Cost-benefit analysis of a system with inspection, replacement and two types of repair

This paper investigates a mathematical model of a system composed of two units—one operative and the other in cold standby. There is a single repair facility which serves the triple role of inspection, repair and replacement of a failed unit. After inspection, the unit goes to minor (major) repair with probability p(q = 1 − p). Whenever the failed unit goes to major repair, an order is immediately placed for a new unit to replace the unit under major repair. Failure, inspection and delivery time distributions are negative exponential, whereas repair time distribution is arbitrary. The system is analysed in detail using the regenerative point technique and several reliability characteristics of interest to system designers and operation managers are obtained. Earlier results are verified in particular cases.     

Probabilistic analysis of a two-unit cold standby system with two-phase repair and preventive maintenance

This paper deals with cost-analysis of a single-server two-unit cold standby system subject to random inspection and k-failure modes. A switch is used to operate the standby unit which works successfully with known probability p(=1 −q). The service facility plays the dual role of inspection and repair of both failed unit and failed switch. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the “up” or “down” state. Laplace transform technique is adopted to solve these equations and various reliability characteristics of interest to system designers and operations managers have been obtained.     

A multi-component standby system subject to inspection and truncated normal failure time distribution

This paper investigates a stochastic model of a single server, two identical unit cold standby system. Each unit consists of n separately maintained independent components arranged in series. After each failure, an inspection is required to detect which component of the unit has failed. The failure time distribution of a unit is truncated normal while all the other time distributions are negative exponential. Using the regenerative point technique, we obtained various measures of system effectiveness to carry out the profit function analysis.     

A two-unit cold standby system with imperfect repair and excessive availability period

A two-unit cold standby redundant system supported by a single repair facility is considered. The units after repair do not behave like new ones and a unit can be repaired, at most, k(k < ∞) times. The failure time distribution of either unit is different after each repair. Further, the system performance is maintained for a random time even after breakdown. The reliability characteristics are provided for the model.     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

Replacement models with inspection and preventive maintenance

This paper considers the maintenance policy where a unit is inspected and maintained preventively at periodic intervals, and as the effectiveness, the age after maintenance becomes younger. The mean time to failure and the expected number of maintenances before failure are obtained. Two replacement models are considered and an optimum policy for each model is discussed.     

On the characteristics of a system having master and helping unit

A system having one master and one helping unit with two failure modes-partial and total-is analysed. The helping unit is used to support the master unit in operation. Whenever the helping unit fails it is either repaired or replaced with probability p(q). Failure time distributions are taken to be negative exponential whereas repair time distributions are taken to be arbitrary. Using the regeneration point technique, several system characteristics such as mean time to system failure, availability, busy period of the repairman, etc. are obtained. Finally, some graphs are drawn in order to highlight the important results in particular cases.     

Stochastic analysis of a multi-unit cold standby system working in orbit form

This paper considers the analysis of a single server n-similar unit system. Initially k(<n) units form an orbit which functions if one unit functions at a time and the remaining n − k units work as cold standbys. When a unit fails in the orbit it is instantaneously replaced by one of the standbys with the help of a perfect transfer switch. The system is said to fail when n − k + 1 units have failed. The distribution of time to failure and time to repair of a unit are negative exponential. Using the regenerative point technique several reliability characteristics are obtained to carry out the cost-benefit analysis.     

Analysis of a two-unit standby system with three modes and imperfect switching device

In this paper we study the effect of imperfect switching on a two-unit cold standby system in which each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units are negative exponential whereas repair time distributions of units and switch are general. The switch is available at the time of need with probability p(= 1?q). Using the regeneration point technique reliability characteristics of interest to system designers as well as operation managers have been evaluated.     

Cost-benefit analysis of a one-server two-unit standby system subject to imperfect switching device,random inspection and k-failure modes

This paper deals with cost-analysis of a single-server two-unit cold standby system subject to random inspection and k-failure modes. A switch is used to operate the standby unit which works successfully with known probability p(=1 −q). The service facility plays the dual role of inspection and repair of both failed unit and failed switch. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the “up” or “down” state. Laplace transform technique is adopted to solve these equations and various reliability characteristics of interest to system designers and operations managers have been obtained.     

Cost-benefit analysis of single server n-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.     

