System characteristic and cost analysis of a two unit standby system with spare units

This paper deals with the stochastic analysis of a standby system having two main units and two spare units.A spare unit is only used for operation when both main units fail and if it fails,it is replaced by the new one until the repair of the failed main unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. Using renewal theoretical arguments, certain characteristics of the system are derived and using them the cost of the system is calculated. Particular cases of the model are also considered.     

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.     

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.     

Reliability analysis and optimization applications of a two-unit standby redundant system with spare units

Consider a two-unit standby redundant system with two main units, one repair facility, and n spare units. When the main unit has failed and the other is under repair, a spare unit takes over the operation and if it fails, it is replaced by a new one until the repair of the failed unit is completed. The system fails when the last spare unit fails while one main unit is under repair and the other has failed. In this paper, we derive expressions for 1) the distribution function of the first time to system failure, 2) the probability that the total number of failed spare units during the time interval (0,t] is n and 3) the mean of the total number of failed spare units in (0,t] and its asymptotic behaviour. Introducing costs incurred for each failed main unit and each failed spare unit, the expected cost per unit of time of the system was also derived. Finally an optinmization problem is discussed in order to compare the expected cost of the system with both main units and spare units with that of spare units only, and particular cases are considered.     

Availability of Priority Standby Redundant Systems

A priority standby system consisting of two repairable units is considered. One unit, the priority unit, is always in service except when it is failed. The standby unit is in service only for the duration of repair of the priority unit. Expressions are derived for the availability of such a system for both preemptive and nonpreemptive repair. The results assume reasonably general failure-time and repair-time distributions of the priority and standby units. The preemptive priority results are relatively insensitive to the form of the distributions.     

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.     

Two models for two-dissimilar-unit cold standby redundant system with partial failure and two types of repairs

This paper deals with the availability function and the mean time to the first failure for two models of a cold standby redundant system with two different types of repair. Each model consists of two dissimilar units. In the first model, the operative unit has two modes of operation, normal mode and partial failure mode. The standby unit has one mode of operation, normal mode. In the second model, each unit has three modes of operation, normal mode, failure mode and total failure mode. Both models are analyzed by the semi-Markov process technique, assuming that the failure time and repair time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Moreover, we give computer programs for calculating the MTSF for each model (see Appendix).     

Stochastic analysis of a two unit cold standby system with preparation time for repair

This paper deals with the cost-benefit analysis of a two unit cold standby system in which the cold standby unit replaces the failed operative unit after a random amount of time. Inspection is required to decide whether it needs type I or type II repair. Failure, repair, replacement and inspection time distributions are arbitrarily distributed. A repair man is not always available with the system, but is called for repair whenever the operative unit fails.     

Two-unit redundant system with inspection and adjustable rates

A two-unit redundant system is studied, in which one unit is operative and the other is a warm standby which replaces the operative failed unit instantaneously. To increase system availability, the failure rate of the operative unit and the repair rate of the failed unit adjust automatically according to the state of the standby unit. Also, after repair of the operative failed unit it is sent for inspection to decide whether the repaired unit is perfect or not. If the repaired unit is found to be imperfect, it is sent for post repair. Using a regenerative point technique in the Markov renewal process, several reliability characteristics of interest to system designers and operation managers are obtained.     

Reliability of Special Redundant Systems Considering Exchange Time and Repair Time

The reliability of a 2-out-of-3 parallel redundant system having a limited number of standby spare units is derived when the exchange of the failed unit for a spare unit is not instantaneous. The reliability can be represented in the form of a failure state diagram. When the number of standby spares and the repair rate are both small, the influence of the exchange rate is small. When the number of standby spares and the repair rate are both large, the influence of the exchange rate is large. The number of standby spares and the repair rate influence the probability that system failure occurs after all spare units have failed. The exchange rate strongly influences the probability of system failure during the exchange time.     

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.     

