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.     

Stochastic behaviour of a two-unit cold standby redundant system with administrative delay and two types of repairs

In this paper we consider a two-unit cold standby redundant system in which each unit works in three modes—normal, partial failure and total failure with two types of repairs (major and minor) after partial failure mode, with administrative delay to locate expert repair man for major repair. The administrative time distribution is assumed to be exponential, whereas the repair and failure time distributions are exponential and arbitrary. The technique of regenerative processes is applied to obtain various reliability characteristics of interest to system designers.     

Analysis of a two-unit cold standby system with three modes

This paper analyses a two-unit cold standby system under the assumption that each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units are exponential, whereas repair time distributions are arbitrary. Breakdown of the system occurs when both the units are in total failure mode. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

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.     

Two models for two-dissimilar-unit standby redundant system with three types of repair facilities and perfect or imperfect switch

This paper deals with two models for two-dissimilar-unit cold standby redundant systems under the assumption that each unit works in three different modes—normal, partial failure and total failure. In model I, the switch is perfect but it is imperfect in model II. The failure and repair times are assumed to have different arbitrary distributions.Explicit expressions for the mean time to system failure and the availability analysis are obtained in each model. A computer program is shown for comparison between the two models.     

Reliability analysis of a two-unit cold standby redundant system with two operating modes

This paper considers a two unit cold standby redundant system subject to a single repair facility with exponential failure and general repair time distribution. Each unit can work in three different modes — normal, partial failure and total failure. There is a perfect switch to operate the standby unit on total failure of the operative unit. The system has been analysed to determine the reliability parameters e.g. mean time to system failure (MTSF), steady state availability, mean recurrence to a state and expected number of visits to a state, first two moments of time in transient state, by using the theory of Semi-Markov Process. Howard's reward structure has been super-imposed on the Semi-Markov Process to obtained expected profit of the system. A number of results obtained earlier are derived as particular cases.     

Cost analysis of a two-unit standby system under the influence of earthquakes

This paper deals with two models. In model 1, which is cold standby, when an earthquake comes the operation of the unit is stopped. In model 2, which is warm standby, a medium intensity earthquake will cause a short circuit failure mode. The repair is available immediately upon calling. In model 1, the failure rate is taken to be constant whereas the repair time distribution is arbitrary. In model 2, the failure and repair time distributions are considered to be arbitrarily distributed. Applying the regenerative theory in Markov renewal processes, various reliability characteristics of interest have been explicitly obtained.     

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.     

Stochastic behaviour of a two-unit cold standby system with three modes and allowed down time

This paper discusses the stochastic behaviour of a two-unit cold standby redundant system under two very general sets of conditions: (i) each unit of the system having three different modes of working—normal, partial failure and total failure; (ii) breakdown of the system occurring when with both the units in total failure mode, the system is not regarded as failed (the system fails only when the breakdown does not terminate within the allowed down time). Failure-time distributions of units are exponential, whereas repair time distributions are arbitrary. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated.     

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.     

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.     

Analysis of a two-unit standby system with three modes and imperfect switching device

In this paper we study the effect of imperfect switching on a two-unit cold standby system in which each unit works in three different modes—normal, partial failure and total failure. Failure time distributions of units are negative exponential whereas repair time distributions of units and switch are general. The switch is available at the time of need with probability p(= 1?q). Using the regeneration point technique reliability characteristics of interest to system designers as well as operation 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.     

Switch failure in a two-unit standby redundant system

In this paper we study the effect of imperfect switching on a two-unit standby redundant system, in which each unit works in three different modes (normal, partial failure and total failure) when the failure time distributions are exponential with different means and the repair times are arbitrarily distributed. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and particular cases are shown to corroborate earlier results.     

Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

Analysis of a two-dissimilar unit cold standby redundant system subject to inspection and random change in units

This paper deals with the stochastic behaviour of a two-dissimilar unit cold standby redundant system with random change in units. In this system each unit works in two different modes—normal and total failure. It is assumed that the failure, repair, post repair, interchange of units and inspection times are stochastically independent random variables, each having an arbitrary distribution. 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. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure are obtained. Certain important results have been derived as particular cases.     

Some applications of semi-regenerative processes to two-unit warm standby system

We deal with a two-unit warm standby system with a single repair facility; a failure of an operating unit can be detected immediately but a failure of a warm standby unit can not be observed until the system is inspected. According to whether the operation of the system is stopped or not during each inspection, we consider two models. We describe the stochastic behavior of the system as a semi-regenerative process, and the pointwise availability and the steady state availability of the system are derived applying the limit theorem of semi-regenerative processes. Further, we shall discuss the optimum interinspection time maximizing the steady state availability for Model 1.     

Busy period analysis of a two-unit warm standby system with imperfect switch

Busy period analysis of a two-unit warm standby system with two modes (normal and total failure) and imperfect switching device has been studied by considering the availability of a single repair facility. Failure time distributions of the units are negative exponential whereas repair time distributions of units and switch are arbitrary. Using the regeneration point technique several reliability characteristics have been obtained. Moreover, the present model employs switch failure in non-regenerative states, for the first time.     

Reliability analysis of multi-unit cold standby system with two operating modes

This paper investigates the mathematical model of a system composed of n dissimilar units—one functioning and others either failed or cold standbys. Each unit of the system has three possible modes—normal, partial failure and total failure. There is a perfect switch to operate the leading standby unit on total failure of the operative unit. The failure and repair times of each unit are assumed to follow arbitrary distributions. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are derived as particular cases.     

Cost analysis of a two-unit cold standby system with two types of operation and repair

This paper deals with the cost analysis of a single-server two-identical unit cold standby system and two types of repair—minor and major. The unit requires minor repair if it fails for the first time. The major repair is required only when the unit fails after the minor repair. Upon minor repair the unit does not work as a normal unit but as a quasi-normal unit which has a different (increased) failure rate from that of a new one. Upon major repair the unit works as good as new (normal unit). Failure time distributions are negative exponential whereas repair time distributions are general. Using regeneration point technique the system characteristics of interest to system designers and operations managers have been obtained.