its application to 1-out-of-(m+1):G cold standby system

According to the classical δ-shock model, the system failure occurs upon the occurrence of a new shock that arrives in a time length less than δ, a given positive value. In this paper, a new generalized version of the δ-shock model is introduced. Under the proposed model, the system fails if there are m shocks that arrive in a time length less than δ after a previous shock, m≥1. The mean time to failure of the system is approximated for both discretely and continuously distributed intershock time distributions. The usefulness of the model is also shown to study 1-out-of-(m+1):G cold standby system. Illustrative numerical results are presented for geometric, exponential, discrete and continuous phase-type intershock time distributions.

Bayesian Study of a Continuous Parametric Markov Chain Model of a Three Identical Unit Cold Standby System with Random Shocks

Bayesian Study of a Continuous Parametric Markov Chain Model of a Three Identical Unit Cold Standby System with Random Shocks

Reliability analysis of cold-standby systems using a self-stratifying subset simulation method

Cold-standby systems are often featured with small failure probability and widely used as critical safety systems in current engineering fields. The existing analysis methods for cold standby systems have the problems with low-computional efficiency either for small failure probability events or for the components with mixed distribution types. To solve these problems, we propose a self-stratifying subset simulation (4S) method based on MCMC simulation and the performance function of cold-standby system. Numerical case studies are performed to demonstrate the reasonability and feasibility of the proposed 4S method. The case studies indicate that the results obtained by the proposed 4S method agree well with those obtained by the existing methods and the computation efficiency is greatly improved especially for small probability events. Moreover, the proposed 4S method was applicable for the cold-standby system cold-standby system with not only the exponentially or non-exponentially distributed components but components with more mixed distribution types.

Reliability modelling of a parallel-cold standby system with proviso of repair priority

Here, reliability modelling of a parallel cold standby system of four units has been done with the provision of priority to repair. Initially, the system has two operative units in parallel mode (called phase-I units) and the other two units are taken as spare in the cold standby (called phase-II units). The phase-I units (main units) are assumed as more efficient than that of the phase-II units (duplicate units). The units in phase-I and phase-II are non-identical but they are identical within the phases. The units in phase-II work simultaneously at the failure of units of phase-I. The priority to repair the units of phase-II has been given over the repair of the units of the phase-I. However, no priority is given for operation of the units of both phases. The repair activities are handled by a single server who attends the system immediately when required. The failure rate of the units follows negative exponential distribution while the distribution for repair time of the phase-I and phase-II units is assumed as arbitrary. Some significant reliability characteristics such as mean sojourn times (MST), transition probabilities, mean time to system failures (MTSF), availability, expected number of repairs (for both phase-I and phase-II units), busy period of the server, expected number of visits of the server and finally the profit function are obtained in steady state by making use of well-known semi-Markov process (SMP) and regenerative point technique (RPT). The graphical representation of these reliability characteristics has been made for arbitrary values of the rates associated with failure and repair times. The application of the present study can be seen in the power distribution system.

System reliability-redundancy optimization with cold-standby strategy by fitness-distance balance stochastic fractal search algorithm

Reliability-redundancy allocation problem (RRAP) is an interesting subject in the field of reliability engineering that attracted attention of many researchers. RRAP tries to maximize the system reliability while creating a tradeoff between the component reliability and level of redundancy for each subsystem. Early studies in the cold-standby strategy used the lower bound formula to estimate the system reliability. But in this paper, a newly introduced Markovian process-based approach is applied for calculating the exact reliability values of cold-standby systems with the imperfect switching system. A newly developed evolutionary algorithm called fitness-distance balance stochastic fractal search is adjusted for solving the RRAP as an NP-hard optimization model, and the obtained results are compared with other counterparts by using numerical examples on three well-known benchmark problems. Finally, to justify the performance of the applied Markovian method in practical viewpoint, a pump system with non-identical components in a chemical plant is analysed as a real-world case study.

Optimal preventive switching of components in degrading systems

In practice, at many instances, it is important to maintain the failure-free performance of components in a standby system, as each sudden failure of an operating component can result in a failure of a system, e.g., due to imperfect or/and ‘non-instantaneous’ switching on failure and related adverse effects. Therefore, the scheduled preventive switching/replacement to the standby component that can be executed without these consequences is one of the effective methods for increasing reliability characteristics of such systems, especially in the safety-critical applications. In this paper, the corresponding optimal strategy for switching is described and justified for the cold standby system of two aging components with degradation modeled by the counting Poisson and gamma processes. An inspection is carried out at some optimally predetermined time and based on the observed degradation switching is performed after the optimally obtained delay. Detailed numerical examples illustrate our findings.

Mathematical and Simulation Model for Reliability Analysis of a Heterogeneous Redundant Data Transmission System

In the actual study, we carried out a reliability analysis of a repairable redundant data transmission system with the use of the elaborated mathematical and simulation model of a closed heterogeneous cold standby system. The system consists of one repair unit and two different data sources with an exponential cumulative distribution function (CDF) of their uptime and a general independent CDF of their repair time. We consider five special cases of the general independent CDF; including Gamma, Weibull-Gnedenko, Exponential, Lognormal and Pareto. We study the system-level reliability, defined as the steady-state probability (SSP) of failure-free system operation. The proposed analytical methodology made it possible to assess the reliability of the whole system in the event of failure of its components. Specific analytic expressions and asymptotic valuations are obtained for the steady-state probabilities of the system and the SSP of failure-free system operation. A simulation model of the system in cases where it is not workable to obtain expressions for the steady-state probabilities of the system in an explicit analytical form was considered, in particular for constructing the empirical system reliability function. The issue of sensitivity analysis of reliability characteristics of the considered system to the types of repair time distributions was also studied. The simulation modeling was done with the R statistics package.

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.