Stochastic analysis of standby system with duplex units

This paper investigates a mathematical model of a system composed of two units, one operative and the other cold standby. Each unit of the system is made of two non-identical parallel components and each component is made of n-elements. Henceforth we call each unit of the system a duplex unit. Failure and repair time distributions of each element of a component are negative exponential and vary from element to element, whereas the repair time distribution of a unit is arbitrary. Upon the failure of the operative unit the standby unit does not operate instantaneously. This type of situation may be found in many electronic networks. Several reliability characteristics of interest have been obtained.     

Two-unit cold-standby redundant system subject to random checking, corrective maintenance and system replacement with repairable and non-repairable types of failure

We consider a system comprising two identical units. Initially one unit operates and the other remains as a cold standby. At random intervals, checking is done to ascertain the need of Corrective Maintenance (CM). In case CM has to be carried out, the standby unit starts operating. While the unit is operative, it may fail. Failures are of two types, repairable and non-repairable. When the system fails with non-repairable failure of both the units, it is replaced. Several reliability characteristics of interest to system designers as well as to operations managers have been evaluated.     

Multi-state device redundant systems with common-cause failures and one standby unit

This paper presents two mathematical models. Model I represents a two identical unit active redundant system whose units may fail in either of the two mutually exclusive failure modes. Similarly, model II represents a two non-identical unit active parallel system whose units either fail or survive. In addition, models I and II comprise the occurrence of common-cause failures and one standby unit. Systems are only repaired when all the system units fail (including the standby unit). System repair times are arbitrarily distributed. Laplace transforms of the state probability equations are developed.     

Cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair

This paper deals with the cost analysis of a two dissimilar-unit cold standby redundant system subject to inspection and two types of repair where each unit of the system has two modes, normal and failed. It is assumed that the failure, repair, replacement and inspection times are stochastically independent random variables each having an arbitrary distribution. The cold standby unit replaces the failed operative unit after a random amount of time. An inspection is required to decide whether it needs type I (minor repair) or type 2 (major repair). In this system the repairman is not always available with the system, but is called whenever the operative unit fails. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Pointwise availability, steady-state availability, busy period by a server and the expected cost per unit time of the system are obtained. Certain important results have been derived as particular cases.     

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.     

Cost-benefit analysis of single server n-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a single-server n-unit system with an imperfect switch where failures of the items (units or the switch) are not detected unless either inspected by the server or when the system is down. Initially, one unit is put into operation (the switch is working at t = 0) and n − 1 units are kept as cold standbys. A failed unit is replaced by a standby if the switch and a standby are available. The server visits the system at random to check for the failed item and the check is instantaneous. When the system is down, either because of want of the standby or failure of the switch, the server is called for, and is assumed to arrive instantaneously. The revenue as well as the cost of repair are arbitrary functions of time. The expected net gain in (0, t) is evaluated assuming that all the life-time distributions are exponential and all the repair time distributions are arbitrary.     

Multi-standby system with repair and replacement policy

This paper investigates the mathematical model of a system composed of (m + 1) non-identical units—one functioning and m standbys. Each unit of the system has four possible states—normal, partial failure, total failure and repair facility—the last one meaning that the totally failed unit is being attended to at the repair facility where it might be either repaired or eventually rejected and replaced. The normal and partial failure states are up states while the other two are down states. The system breaks down when the (m + 1)th unit after total failure is finally rejected and no standby remains to replace it. Several reliability characteristics of interest to system designers as well as operations managers have been computed. Results obtained earlier are verified as particular cases.     

Cost analysis of a two unit cold standby system with preparation time for repair

This paper deals with a model of a two unit cold standby system with imperfect switch in which the repair man appears and disappears from the system randomly. The standby unit takes random switchover time for operation when the operative unit fails. Failure time of a unit, appearance and disappearance time of the repair man and switchover time of the standby unit are negative exponential, whereas repair time is arbitrary. The system is analysed by using regenerative point technique and several parameters of interest are obtained.