Optimal replacement policies for systems with multiple standbycomponents

The authors consider two new preventive replacement policies for a multiple-component cold-standby system. The failure rate of the component in operation is constant. The system is inspected at random points over time to determine whether it is to be replaced. The replacement decision is based on the number of failed components at the time of inspection. There are two replacement options if the complete system fails during operation: (i) replace the system if an inspection reveals that it has failed (system failure is not self-announcing), and (ii) replace the system the instant it fails (system failure is self-announcing). There is a threshold value on the number of failed components (at the time of inspection) which minimizes the mean total cost. The authors develop a simple efficient procedure to find the optimal threshold value. They compare the cost of operating a system that is inspected at random points in time, with the cost of operating a system that is monitored continuously through an attached monitoring device, and discuss cost tradeoffs     

A semi-regenerative process of two-unit warm standby system

This paper deals with two identical units warm standby system; a failure of operating unit can be detected at any time but a failure of standby unit can not be done until a system is inspected. We are able to look upon the stochastic behavior of our model as that of semi-regenerative process. The pointwise unavailability and the steady state unavailability of the system are derived by using the limit theorem of semi-regenerativeprocess. Further, we shall discuss the optimum inspection period minimizing the steady state unavailability. A numerical example is presented.     

Availability analysis of a two-unit cold standby system with two switching failure modes

We consider a 2-unit cold standby redundant system with two switching devices—transfer switch and connect switch. The system is analysed under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units and connect switch are exponential, whereas repair time distributions are general. At any instant after use the transfer switch fails with probability q = 1?p. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated. A few particular cases are discussed.     

求解贮存失效率的条件中位数算法改进

利用定期检测数据求解贮存失效率是电子产品贮存可靠性研究的重点和难点。条件中位数算法是求解贮存失效率的算法之一,但其估计性能不理想,实际应用并不多见。为了改善条件中位数算法的估计性能,对该算法进行了改进。数字仿真结果显示,改进算法的估计均值和相对估计误差明显优于改进前的条件中位数算法,可广泛地应用电子产品的贮存可靠性研究。     

Common-cause failure analysis of a redundant system with non-repairable units

This paper presents a newly developed generalized expression for mean time to failure, MTTF, of a non-repairable identical unit parallel system with warm standby and common-cause failures. Also presented is a modified version of this formula that takes into account the repairability of the warm standby and/or switching mechanism. Generalized expressions for system reliability and variance of time to failure are presented along with some tables and plots of system reliability and MTTF.     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

An M/M/1 system with an unreliable device and a threshold recovery policy

An M/M/1 queueing system with an unreliable device is considered in the study. The device fails in an exponentially distributed time during which it is in the working condition and serves a demand. The device recovers during an exponentially distributed time according to the threshold policy specified by threshold level q ≥ 1. After a successive failure, the device does not recover until the number of demands exceeds level q. In the study, the system operating in the stationary regime is analyzed and the problem of optimal recovery control aimed at the minimization of the mean cost for a given penalty structure is solved.     

Continuous-time predictive-maintenance scheduling for adeteriorating system

A predictive-maintenance structure for a gradually deteriorating single-unit system (continuous time/continuous state) is presented in this paper. The proposed decision model enables optimal inspection and replacement decision in order to balance the cost engaged by failure and unavailability on an infinite horizon. Two maintenance decision variables are considered: the preventive replacement threshold and the inspection schedule based on the system state. In order to assess the performance of the proposed maintenance structure, a mathematical model for the maintained system cost is developed using regenerative and semi-regenerative processes theory. Numerical experiments show that the s-expected maintenance cost rate on an infinite horizon can be minimized by a joint optimization of the replacement threshold and the a periodic inspection times. The proposed maintenance structure performs better than classical preventive maintenance policies which can be treated as particular cases. Using the proposed maintenance structure, a well-adapted strategy can automatically be selected for the maintenance decision-maker depending on the characteristics of the wear process and on the different unit costs. Even limit cases can be reached: for example, in the case of expensive inspection and costly preventive replacement, the optimal policy becomes close to a systematic periodic replacement policy. Most of the classical maintenance strategies (periodic inspection/replacement policy, systematic periodic replacement, corrective policy) can be emulated by adopting some specific inspection scheduling rules and replacement thresholds. In a more general way, the proposed maintenance structure shows its adaptability to different possible characteristics of the maintained single-unit system