R. Radhakrishnan

Cost-benefit analysis of a 2-unit cold standby system subject to slow switch

Abstract This paper deals with the cost-benefit analysis of a 2-unit cold standby system subject to slow switch. The time to failure of a unit, repair time and the switchover time of a unit from standby to operative state are assumed to be arbitrarily distributed. The system has been characterized by its probability of its being in up or down state at a given instant. Integral equations have been set up for identifying the system at suitable regeneration epochs. Explicit expressions for the system characteristics, namely: 1. 1. expected switchover time of a unit from standby state to operative state in (0, t ]; 2. 2. expected repair time of a unit in (0, t ]; have been obtained to carry out the cost-benefit analysis. The case when all the time distributions involved are exponential is also discussed.

Stochastic analysis of a one-server two-unit (dissimilar) system subject to slow switch

Abstract The paper deals with the cost-benefit analysis of a one-server two-unit system subject to slow switch. The failure times of the units, the repair times and the switchover (installation) times are assumed to be arbitrarily distributed. The role of the server is not only to repair a failed unit but also to install the standby whenever required. Installation work gets priority over repair. The system is analysed by employing the regeneration point technique. Systems characteristics such as 1. (1) expected up-time of each of the units in (0, t], 2. (2) expected repair time of each of the units in (0, t] and 3. (3) expected time each unit spent in the installation/switchover state in (0, t], have been evaluated to carry out the analysis. The particular case when the units are identical is also discussed.

Cost-benefit analysis of a two-unit adaptive system with slow switch

In this paper, a two-unit shared parallel system (repairable) is considered. Initially, both the units share the total load equally, and when one unit fails, it goes in for the repair facility. Simultaneously, the other surviving unit takes over the entire load until the repair is completed and the repaired unit is ready for operation after installation. The installation time is assumed to be non-negligible. Assuming that failure rates and repair rates are different when a unit functions under half-load and full-load, explicit expressions for the system characteristics, namely, 1. (1) expected available time of the system during the period (0,t], 2. (2) expected repair times of the units which failed due to half-load/full-load during the period (0, t], 3. (3) expected time the units spend in the installation/switchover state during the period (0, t], are obtained corresponding to the models of system functioning. These system characteristics are used to carry out the cost-benefit analysis.

Analysis of a 2-unit (dissimilar) repairable system subject to slow switch

Abstract This paper deals with the cost-benefit analysis of a cold standby system composed of two non-identical units, subject to slow switch. The time to failure of a unit, repair time and the switchover time of a unit from standby to operative state are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in “up” or “down” state at a given instant. Breakdown of the system occurs when both the units are not in operating condition. Integral equations are set up to these probabilities by identifying the system at suitable regeneration epochs. The cost-benefit analysis is carried out by finding out: 1. (1) expected up-time of the individual units in (0, t], 2. (2) expected time each unit was under repair in (0, t], 3. (3) expected time each unit spent in the installation/switchover state in (0, t]. The case when all the distributions concerned are exponential is also discussed.

On the expected net revenue of a one-server two-unit system with arbitrary installation time

Abstract This paper considers a two-unit cold standby repairable system subject to slow switch under the assumption that the standby unit is replaced if the basic unit is ready for operation after repair and installation. The failure rates of the units are assumed to be constants while the installation times and the repair times of the units are non-negligible and are arbitrarily distributed. The system is characterized by the probability of its being in up or down state at a given instant. Integral equations are set up for these probabilities by identifying the system at suitable regeneration epochs. The cost-benefit analysis of the system is carried out by finding the following systems characteristics: 1. (1) expected up-times of the units during the period (0, t ], 2. (2) expected repair times of the units during the period (0, t ] and 3. (3) expected time spent by the units in the installation state during the period (0, t ].

