Cost-benefit analysis of a one-server two-unit cold standby system with repair and preventive maintenance

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the type where the operating unit is taken up for PM whenever the other unit is available for operation. Initially, one unit is placed in operation and the other unit is kept as a cold standby. When the operating unit fails while the other unit is under service (repair or PM), the system breaks down. The busy period of the server in a time interval (O, t] is divided into time spent for repair and time spent for PM. By identifying regenerative epochs, suitable expressions for the expected values of these times are obtained. The pointwise availability is also derived. With the assumptions that a revenue is earned linearly with up-time, and repair and PM costs are incurred linearly with repair and PM times, respectively, the net expected revenue for a period (O, t] is derived. A particular case where the time to failure of the operating unit is 2-Erlang and the times for repair and PM are exponential has been analysed.     

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.     

On a two-unit standby redundant system subject to repair and preventive maintenance

This paper derives the mean life and the Laplace-Stieltjes transform of the distribution of the first time to system-down for two dissimilar units standby redundant system with repair and preventive maintenance.Further, special cases of the results obtained here coincide with earlier results for the two-unit standby redundant system. The case when the system is not subject to preventive maintenance is considered as a particular case.     

Profit analysis of a two-unit standby system with two types of repair and preventive maintenance

This paper deals with the profit analysis of a two-unit cold standby system with two types of repairs—cheap and costly. Cheap repair becomes available after a random amount of time while costly is available instantaneously. The preventive maintenance (P.M.) of an operative unit starts at random epochs of time and is done only if the other unit is in standby. The distribution of time to accomplish P.M. is negative exponential while the distributions of failure time, repair times and time to commence P.M. are general. Various economic reliability measures of interest to system designers as well as operation managers have been obtained using regenerative point technique.     

Stochastic analysis of a two-unit parallel system with partial and catastrophic failures and preventive maintenance

This paper studies a two-unit parallel system with each unit having two types of failure and two modes of operation—normal or partial failure mode. A unit fails either due to change in operating characteristics or due to catastrophe. The system goes for preventive maintenance randomly (in time). Failure rates are constant while repair and (preventive) maintenance rates are general. Using the theory of regenerative and Markov-renewal processes several important measures of reliability are obtained.     

Analysis of a two-unit system subject to repair and preventive maintenance with non-linear revenue and costs

The cost-benefit analysis of a one-server two-identical-unit cold standby system subject to repair and preventive maintenance (PM) with non-linear revenue and costs is presented in this paper. Initially, one unit is in operation and the other is cold standby. When a unit fails, it is taken up for repair or waits for repair if the server is busy. The latter results in a system breakdown. If a unit returns from service (repair or PM) and the other unit is operating, the operating unit is taken up for PM. The revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of the interval. Similarly, the cost of a repair or PM action is a function of the length of the repair or PM time, respectively, for that action. With the help of regeneration point technique, the expected net revenue over an interval (0,t] is obtained. It is shown that the results for the special case when the revenue and cost function are linear agree with previously obtained results.     

A maintenance model for two-unit redundant system

In this paper, a maintenance model for two-unit redundant system with one repairman is studied. At the beginning, unit 1 is operating, unit 2 is the standby unit. The costs include the operating reward, repair cost and replacement cost, besides, a penalty cost is incurred if the system breaks down. Two kinds of replacement policy, based on the number of failures for two units and the working age, respectively are used. The long-run average cost per unit time for each kind of replacement policy is derived. Also, a particular model in which the system is deteriorative, two units are identical and the penalty cost rate is high, is thoroughly studied.     

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

The object of this paper is to carry out the availability and the reliability analysis of a two-unit system with a warm standby having a single service facility for the performance of preventive maintenance and repair. The failure times, the repair times, the inspection times and the preventive maintenance times of the main unit and of the standby one are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. Explicit expressions for the mean down time of the system and for the mean time to system failure are obtained. Some previous results are derived from this work as special cases.     

Optimal planned maintenance with salvage cost for a two-unit standby redundant system

This paper considers the optimal spare ordering policies for a cold standby redundant system with two dissimilar units. Especially, the planned maintenance schedule with salvage cost is discussed. The failure time distributions for respective units are assumed to be arbitrary. By applying the expected cost per unit time in the steady-state and the stationary availability as criteria of optimality, the optimal ordering policy minimizing or maximizing each criterion is obtained under some economical and/or physical assumptions. Finally, numerical examples are presented, and the effect of the failure time distributions for the optimal ordering policy is examined in detail.     

