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 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.     

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.     

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 redundant system with switchover time

There is a two-unit standby redundant system. Standby is kept in cold state. Whenever one unit is operating and the other is in the waiting standby state, switching is initiated on the latter after a random time. If the operative unit fails before the time to initiate switching action on the waiting standby unit, the system fails and the failed unit immediately undergoes repair type 2 along with the switching. However, if the operative unit fails when the other unit is as standby (after switchover), the failed unit undergoes repair type 1 and the unit as standby takes over the operation. All the distributions are arbitrary except failure-time, which is exponential.The system is defined with the help of states which generate a pseudo semi-Markov process. Abundant use of results from the theory of SMP has been made to obtain a large number of parameters which measure reliability characteristics of the system viz. MTSF, steady-state availability, expected number of visits to a state, conditional transition probabilities, first passage time distributions, expected profit rate, etc. Numerical examples are included to illustrate the results.     

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.     

On the effect of random operation and preparation time for operation in a two unit cold standby system

This paper deals with the stochastic analysis of a two unit cold standby system in which an operative unit is stopped after a random operation time and the standby unit is prepared for operation before it goes to an on-line state. All the time distributions are assumed to be negative exponential. Various reliability characteristics are obtained in order to analyse the expected profit earned by the system. Lastly, a numerical example is discussed to highlight important results.     

CHE failure in a two-unit standby system with slow switch, repair and post repair

A mathematical model of a two-unit cold standby system with critical human errors (CHE) and slow switch is investigated. The CHE leads to complete system failure, and repair and post-repair are needed before the system can be put back into operation. Slow switch means that on failure of the operative unit the switch puts the standby unit into operation after a random time. Failure time and switchover time distributions are negative exponential whereas all the repair and post repair time distributions are general. Using a regenerative point technique, we obtain various reliability characteristics which can be used to carry out the cost-benefit analysis. In a particular case, the behaviour of the cost function is also studied graphically.     

A redundant system with non-instantaneous switchover and “preparation time” for the repair facility

This paper discusses two models of two-unit standby redundant systems in which the switchover time is a random variable and the repair facility is not available for a random time immediately after each repair completion. In model I the probability distributions of the life time of the online unit and switchover time are general while all the other distributions are exponential. Model II is a cold standby system in which the probability distributions of the “preparation time” of the repair facility is exponential and all the other distributions are general. Using the regeneration point technique the availability functions of the two systems are determined. Several special cases are also discussed.     

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.     

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.     

A Two-Unit Cold Standby Repairable System with One Replaceable Repair Facility and Delay Repair: Some Reliability Problems

1 Model and Assumption In reliability analysis of repairable systems, it is usually assumed that the repair facility neither fails nor deteriorates as well as the repairman is instantaneously available. So that the repair is started immediately upon the failure of a unit provided that he is not busily repairing another unit. However, in actual practice, the repair facility in a repairable system is subject to failure and can be replaced (or can be repaired) after it fails, and certain delay ac…     

Reliability analysis of a two-unit cold standby system with inspection, replacement, proviso of rest, two types of repair and preparation time

This paper deals with a two-unit standby system-one operative and the other in cold standby. Single repair facility which acts the inspection, replacement, preparation and repair. We wait the serverman for some maximum time or until the other unit fails. The analysis is carried out on the supposition that all time distributions are general except failure, delivery, replacement and inspection time distributions are exponentials. Stochastic behavior of the system has been studied by the regeneration point technique and several parameters of interest are obtained. Numerical results pertaining to some special cases are also added.     

Cost analysis of a two dissimilar cold standby system with preventive maintenance and replacement of standby

This paper deals with the cost analysis of a two dissimilar unit cold standby redundant system with preventive maintenance, under the assumption that the standby, being substandard, is not repairable and has to be replaced on failure. The failure times have negative exponential distributions while all other distributions involved are general.     

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.     

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.     

Profit analysis of a two-unit standby system with two types of repair and preventive maintenance

This paper deals with the profit analysis of a two-unit cold standby system with two types of repairs—cheap and costly. Cheap repair becomes available after a random amount of time while costly is available instantaneously. The preventive maintenance (P.M.) of an operative unit starts at random epochs of time and is done only if the other unit is in standby. The distribution of time to accomplish P.M. is negative exponential while the distributions of failure time, repair times and time to commence P.M. are general. Various economic reliability measures of interest to system designers as well as operation managers have been obtained using regenerative point technique.     

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.     

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-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.