Reliability analysis of an (N+1)-unit standby system with ‘preemptive priority’ rule

This paper deals with a repairable standby system consisting of N+1 units and a single repair facility, in which unit 1 has preemptive priority both in getting operation and in getting repaired. Under the general assumptions that life time and repair time of unit 1 have general continuous distributions, we discuss the system's stochastic behavior and obtain the explicit expressions, both in transient state and in steady state, of some main interesting reliability indices of the system.     

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.     

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.     

Analysis of a system having super-priority, priority and ordinary units with arbitrary distributions

This paper deals with the analysis of a three non-identical unit cold standby system model. A single repairman is available to repair a failed unit. The priority in respect of operation and repair is being given to the units in order. All failure and repair time distributions are assumed to be general having different p.d.f.'s. Several measures of system effectiveness are obtained by using a regenerative point technique.     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

Stochastic behaviour of a two-unit (dissimilar) hot standby system with three modes

A hot standby system composed of two non-identical units is analysed under the assumption that each unit works in three possible modes—normal, partial failure and total failure. For each unit the failure time distribution is negative exponential and the repair time distribution is arbitrary. Breakdown of the system occurs when both the units are in total failure mode. There is only one repair service and when both the units are in the same mode, priority is given to the first unit in the matter of operation as well as repair. Several reliability characteristics of interest to system designers and operations managers have been evaluated.     

Comparison of two stochastic models for two-unit series system with cold standbys

Reliability characteristics are compared for two stochastic models of a system that has two non-identical units, arranged in series, each unit with its identical cold standby. The same set of assumptions is used for both models, except that in model 2 both of the standby units replace the failed operative unit instantaneously whereas in model 1 an operative failed unit is replaced by its corresponding standby unit (i.e. only one unit is replaced in this case). A single repair facility is available to repair the failed unit. Failure and repair time distributions are assumed to be negative exponential.     

Analysis of a repairable redundant system with delayed replacement

The 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. Failure time distributions of operative and standby units are exponential whereas all repair times follow arbitrary distributions. The system has been studied in detail by applying the results from the theory of semi-Markov process and mean-time-to-system-failure, steady-state availability, expected number of visits to a state, second moment of time in an up-state and expected profit of the system have been obtained.     

Analysis of a two unit standby system with partial failure and two types of repairs

A two dissimiliar unit standby system is analysed. The priority unit can either be in normal or partial operative mode. When the unit fails from the partial mode, it undergoes minor repair and the unit becomes operative with different failure rate. If this unit fails again, it goes to major repair after which it works as good as new. The standby unit while in use is either operative or failed. This non priority unit fails without passing through the partial failure mode and undergoes only one type of repair with different repair time distribution. Failure and repair time distributions are negative exponential and general respectively. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.     

Cost analysis of a two-dissimilar unit cold standby redundant system with administrative delay and no priority in repair

This paper deals with the cost analysis of a two-dissimilar unit cold standby redundant system with three modes for each unit under the assumption that there is administrative delay and no priority in repair. The failure time, repair time and administrative time distributions are general and arbitrary. Some reliability measures of interest to system designers have been obtained. Moreover some previous results are derived from the present results as special cases.     

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.     

Availability of a two-unit standby system with switchover time and proper initialization of connect switching

A 2-unit standby redundant system with connect switching (CS) is considered. The standby unit takes random switchover-time when the operative unit fails and CS is properly initialized in a random time after each repair. Failure-time distributions of units are exponential whereas all other distributions are arbitrary. In this note we employ the method of semi-Markov process to obtain steady-state availability of the system.     

On a two dissimilar unit cold standby system with switchover time and proper initialization of connect switching

This paper investigates the stochastic behaviour of a two dissimilar unit cold standby system with connect switching. The connect switch keeps this system in good connection with other systems. The standby unit takes random switchover time to assume the operative state when the operative unit fails. The failure times of the units and connect switch and the repair times of the units are assumed to have different arbitrary distributions. The mean waiting times in the states of the system and expression for the steady state availability of the system are obtained. The results obtained by Kumar and Lal and Laprie [1, 2] are derived from the present results as special cases.     

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.     

Stochastic behaviour of a two-unit standby system with better utilization of units

This paper obtains various measures of reliability of a two-unit redundant system with three modes. Upon partial failure of an operative unit the cold standby starts operation only when it becomes active. A single service facility is available (1) for repairing a partially or totally failed unit and (2) to activate the cold standby unit whenever required. Failure time distributions are negative exponential while repair and activating time distributions are general.     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

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.     

Cost analysis of a two-unit warm standby reliability system with two types of repair facilities

This paper deals with a two-unit warm standby system. These units are identical, but have different failure rates and repair time distributions, when failed in operating or standby state. If the unit fails in operating state, we wait for the repairman for some maximum time or until the other unit fails, and if the unit fails in standby state we wait for the repairman until the other unit fails. On the failure of the second unit or on the completion of the maximum time, we call the repairman immediately at the higher cost.The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results pertaining to some particular cases are also added.     

A two-unit priority standby system subject to random shocks and Releigh failure-time distribution

This paper deals with the cost-benifit analysis of a two-unit priority standby system subject to random shocks. The priority unit gets preference both for repair and operation over the ordinary unit and has three modes- Normal, Quasi-normal and Total-failure. The ordinary unit has only two-modes- Normal and Total-failure. The distributions of shock-time, repair-time of the ordinary unit and failure time of the priority unit are negative exponential. The distribution of the repair-time of the priority unit is taken to be general while the time to failure of ordinary unit follows Releigh distribution. Various characteristics related to system effectiveness have been obtained by using the regenerative point technique.