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 a system with inspection, replacement and two types of repair

This paper investigates a mathematical model of a system composed of two units—one operative and the other in cold standby. There is a single repair facility which serves the triple role of inspection, repair and replacement of a failed unit. After inspection, the unit goes to minor (major) repair with probability p(q = 1 − p). Whenever the failed unit goes to major repair, an order is immediately placed for a new unit to replace the unit under major repair. Failure, inspection and delivery time distributions are negative exponential, whereas repair time distribution is arbitrary. The system is analysed in detail using the regenerative point technique and several reliability characteristics of interest to system designers and operation managers are obtained. Earlier results are verified in particular 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.     

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.     

Reliability analysis of a system with preventive maintenance, inspection and two types of repair

This paper considers a two-unit (identical) parallel system with facilities of preventive maintenance, inspection and two types of repair, type I and type II. These two types of repair facilities have a considerable difference in their costs. Both the units of the system can fail simultaneously due to some common-cause or they can fail one by one. The time of failure of a unit and system, the commencement of maintenance and inspection are assumed to be constant while repair and maintenance times are arbitrarily distributed. Various measures of system effectiveness are evaluated using regenerative point technique.     

A three-unit standby redundant system with repair and preventive maintenance

This paper deals with the reliability of a renewable three-unit system under preventive maintenance activity. The Laplace transform of the reliability function and the mean lifetime of the system have been obtained under the assumption that the failure times, repair times, inspection times and maintenance times are random variables having different distributions. Some special cases also have been obtained.     

Cost-benefit analysis of a system with intermittent repair and inspection under abnormal weather

This paper studies a repairable system with intermittent repair. Weather under which the system works changes randomly (in time) from normal to abnormal weather and vice-versa. By intermittent repair, we mean that the repair facility is not available instantaneously but takes random time to be available. The system operating under abnormal weather is sent for inspection randomly with Poisson process. Failure rates of the system and rates of change of weather are constant while repair times, inspection time and inter-inspection time are arbitrarily distributed. The system is analysed by using regenerative point technique to obtain various economic measures such as mean time to system failure, steady state availability, probability that the repairman is busy, expected number of visits by repairman and expected profit earned by the system.     

Cost-benefit analysis of a one-server two-unit imperfect switch system with delayed repair

This paper deals with the cost-benefit analysis of a one-server two-unit system with imperfect switch where the server is summoned upon failure of an item (i.e. unit or switch). The amount of time the server takes to arrive is a random variable, distributed arbitrarily. The server leaves when there is no item waiting for repair. The repair times are arbitrarily distributed whereas all failure rates are constant. Initially one unit is switched on (switch is working at t = 0) and the other is kept as cold standby. Explicit expressions for the expected uptime in (0, t) of the system, busy period of the server due to repair of a unit and that of the switch are obtained to carry out the cost-benefit analysis.     

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.     

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 redundant system with two types of failure

This paper deals with the analysis of a system model consisting of two units, in which one is operative and the other is on cold standby. The failure of an operative unit may be caused by a machine as well as by random shocks which occur after a certain interval of time.Using the regenerative point technique in Markov renewal processes, several effective measures of reliability are obtained.     

Cost analysis of a two unit, three state standby redundant complex system with two types of repair facilities under waiting

This paper deals with the cost analysis of a two unit, three state standby redundant complex system, incorporating the concept of two types of repair facilities, viz. minor and major repair. The concept of waiting time for the major repair of the failed system has also been introduced. The system can suffer from two types of failures, namely catastrophic and partial. Failure and waiting times of units follow exponential time distribution, whereas repair of units follows general time distribution. Using the supplementary variable technique, Laplace transforms of probabilities of the complex system being in various states have been computed. In addition, using Abel's lemma, steady state behaviour has also been examined. Some important graphs have been sketched at the end to highlight the important results.     

Cost-benefit analysis of a one-server two-unit cold standby system with repair and age replacement

This paper deals with the cost-benefit analysis of a one-server two-identical-unit cold standby system with repair and preventive maintenance (PM). The PM is of the age replacement type, where, if a unit has been in operation for a certain period of time, which may be a random variable, and if the other unit is in standby, the operating unit is taken off for PM. The expected net revenue in the interval [0,t) is obtained using two different approaches. The first approach is more general and allows nonlinearities in the revenue and costs. It is assumed that the revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of that interval. Similarly, the cost of a repair or PM action is function of the length of the repair or PM time, respectively, for that action. The second approach assumes that the revenue, repair cost and PM cost vary linearly with time. The pointwise availability is derived. The busy period of the server is divided into time spent in performing repair and time spent on PM. The expected net revenue in [0,t) is obtained. Both techniques make use of regeneration points. It is finally shown that the results of the first approach under assumptions of linear revenue and cost functions reduce to those of the second approach.     

Stochastic analysis of a two-unit redundant system with two types of failure

The present paper investigates a stochostic model of a two-unit warm standby system with a single repair facility. Before repair, the failed unit is sent for fault detection to decide whether it failed due to machine defect or critical human error. The probability of having machine defect and C.H.E. has been fixed. Using the regenerative point technique in the Markov renewal process various measures of system effectiveness are obtained.     

A parallel redundant complex system with two types of failure under preemptive-repeat repair discipline

This paper presents the availability analysis of a complex system, which consists of two s-independent repairable subsystems A and B in series (1-out-of-2:F). Subsystem A has two identical units arranged in parallel redundancy (1-out-of-2:G), sub-system B is a single unit with two types of failure, viz., partial and catastrophic. There is only one repair facility, which is always available. The failure and repair times for both subsystems follow exponential and general distributions respectively. The model so developed is analysed under “preemptive-repeat repair discipline”. By employing supplementary variable technique Laplace transforms of various probability states are obtained along with steady-state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any time.     

Behaviour of a two-unit standby redundant system with imperfect switching and delayed repair

A 2-unit standby redundant system with imperfect switchover is considered. A repair facility is assumed to be available only at a fixed proportion of time. Failure-time distributions of units are exponential whereas repair-time distributions, distribution of time for the repairman to become available are general. The system has been investigated in detail by the help of semi-Markov process and closed form results are obtained for mean-time-to-system-failure, steady-state availability, expected number of occurrences of a state, expected profit and second moment of time in up state. Behaviour of several parameters has also been studied and several earlier models are included as particular cases.     

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 two-server, two-unit, warm standby system with different types of failure

This paper deal with a two-server, two-unit redundant system in which one unit is operative and the other is a warm standby. The operative unit can fail completely, either directly from the normal state or via a partial failure, while the warm standby unit only fails due to minor faults within it. One repairman is “regular”, he always remains with the system, and the other is an “expert” who is called when needed. The system has been analysed to determine the various reliability measures by using semi-Markov processes and regenerative processes. Numerical results and some graphs pertaining to a particular case are also included.