Stochastic behaviour of a two-unit standby system with contact failure and intermittently available repair facility

A two-unit standby redundant system with exponential failure-time distribution is considered. It is assumed that system must keep good contact with other systems otherwise its operation is just futile. Contact ceases at an exponential rate. A switch is used to switch in standby unit to operate and it is successful with a known probability. Repair facility is available at the time of failure of a unit with a known probability. If it is available, repair starts, otherwise the unit waits for repair. Repair facility can be made available by paying extra cost. Times to restore contact and time for which repair facility is preoccupied are also general.

The system is analysed by studying the underlying semi-Markov process and a large number of system parameters are obtained viz. MTSF, steady-state availability, expected number of visits to a state, absorption probabilities. Some of the parameters have been studied for their behaviour. In the sequence Howard's reward structure has been superimposed on the above semi-Markov process to obtain expected profit. Discounting is also mentioned at the end. Two optimization problems are posed treating mean-time to repair, mean time to preoccupation, etc., as decision variables and expected profit as the criterion. Several earlier models are included as special cases.     

Optimization of predetermined standby mode transfers in 1-out-of-N: G systems

Warm standby redundancy is an important fault-tolerant design technique for improving the reliability of many systems used in life-critical or mission-critical applications. Traditional warm standby models aim to reduce the operational cost and failure rate of the standby elements by keeping them partially powered and partially exposed to operational stresses. However, depending on the level of readiness of a standby element, significant restoration delays and replacement costs can be incurred when the standby element is needed to replace the failed online element. To achieve a balance between the operation cost of standby elements and the replacement costs, this paper proposes a new warm standby model with scheduled (or time-based) standby mode transfer of standby elements. In particular, each standby element can be transferred from warm standby mode to hot standby mode (a mode in which the standby element is ready to take over at any time) at a fixed/predetermined time instants after the mission starts. To facilitate the optimal design and implementation of the proposed model, this paper first suggests a new algorithm for evaluating the reliability and expected mission cost of 1-out-of-N: G system with standby elements subject to the time-based standby mode transfer. The algorithm is based on a discrete approximation of time-to-failure distributions of the elements and can work with any type of distributions. Based on the suggested algorithm the problem of optimizing transfer times of standby elements to the hot standby mode and optimal sequencing of their transfer to the operation mode is formulated and solved. In this problem the expected mission cost associated with elements’ standby and operation expenses and mode transfer expenses is minimized subject to system reliability constraint. Illustrative examples are provided.     

Warm standby in hierarchically structured process-control programs

We classify standby redundancy design space in process-control programs into the following three categories: cold standby, warm standby, and hot standby. Design parameters of warm standby are identified and the reliability of a system using warm standby is evaluated and compared with that of hot standby. Our analysis indicates that the warm standby scheme is particularly suitable for long-lived unmaintainable systems, especially those operating in harsh environments where burst hardware failures are possible. The feasibility of warm standby is demonstrated with a simulated chemical batch reactor system     

Two unit cold standby system with correlated failures and repairs

A two unit cold standby system with correlated failure and repair processes is studied. Such a system has not been studied so far in the context of reliability. We obtain the reliability characteristics of interest to system designers such as the mean time to system failure, pointwise and steady state availablity of the system, expected up time and down time of the system in a finite interval, etc. In fact the joint distribution of failure and repair times is taken as bivariate exponential. Earlier results with independent failure and repair times are verified.     

相依多模失效下冷贮备系统最优切换及视情维护决策

针对存在冲击影响的冷贮备系统,研究其最优切换及视情维护决策问题.首先,在系统结构和切换式运行和维护特性分析的基础上,制定基于周期切换和状态检测的切换式离线视情维护策略;其次,建立累积冲击过程影响下系统退化所致的软失效和极端冲击过程所致的硬失效竞争可靠性模型;再次,通过分析两类冲击过程影响下系统运行与备用设备交替使用、维修过程中的状态转移特性,重点推导各检测周期时刻系统状态概率分布的迭代计算模型;然后,以系统平均费用率最小为目标,建立解析决策模型,以求解系统的最优切换周期和维护阈值.最后,以矿井主通风系统为案例验证策略及模型的有效性,并分析模型对参数的灵敏度.结果表明,系统的最优维修策略随机冲击影响的不同而变化显著.     

Comparative analysis for the M/Kk/1 machine repair problem with spares

This paper deals with the M/E_k/1 machine repair problem with spares under steady-state conditions. Spares are considered to be either cold standby, warm standby, or hot standby. We present exact formulas for the probability mass functions of the number of failed machines in the system. Approximate formulas for the probability density function of the number of failed machines in the system are obtained through diffusion approximation. A study of the derived exact results, compared to the approximate results, shows that the diffusion approximation approach is sufficiently accurate for practical use.     