Light maintenance for a two-unit parallel redundant system with bivariate exponential lifetimes

Maintenance is of great interest in reliability theory. A two-unit parallel redundant system is a typical redundant repairable system and is applied in many practical fields such as computer systems. Many contributions to such systems have been proposed and analyzed extensively. The earlier models have mainly assumed that the lifetimes of two units are independently distributed. However, some papers considered a two-unit parallel redundant system in which the lifetimes of two units are dependent and distributed by a Bivariate Exponential (BVE) distribution. In this paper we discuss a two-unit parallel redundant system with single repair facility in which the lifetimes of two units obey a BVE distribution. Consider the maintenance policy for the operative unit. The time of the beginning of the lightly maintenance measured from the instant that the unit begins to be operative, is assumed to obey a BVE distribution. We derive the limiting availability for the system by applying a unique modification of regeneration point techniques in Markov renewal processes. This paper also gives a numerical example of the limiting availability for the system.     

Optimal maintenance of a two-unit standby redundant system with a generalized cost structure

To maintain a system there are generally several alternatives available to a decision maker. In this paper a usual 2-unit standby system is considered with exponential distribution for life-time of units and arbitrary distribution for repair time. A generalized cost structure with different earning rates in different states, transition rewards and discounting, has been superimposed upon the semi-Markov process generated by the system model. An optimal maintenance policy for the system is the one that maximizes profit rate of the system. A solution algorithm, based on Howard's policy iteration method, is developed. An illustration is presented at the end.     

Cost-benefit analysis of a n-unit two-server system with preventive maintenance

This paper deals with the cost-benefit analysis of a 1 out of n:G system with two servers, one for preventive maintenance (PM) and one for repair. All standby units are cold. An operating unit is taken off for repair when it fails or for PM when a PM action is due. If a unit that needs service (PM or repair) finds the corresponding server busy it enters a first-come-first-served queue. When a unit is taken off for service and no standby is available, the system goes down. Expressions for steady-state expected up-time, time spent on PM and time spent on repair are obtained. These, along with linearity assumptions on the revenue and costs, are used to obtain an expression for the steady-state expected net revenue per unit time. A special case with age replacement is taken up for study and numerical results are presented.     

A three-unit standby redundant system with repair and preventive maintenance

This paper deals with the reliability of a renewable three-unit system under preventive maintenance activity. The Laplace transform of the reliability function and the mean lifetime of the system have been obtained under the assumption that the failure times, repair times, inspection times and maintenance times are random variables having different distributions. Some special cases also have been obtained.     

Optimal preventive maintenance with repair

A minimal preventive-maintenance model is developed for repairable, continuously-operating devices whose conditions deteriorate with the time in service. The times to preventive maintenance have an Erland distribution and can be, in a limiting case, deterministic. The optimal value of the mean time a preventive maintenance is determined by minimizing the unavailability of the device due to preventive maintenance, to Poisson-distributed failures, and to deterioration failures. The model is useful for many devices, including electric power-system components such as coal pulverizers, circuit breakers, and transformers     

A two-unit deteriorating standby system with inspection

This paper studies a single server two-unit standby system in which the standby can fail when offline and its repair starts only after knowing about its failure from its time to time inspection. The inter-inspection time is assumed to be arbitrarily distributed. Various measures of reliability useful to system designers and operations managers are obtained.     

The effect of preventive maintenance on a system with imperfect switchover

A two-unit standby redundant system with repair, preventive maintenance and imperfect switchover is considered. The Laplace-Stieltjes transform (LST) of the survivor function (sf) of the time to the first system failure (TFSF) and the mean are derived. Finally a theorem about the effect of preventive maintenance is proved.     

Reliability of a reparable system with preventive maintenance and imperfect switch

A two-unit cold standby redundant system with repair, post-repair, preventive maintenance (PM) and imperfect switchover is considered using three types of PM [types (a), (b) and (c)]. The Laplace transform (LT) of the survivor function (sf) of time to the first system failure (TFSF) and the mean TFSF are derived. A theorem about the effect of PM [type (a)] is proved. Finally numerical calculations are presented to illustrate the results.     

Optimal replacement policy for a warrantied system with imperfect preventive maintenance operations

This paper determines the optimal replacement time for a system with imperfect preventive maintenance operations under the modified warranty policy. The hazard rate after preventive maintenance lies between the states as good as new and as bad as old. After minimal repair, the hazard rate remains unchanged. Modified warranty policy is a mixed type of free and pro-rata warranty policy. Numerical examples using the Weibull case are presented.     

A complex two-unit parallel system

Reliability and availability functions are obtained for a complex two-unit parallel system by the use of regeneration point technique. The system consists of two dissimilar units. There is only one repair facility. The repair facility is not available for a random time immediately after each repair completion.