On standby redundant system with repair,post repair and preventive maintenance

A two-unit standby system with repair, post repair and preventive maintenance (PM) is considered. The Laplace transform (LT) of survivor function (SF) of time to the first system failure (TFSF) and the mean are derived. Finally one theorem about the effect of (PM) is proved.     

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.     

An n-unit standby redundant system with r repair facilities and preventive maintenance

Identifying suitable regeneration points the availability and reliability of an n-unit warm standby system with r repair facilities, in which the operating online unit is subjected to preventive maintenance are obtained. A numerical example is provided to illustrate the results obtained. Based on the numerical result, an optimal PM policy is also derived.     

Stochastic behavior of a two-dissimilar-unit standby redundant system with repair maintenance

A standby redundant system of two dissimilar units is considered under the assumptions that both the failure and the repair time distributions are arbitrary. The system states are defined corresponding to the failure of the specified units. The first passage time distributions, the expected numbers of visits to a certain state, the transition probabilities, and the limiting probabilities are obtained using the unique modifications of the regeneration point techniques in Markov renewal processes. Two particular cases are finally presented.     

Stochastic behavior of a 2-unit standby redundant system with imperfect switchover and preventive maintenance

We discuss a 2-unit standby redundant system with imperfect switchover and preventive maintenance (PM). The switch assumes up and down states repeatedly, independently of the behavior of the main unit. We have the stochastic behavior of the system.     

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.     

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.     

Optimum preventive maintenance policies for a 2-unit redundant system with repair and post-repair

Stochastic behaviour of a 2-unit cold-standby redundant system with repair and post-repair and subject to slide preventive maintenance is discussed under the most generalized assumptions. We employ (MRP) Markov Renewal processes technique to obtain various reliability measures. Optimum preventive policies which maximize the availability are derived under suitable conditions. A numerical example is presented.     

Analysis of a three-unit redundant system with two types of repair and inspection

This paper deals with a redundant system with two types of spare units—a warm standby unit for instantaneous replacement of a failed operative unit and a cold standby which takes a random amount of time to become operative/warm. After each repair a unit is sent for inspection to decide whether the repaired unit is perfect or imperfect. If the repaired unit is found to be imperfect then it goes for post-repair. Using the regenerative point technique in the Markov renewal process several reliability characteristics of interest to system designers and operation managers are obtained.     

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.     

Behaviour of a two-unit standby redundant system with imperfect switching and delayed repair

A 2-unit standby redundant system with imperfect switchover is considered. A repair facility is assumed to be available only at a fixed proportion of time. Failure-time distributions of units are exponential whereas repair-time distributions, distribution of time for the repairman to become available are general. The system has been investigated in detail by the help of semi-Markov process and closed form results are obtained for mean-time-to-system-failure, steady-state availability, expected number of occurrences of a state, expected profit and second moment of time in up state. Behaviour of several parameters has also been studied and several earlier models are included as particular cases.     

Cost analysis of a two dissimilar cold standby system with preventive maintenance and replacement of standby

This paper deals with the cost analysis of a two dissimilar unit cold standby redundant system with preventive maintenance, under the assumption that the standby, being substandard, is not repairable and has to be replaced on failure. The failure times have negative exponential distributions while all other distributions involved are general.     

A warm standby redundant system with correlated failures and repairs

This paper presents the analysis of a two-unit warm standby system assuming a bivariate exponential density for the joint distribution of failure and repair times of the units. Investigations regarding the stochastic behaviour and important reliability characteristics of the system have been made and earlier results have been verified as particular cases. A few graphs have also been provided to support the theoretical results.     

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.     

Effect of intermittent repair in a two unit redundant system with standby failure

A two-unit standby redundant system with exponential failure time distribution of the operative unit is considered. It is assumed that failure of the standby unit is detected only at the time of use and is available with a known probability. Repair facility is also available at the time of need with a known probability. Repair and preoccupation times are general. Stochastic behaviour of the system has been studied by Semi-Markov process and parameters of interest eg. MTSF, steady state availability, expected profit have been obtained. Expected profit of this model is compared with that of an earlier model and a condition on extra incurred cost is obtained.     

Human error analysis of a standby redundant system with arbitrarily distributed repair times

This paper presents human error analysis of a (two units working and one on standby) system with arbitrarily distributed repair times. The supplementary vairables method is used to develop the system availability expressions. A general formula for the system steady-state availability is developed when the failed system repair times are gamma distributed. Time-dependent availability, system reliability with repair, mean time to failure and variance of time to failure formulae are developed for some particular cases. Selective plots are shown to demonstrate the impact of critical human error on system availability and reliability.     

Behaviour of a priority standby redundant system with different types of repair facilities

This paper discusses the stochastic behaviour of a two unit priority standby redundant system, in which priority units gets priority for all operations, with different types of repair facilities. Failure time distributions of Unit are exponential, whereas other distributions are arbitrary.     

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     

Two unit repairable redundant standby system

The Laplace-Stieltjes (LS) transform for the distribution of time to first system failure (TFSF), transition probability, availability and mean time to system failure have been derived for two unit repairable redundant standby system with perfect as well as imperfect switchover condition. General expressions for computing various reliability performance indices have been obtained by using Markov Renewal techniques considering general distributions for time to failure and time to repair for the units.