Replacement and standby redundancy policies in a deteriorating system with aging and random shocks

This study investigates the state-dependent maintenance policy in a multistate deteriorating production system with standby redundancy, assuming that the production system consists of one production unit and one single-server service center, and the key component of the production unit deteriorates over time. The key component deteriorates either from the current operating state to the next inferior operating state, due to aging, or from the current operating state to the failure state, due to a random shock. The deteriorating key component is replaced with a standby, according to a certain replacement policy, and sent to the service center for perfect repair; once completing the service, it joins the standbys for later production use. Both the sojourn time of a key component in each operating state, except the failure state, and the service time of a key component at the service center are assumed to be exponentially distributed. Taking into account the annual operating profit, measured in terms of production utilization and yield percentage of perfect items, and the annual operating costs, including the costs of key components and maintenance, this study jointly selects the operating state for replacing deteriorating key components and the level of standby redundancy in the system under the profit maximization objective. Numerical examples are given to illustrate the maintenance policies for systems with different transition probabilities in the deteriorating process, and the influence of transition probabilities on the maintenance policies are discussed.     

冷/温混合贮备系统最优切换及视情维修决策

针对周期性切换冷/温混合贮备系统,研究其最优切换以及视情维修决策,在系统劣化建模的基础上,分析系统结构和切换式运行维修特性,制定基于周期切换和检测的离线视情维修策略.首先,通过分析系统运行与备用设备交替使用、维修过程中的状态转移特性,推导各检测周期时刻系统状态概率分布模型以及各维修活动的概率;然后,以系统有限时间范围内平均费用率最小为目标建立解析优化模型,以决策最优切换周期和维护阈值,并采用遗传算法对模型进行求解;最后,以汽轮发电机定子冷却水泵系统为对象验证策略和模型的正确性和有效性,并对参数进行灵敏度分析.实验结果表明,所提出离线视情维修策略能够有效地降低系统的维修成本.     

考虑多维修台异步多重休假的温贮备冗余系统可靠性模型

考虑多维修台保障多个系统时维修力量存在调度与分配的情况,引入多维修台异步多重休假策略;以温贮备冗余系统为研究对象,针对以往研究利用指数分布等典型分布导致模型约束条件过于严格的问题,采用连续phase-type(PH)分布描述系统中工作部件寿命、温贮备部件寿命以及维修台休假时间和维修时间,建立通用性更好的系统可靠性解析模型,给出系统可靠度、系统稳态可用度等冗余系统可靠性指标和稳态忙期维修台数量等维修台稳态指标;利用算例验证模型适用性,演示了维修台数量、系统温贮备部件数量变化以及修理工休假速率、维修速率变化对系统各可靠性指标和维修台稳态指标的影响.算例计算结果表明,所提出的可靠性模型能够有效复现多维修台调度对冗余系统可靠性的影响,从而为维修台数量的合理安排及系统部件数量的优化配置提供理论基础和实践参考.     

具有单重休假和修复不如新的两部件温贮备系统

研究了修理工单重休假且由两个不同型部件和一个修理工组成的可修型温贮备系统. 系统考虑了在工作故障和贮备 故障都不能 “修复如新”, 部件 1 是修复非新而部件 2 修复如新的条件下, 假设部件的工作寿命、贮备寿命、故障后的修理时间和贮备故障后的修理时间均服 从不同的指数分布, 修理工休假服从一般连续型分布. 运用几何过程理论、补充变量法、 拉普拉斯变换及拉普拉斯--司梯阶变换, 得到了系统的可用度、可靠度和系统首次故障前平均时间等可靠性指标. 最后, 通过数值模拟验证了结果的有效性.     

Bayesian assessing for a repairable system with standby imperfect switching and reboot delay

System performance measures of a repairable system are studied from a Bayesian viewpoint with different types of priors assumed for unknown parameters, in which the system consists of two active components and one warm standby. There is a failure probability q that switches from standby state to active state. Time-to-failure of components is assumed to be an exponential distribution. The reboot time and repair time are also exponential distributions. When time-to-failure, time-to-repair and reboot time are with uncertain parameters, a Bayesian assessing is adopted to evaluate system performance measures. Monte Carlo simulation is used to derive the posterior distribution for the steady-state availability and the mean time-to-system failure. Some numerical experiments are performed to illustrate the results derived in this article.     

大方电厂6kV厂用电系统互联技术研究及应用

某电厂四台机组的启动/备用电源采用外接单电源供电。为解决外接单电源线路故障后，机组会失去备用电源，运行安全风险大，以及机组正常的检修、启动期间，采用外网购电，购电成本较高等问题。通过对6kV厂用电系统多种方式下进行改造可行性研究，提出了三种6kV厂用电系统改造方案，通过对其优点和缺点进行综合技术研讨和方案论证，综合考虑了投资费用、施工条件、设备状况等因素，最终采用1~4号机组6kV 厂用A、B 段分别用电缆与6kV公用C（D）段之间实现并联的方式进行改造。2017年完成6kV厂用电系统的技术改造，经过1年时间的运行，验证了本方案的可行性和优越性。通过改造不仅极大提高了厂用系统运行方式的灵活性、机组运行的安全性和经济性，消除了启备电源停电带来的安全风险，同时实现了运行机组对停运机组的供电，节约外购电量降低运行成本，最大限度减少外购电量。     

Reliability analysis of a repairable duplex system

We analyse the survival time of a repairable duplex system characterised by cold standby and by a pre-emptive priority rule. We allow general probability distributions for failure and repair. Moreover, an important realistic feature of the system is the general assumption that the non-priority unit has a memory. This combination of features has not been analysed in the previous literature. Our (new) methodology is based on a concatenation of a Cauchy-type integral representation of the modified Heaviside unit-step function and a two-sided stochastic inequality. Finally, we introduce a security interval related to a security level and a suitable risk-criterion based on the survival function of the system. As a practical application, we analyse some particular cases of the survival function jointly with the security interval corresponding to a security level of 90.     

