Cost analysis of a two-unit standby system with delayed replacement and better utilization of units

This paper develops the model for a system, having two identical units—one operative and the other cold standby. Each unit of the system has three modes—normal, partial failure and total failure. The replacement time of a failed unit by a standby unit is not negligible but is a random variable. System fails when both the units fail totally. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers and operations managers have been evaluated using the theory of regeneration point technique.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…     

An Optimal Decision Rule for Repair vs Replacement

This paper presents a policy for either repairing or replacing a system that has failed. The policy applies to systems whose mean residual life function is decreasing. An optimal policy is developed that minimizes the cost per unit time for repair and replacement. Results are shown graphically for a particular distribution of time to failure and are motivated in terms of an automobile replacement problem.     

A maintenance policy for repairable systems based on opportunisticfailure-rate tolerance

An opportunistic hazard rate replacement policy for a repairable system with several types of units is presented. A unit is repaired at failure when the hazard rate falls in (0, L-u). A unit is replaced at failure when the hazard rate falls in (L-u , L). An operating unit is replaced when its hazard rate reaches L. When a unit is replaced because its hazard rate reaches L, all operating units with their hazard rates falling in (L-u, L) are replaced. The long-run mean cost rate as a function of L and u is derived. Optimal L and u are obtained to minimize the total maintenance cost rate. Application and analysis of results are demonstrated through a numerical example. The maintenance model is designed for a system with multitype units. Each type has its own increasing hazard rate. Units are repaired or replaced depending on their hazard rate at a failure or active replacement of another unit. The repair interval, replacement limit, and replacement tolerance are determined to yield the optimal total maintenance cost rate     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as particular cases.     

Calculation of Age-Replacement with Weibull Failure Times

An age-replacement policy with Weibull failure times is considered. It is troublesome to compute an optimum replacement time numerically. Upper and lower bounds of an optimum time are given in simple terms of replacement costs and parameters of a Weibull distribution. A numerical example shows that the approximation can be used when the ratio of the replacement cost for a failed unit to that for a nonfailed unit is large. The approximation is best when the optimum age of replacement is small.     

Cost-benefit analysis of a 2-unit priority-standby system withpatience-time for repair

The cost of a one-server two-unit (one priority and the other ordinary) cold-standby system with two modes-normal and total failure-is analysed. Whenever the repair time of a failed priority unit exceeds some given maximum time, it is rejected and an order is placed for a new unit. Failure and delivery time distributions are negative exponentials, whereas repair and replacement time distributions are arbitrary. An analysis of the system is made to determine the reliability measures (MTSF (meantime to system failure), steady-state availability, busy period analysis of repairman, etc.) by using the regenerative point technique     

The branching nonhomogeneous Poisson process and its application to a replacement model

In studying and analysing the failure patterns of complex system, plausible stochastic models are needed to represent the sequence of events. A simple and frequently used model is derived by the assumption that the times-between-failures of a system are exponentially distributed and independent. Experience has shown, however, that successive times-between-failures are not exponentially distributed and not independent.These deviations are due to imperfect search of failed components. We constitute a plausible stochastic process which describes the sequence of events, and obtain the interval reliability and the expected number of failures.As an application of these results, we deal with the replacement model where a system undergoes minimal repair before time T and is replaced at time T. We discuss an optimum policy minimizing the total expected cost per unit time.     

Availability analysis of a repairable system with common-cause failure and one standby unit

This paper investigates the mathematical model of a system consisting of two non-identical parallel redundant active units, with common-cause failure, and a cold standby unit. The failed units are repaired one at a time or are repaired together, if they fail due to common cause failure. All repair time distributions are arbitrary and different. The analysis is carried out under the assumption of having a single service facility for repair and replacement.Applying the supplementary variable technique, Laplace transforms of the various state probabilities are developed. Explicit expressions for the steady state probabilities and the steady state availability are derived.Some well known results are obtained as special cases. A numerical example is given to illustrate the effect of the repair policy on the steady state probabilities and the availability of the system.     

