Cost-benefit analysis of one-server two-unit system with imperfect switch

This paper deals with the cost-benefit analysis of a one-server two-unit system subject to imperfect switch. The repair times of a unit and the switch are assumed to be arbitrarily distributed while the failure rate of a unit and of the switch are constants. Initially, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The system breaks down when no unit is available or when the switch is not available although the unit is available for operation. The system is characterised by the probability of its being in the up or down state at an instant and integral equations have been set up for these probabilities by identifying the system at suitable regeneration epochs. These equations have been solved using Laplace Transform Technique. Explicit expressions for the expected durations the server is busy in (0, t) with the repair work of the unit and the switch have been obtained to carry out the analysis.     

Cost-benefit analysis of a one-server two-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the server is summoned upon failure of an item (i.e. unit or switch). The amount of time the server takes to arrive is a random variable, distributed arbitrarily. The server leaves when there is no item waiting for repair. The repair times are arbitrarily distributed whereas all failure rates are constant. Initially one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. Explicit expressions for the expected uptime in (0, t) of the system, busy period of the server due to repair of a unit and that of the switch are obtained to carry out the cost-benefit analysis.     

Cost-benefit analysis of one-server two-unit imperfect switch system with degradation

This paper deals with the cost-benefit analysis of 1-server 2-unit system with imperfect switch where the items (units/switch) are not ‘as good as new’ after the repair. The successive repair times of each item are arbitrarily distributed while the successive failure rates are constants. If repair of a unit is not possible it is discarded incurring some salvage value. After a fixed number of failures the unit is scrapped without any salvage value. The switch is always repairable and is scrapped only when both the units are scrapped. The expected revenue, expected busy period due to different types of repairs of units/switch, expected salvage value and expected number of repair completions of the switch, all in [0, t], are obtained to carry out the cost-benefit analysis.     

Cost-benefit analysis of a one-server two-unit system subject to shock and degradation

This paper deals with the cost-benefit analysis of 1-server 2-unit system subject to two modes of failure, namely, shock and degradation. Initially, one unit starts operating and the other is kept as cold-standby. The type of repair a unit undergoes depends upon the nature of its failure. The various essential characteristics of the system have been found out to carry out the cost-benefit analysis.     

Cost-benefit analysis of one-server two-unit replacement system with imperfect switch

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the unit, if available, is preferred to the standby. The repair time of an item (unit/standby/switch is arbitrarily distributed while failure rate of an item is constant. Initially, the unit is switched on (switch is working at t = 0). The repair of the switch is given preference after the current repair of the unit or standby is over. Explicit expressions for the expected up-time due to the unit, expected up-time due to the standby; expected busy period of the server due to the unit, due to the standby and that due to the switch are obtained to carry out the cost-benefit analysis.     

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

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 age replacement type, where, if a unit has been in operation for a certain period of time, which may be a random variable, and if the other unit is in standby, the operating unit is taken off for PM. The expected net revenue in the interval [0,t) is obtained using two different approaches. The first approach is more general and allows nonlinearities in the revenue and costs. It is assumed that the revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of that interval. Similarly, the cost of a repair or PM action is function of the length of the repair or PM time, respectively, for that action. The second approach assumes that the revenue, repair cost and PM cost vary linearly with time. The pointwise availability is derived. The busy period of the server is divided into time spent in performing repair and time spent on PM. The expected net revenue in [0,t) is obtained. Both techniques make use of regeneration points. It is finally shown that the results of the first approach under assumptions of linear revenue and cost functions reduce to those of the second approach.     

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.     

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.     

Cost-benefit analysis of one-server two-unit imperfect switch system subject to multistage repairs

This paper deals with the cost-benefit analysis of 1-server 2-unit system with imperfect switch where repairs take place in stages. The repair times of the unit and of the switch are assumed to be arbitrarily distributed while the failure rates of units and of the switch are constants. Initally, one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. The repair of the switch is given preference after completion of current repair of a unit. The analysis is carried out by regeneration point technique. Explicit expressions for the expected durations the server is busy in (0, t) with particular stages of repair of the unit and of the switch are obtained to carry out the cost-benefit analysis of the system.     

Inspection policy for two-unit parallel redundant system

This paper deals with a single-server two-unit parallel redundant system with non-negligible inspection time. We shall assume that a failure of a unit or the system failure is detected by inspection only. We consider two inspection policies and under each inspection policy the stationary availability is derived by applying Piecewise Markov Process. Optimum inspection schedule is discussed to maximize the stationary availability of the system. A numerical example is presented.     

Analysis of a two-unit parallel redundant system with phase type failure and general repair

Explicit expressions for the Laplace transform of the reliability and availability of a general two-unit parallel redundant system are obtained. The mean time to system failure and steady state availability are deduced as special cases. Some particular cases of our result are also obtained.