考虑维修优先权的多状态温贮备系统可靠性模型

针对工程应用中装备维修和保养两类活动具备不同优先级这一问题,考虑单一维修台可进行维修和保养两类工作,其中维修具有优先权.以多状态温贮备系统为研究对象,采用可近似拟合任意分布的Phase-type(PH)分布构建一种描述能力更强的系统可靠性模型,得出系统稳态可用度、系统故障率、平均故障间隔时间等一系列可靠性指标的解析表达式.最后利用算例验证PH分布的适用性,演示系统可靠性函数随时间的变化趋势,并讨论维修台工作速率对系统故障率、稳态可用度、维修台忙期稳态概率和平均故障间隔时间的影响.算例结果表明,所提模型具有较广泛的应用价值.     

备用复式控制系统的可靠性预计及其应用

本文全面分析了备用复式系统的可靠性问题,推导出成套的预计公式并给出一个详细的计算实例. 首先,通过考虑监控器和转换开关的动态和静态故障,细致地剖析了自动控制器本身的故障.然后,按照公用与独立两种型式的转换器,划分这些故障为独立与相依两类,并且归结到独立转换器远比公用转换器为优.同时指出转换器本身的故障必须小于各个分系统的故障,否则就不可能提高总系统的可靠性.此外,对自动停车措施的得失及温冷混合贮备的优点,也都得到了明确的结论.     

恒温恒湿空调主/备机控制系统的设计

针对在众多的恒温恒湿空调机组的用户中,经常要求主/备机控制系统满足程控交换机房、计算机房等设备环境的长期一致稳定性,以有效地保证这些设备的正常运行问题,介绍了恒温恒湿空调机组主/备机控制系统的功能特点。以西门子PLCS7-200作为恒温恒湿空调机组的电脑控制器,分别提出了3种解决方案,着重讨论了其控制原理、设计方法及实现可行性。其中,利用PLCS7-200本身内部的PPI通信功能实现主/备机控制的方法,实际应用效果稳定、可靠,具有较强的实用性。     

Reliability of a system with cold redundancy and repaired failures: Series scheme analysis

We consider a system which consists of one operating element and cold redundant elements of the same type. System failures are partially eliminated by repair and partially by replacement of the faulty element with a normally operating standby element (if no such element is available, the system fails). A comprehensive analysis of system failure probability is performed.Translated from Kibernetika, No. 1, pp. 94–98, January–February, 1991.     

Human error modelling of parallel and standby redundant systems

Four newly developed probabilistic models representing two unit parallel and standby redundant systems with human errors are presented. The supplementary variables method is used to develop the system availability expressions for all four models. In the case of Models II and IV, a general formula for the system steady-state availability is developed when the failed system repair times are erlangian distributed. System reliability, mean time to failure and variance of time to failure formulae are developed for Models I and III. Specific plots are shown to demonstrate the impact of human error on system reliability, availability and mean time to failure.     

Reliability and sensitivity analysis of a repairable system with imperfect coverage under service pressure condition

This paper investigates reliability and sensitivity analysis of a repairable system with imperfect coverage under service pressure condition. Failure times and repair times of failed units are assumed to be exponentially distributed. As a unit fails, it may be immediately detected, located and replaced with a coverage probability c by a standby if one is available. When the repairmen are under the pressure of a long queue, the repairmen may increase the repair rate to reduce the queue length. We derive the explicit expressions for reliability function and mean time to system failure (MTTF). Various cases are analyzed to study the effects of different parameters on the system reliability and MTTF. We also accomplish sensitivity analysis and relative sensitivity analysis of the reliability characteristics with respect to system parameters.     

A preventive maintenance policy for a standby system subject to internal failures and external shocks with loss of units

In many situations, serious damage and considerable financial losses are caused by non-repairable failures of a system. Redundant systems and maintenance policies are commonly employed to improve reliability. This paper is focused on the modelling of a complex cold standby system by analysing the effectiveness and costs of preventive maintenance, always in an algorithmic form. The online unit of the system is subject to wear failures and external shocks. The online unit can go through an indeterminate number of degradation levels before failure. This one is observed when inspections occur. Inspections are performed at random intervals, and when one takes place, the unit is taken to the preventive maintenance facility if it is necessary. The preventive maintenance time and cost is different depending on the degradation level observed. If only one unit is performing, a minimal maintenance policy is adopted in order to optimise system behaviour. Reliability measures such as the conditional probability of failure are worked out in a well-structured and algebraic form in transient and stationary regimes by using algorithmic methods. The stationary distribution is calculated using matrix analytic methods, and rewards are included in the model. An optimisation example shows the versatility of the model presented.