A two-unit duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.     

Common-cause failure analysis of a redundant system with non-repairable units

This paper presents a newly developed generalized expression for mean time to failure, MTTF, of a non-repairable identical unit parallel system with warm standby and common-cause failures. Also presented is a modified version of this formula that takes into account the repairability of the warm standby and/or switching mechanism. Generalized expressions for system reliability and variance of time to failure are presented along with some tables and plots of system reliability and MTTF.     

Reliability analysis of a system with a mixture of warm and cold standby

A single-server two-unit standby system with two modes of each unit—normal and total failure—is considered. The standby units are repeatedly interconverted after a random time from warm to cold and cold to warm. Upon failure of the operative unit, the standby unit, if it is warm, starts to operate instantaneously; otherwise, the system goes down until the cold standby starts to operate. System failure occurs when both units fail totally. Identifying the system at suitable regenerative epochs, the integral equations are set up and the expressions for reliability and mean time to system failure (MTSF) are obtained. The graphical behaviour of MTSF is also studied in a particular case.     

A note on the cost analysis of an n-unit system with spares

This paper deals with the cost analysis of a non-repairable standby system consisting of (n + m) identical units; n-units are needed for the system to function, while the remaining m units are warm standbys. The online and standby units have different constant failure rates. There is no facility for repair. Functions expressing the probability that in (0, t) there are i on-line failures and j standby failures and thereby the reliability of the system. MTTF and the expected profit are obtained. Finally, a numerical example with graphs is also given to highlight important results like the reliability of the system, MTTF and the expected profit.     

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.     

A two non-identical three-state units redundant system with common-cause failures and one standby unit

This paper presents a mathematical model for predicting a two non-identical three-state active units redundant system with common-cause failures and one standby unit. The units may fail in either of two mutually exclusive failure modes or by the occurrence of common-cause failures. System is only repaired when all the units fail (including the standby unit). The failure rates of units are constant and system repair times are arbitrarily distributed. Laplace transforms of the state probabilities are derived.     

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.     

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.     

A multi-standby multi-failure mode 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 standby. Each unit of the system has three possible states—normal, degraded and failed. We consider two types of repair facilities—overhaul and minor repair. 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.     

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.     

The effect of preventive maintenance on a two-dissimilar unit standby system

A system which consists of two dissimilar units, one as a main unit the other as a standby, is considered, taking account of repair and preventive maintenance (PM). The standby unit cannot fail and the switch is perfect. The Laplace transform (LT) of the survivor function of the time to the first system failure (TFSF) and the mean are derived. Finally, a theorem about the effect of maintenance is proved.     

Reliability analysis of a complex system with a deteriorating standby unit under common-cause failure and critical human error

This paper presents a stochastic model representing two units and one as a standby unit with critical human error and common cause failure. The deteriorating effect of the standby unit on the system is studied. Repair times of the failed system are arbitrarily distributed while all other transition time distributions are negative exponential. The analysis is carried out using supplementary variable techniques and various measures of system effectiveness such as pointwise availability, steady-state availability, MTTF and variance of the time to failure of the system are obtained.     

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.     

A note on a multi-unit system with r repair facility

This paper deals with a system consisting of (n + m) identical units; n units are needed for the system to function and the remaining m units are warm standby supported by r repair facility. The online and standby units have different but constant failure rates; the repair time distribution for the standby unit is taken to be a constant and the distribution for the online unit is arbitrary. Functions describing the behaviour of all the other units when one unit is undergoing online repair are studied and an earlier result is recovered as a special case.     

A semi-regenerative process of two-unit warm standby system

This paper deals with two identical units warm standby system; a failure of operating unit can be detected at any time but a failure of standby unit can not be done until a system is inspected. We are able to look upon the stochastic behavior of our model as that of semi-regenerative process. The pointwise unavailability and the steady state unavailability of the system are derived by using the limit theorem of semi-regenerativeprocess. Further, we shall discuss the optimum inspection period minimizing the steady state unavailability. A numerical example is presented.     

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.     

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.     

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.     

A two unit series system with correlated failures and repairs

This paper investigates a stochastic model of a system having two identical units, each with two components, arranged in series configuration. Upon failure of a component of the unit, the standby unit replaces the failed unit instantaneously. It is assumed that the joint distribution of the repair and failure times of a component are bivariate exponential. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are verified as a particular case. The MTSF and availability have also been studied through graphs.     

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.