Cost-benefit analysis of one-server two-unit system subject to slow switch and random service

Abstract This paper deals with the cost-benefit analysis of a single-server two-unit cold standby system subject to slow switch and random service facility. Two models of system functioning are studied in this paper. In model 1, the units are non-identical while in model 2, they are identical. In both the models, it is assumed that the distributions of the failure times, the switchover times and the repair times of the units are arbitrarily distributed. Further, it is assumed that there is a single service facility available at random according to a known distribution. k(.) to serve the dual purpose of switchover and repair. For both the models, the system characteristics, namely, 1. (1)|the expected up-time of the system during the period (0, t], 2. (2)|the expected time spent by the service facility in repair work during the period (0, t] and 3. (3)|the expected time spent by the units in the installation/switchover state during the period (0, t] are studied by identifying the system at suitable regeneration epochs to carry out the cost-benefit analysis.

Stochastic analysis of one-server two-unit adaptive system with slow switch

Abstract This paper considers a two-unit repairable shared parallel system with single service facility. Initially, both the units share the total load equally and when one unit fails, it goes for repair. Simultaneously, the other surviving unit takes over the entire load until the repair is completed and the repaired unit is ready for operation after installation. The installation time is assumed to be non-negligible. Failure rate of a unit when it is operating with full load is assumed to be greater than that of a unit when it is operating with half load. Assuming that a unit has to undergo different types of repairs due to the different loads with which it fails, the following system characteristics, namely: 1. (1) expected available time of the system during the period (0, t ]; 2. (2) expected repair times of the units during the period (0, t ] and 3. (3) expected time spent by the units in the installation state during the period (0, t ] are evaluated to carry out the cost-benefit analysis.

Analysis of one-server two-unit system subject to stage-wise installation and repair

Abstract This paper considers a two-unit (dissimilar) standby system subject to slow switch. The failure times of the units are assumed to be exponentially distributed. The installation of a standby unit and the repair of a failed unit take place in r-stages and s-stages respectively. The installation times and the repair times of the units are arbitrarily distributed. The system is characterized by the probabilities of its being in the “up” or “down” state at any instant. Integral equations are set up for these probabilities by identifying the system at suitable regeneration epochs. Laplace-Transform technique is adopted to solve these equations. Various system characteristics, namely, 1. 1. the expected up-time of the units during the period (0,t], 2. 2. the expected time spent by the units in various stages of installation/ switchover during the period (0, t] and 3. 3. the expected time spent by the service facility in various stages of repair during the period (0, t], are evaluated.

Cost-benefit analysis of an n-unit repairable adaptive system

Abstract In this paper, an n -unit shared parallel system is considered. Initially, all the n -units share the total load equally and when one or more units fail, they go in for the repair facility while the other surviving units share the entire load equally till the failed units are ready for operation after installation. The installation time is assumed to be non-negligible. The system will be down only when all the units are non-operative. Assuming that the failure rates are different when the units function under varying loads, the system characteristics, namely. 1. (1) the expected up-time of the system during the period (0, t ], 2. (2) the expected repair time of the units which failed due to varying failure rates during the period (0, t ] and 3. (3) the expected time the units spend in the switchover/installation state during the period (0, t ] are studied by identifying the system at suitable regeneration epochs. The cost-benefit analysis is carried out using these system characteristics.

Cost-benefit analysis of a two-unit system subject to random service

Abstract In this paper, a two-unit cold standby system is considered. Two models of system — functioning are studied here. In model 1 the units are non-identical, while in model 2, they are identical. In both the models, it is assumed that the distributions of the failure time, the switchover time and the repair time of the units are arbitrarily distributed. Further, the service facility is used both to install a standby unit and repair a failed unit and is assumed to be available at random according to a known distribution. The system characteristics, namely, 1. (1) the expected up-time of the system during the period (o, t] 2. (2) the expected time spent by the service facility for carrying out repair of the units during the period (o, t] and 3. (3) the expected time spent by the units in the switchover/installation state during the period (o, t] are studied by identifying the system at suitable regeneration epochs to carry out the cost-benefit analysis.