Hazard-rate tolerance method for an opportunistic-replacementpolicy

A model for a system with several types of units is presented. A unit is replaced at failure or when its hazard (failure) rate exceeds limit L, whichever occurs first. When a unit is replaced because its hazard rates reaches L, all the operating units with their hazard rate falling in the interval (L-u, L) are replaced. This policy allows joint replacements and avoids the disadvantages resulting from the replacement of new units, down time, and unrealistic assumptions for distributions of unit life. The long-run cost rate is derived. Optimal L and u are obtained to minimize the average total replacement cost rate. Application and analysis of results are demonstrated through a numerical example     

(τ, k) block replacement policy with idle count

The authors propose a new block replacement policy for a group of nominally identical units. Each unit is individually replaced on failure during a specified time interval. Beyond the failure replacement interval, failed units are left idle until a specified number of failures occur, then a block replacement is performed. The average cost rate for this two-phase block replacement policy is derived and analyzed. The policy yields lower cost rate than two block replacement policies published previously. Numerical examples demonstrate the results     

Assessing throughput and reliability in communication and computernetworks

System performance and reliability are jointly assessed for highly reliable communication/computer networks. The model assumes that at most a small number of components can be down at a time and that the average repair/replacement time of a failed component is small when compared with the average failure times of network components. The system performance is measured in terms of network throughput at steady-state operation     

Replacement Policies for a Unit with Random and Wearout Failures

This paper considers three replacement models with random and wearout failures; a) the unit is replaced at failure, b) the unit undergoes minimal repair at failure, and c) the unit is replaced at failure only in a wearout failure period. Optimum replacement policies which minimize the s-expected cost rate for each model are discussed.     

Reliability and availability analysis for two non-identical unit parallel systems with common cause failures and human errors

This paper presents three models with common cause failure and human error analysis of a two non-identical unit parallel system. The difference between models I and II is that, in model I the failed system is repaired back to its normal operating state whereas in model II it is not so. Similarly, the basic difference between models II and III is that, in model II it is possible for the partially failed system to be restored to its normal operating state and in model III it is not so. The system reliability, time dependent system availability, steady-state system availability and mean-time to failure are developed for the above models. The problem is discussed with a numerical example.     

All opportunity-triggered replacement policy for multiple-unitsystems

A model is presented for a system which consists of n i.i.d units. Hazard rates of these units are increasing in time. A unit is replaced at failure or when the age of a unit exceeds T, whichever occurs first. When a unit is replaced, all the operating units with their age in the interval (T-w,T) are replaced. Both failure replacement and active replacement create the opportunities to replace other units preventively. This policy allows joint replacements and avoids the disadvantages resulting from replacement of new units, down time, and unrealistic assumptions for distributions of unit life. An algorithm is developed to compute the steady-state cost rate. Optimal T&W are obtained to minimize the mean total replacement cost rate. Application and analysis of results are illustrated through a numerical example     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

Reliability analysis of multi-unit cold standby system with two operating modes

This paper investigates the mathematical model of a system composed of n dissimilar units—one functioning and others either failed or cold standbys. Each unit of the system has three possible modes—normal, partial failure and total failure. There is a perfect switch to operate the leading standby unit on total failure of the operative unit. The failure and repair times of each unit are assumed to follow arbitrary distributions. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are derived as particular cases.     

Availability analysis of a repairable standby human-machine system

This paper presents a model representing a two units active and one unit on standby human-machine system with general failed system repair time distribution. In addition, the model takes into consideration the occurrence of common-cause failures. The method of linear ordinary differential equation is presented to obtain general expressions for system steady state availability for failed system repair time distributions such as Gamma, Weibull, lognormal, exponential, and Rayleigh. Generalized expressions for system reliability, time-dependent availability, mean time to failure, and system variance of time to failure are also presented. Selected plots are presented to demonstrate the impact of human error on system steady state availability, reliability, time-dependent availability, and mean time to failure.     

Cost-benefit analysis of a single server three-unit redundant system with inspection, delayed replacement and two types of repair

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement at the time of failure of the active unit and a cold standby (stock) unit which can be replaced after a random amount of time. The type of the failure of operative or warm standby unit is detected by inspection only. The service facility plays the triple role of replacement, inspection and repair of a unit. Failure time distributions of operative and warm standby units are negative exponential whereas the distributions of replacement time, inspection time and repair times are arbitrary. The system has been studied by using regenerative points.     

An optimal replacement policy for a three-state repairable system with a monotone process model

In this paper, a deteriorating simple repairable system with three states, including two failure states and one working state, is studied. Assume that the system after repair cannot be "as good as new", and the deterioration of the system is stochastic. Under these assumptions, we use a replacement policy N based on the failure number of the system. Then our aim is to determine an optimal replacement policy N/sup */ such that the average cost rate (i.e., the long-run average cost per unit time) is minimized. An explicit expression of the average cost rate is derived. Then, an optimal replacement policy is determined analytically or numerically. Furthermore, we can find that a repair model for the three-state repairable system in this paper forms a general monotone process model. Finally, we put forward a numerical example, and carry through some discussions and sensitivity analysis of the model in this paper.