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.     

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 two-unit-standby redundant system with administrative delay in repair

A two-unit cold standby redundant system is analysed under the assumption that administrative time is spent in locating the repairman and getting him available at the system location. The administrative time distribution is assumed to be exponential and whereas the repair and failure time distribution are exponential and arbitrary. 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.     

Dependability of a Complex System with General Waiting Time Distributions

This paper considers the possibility of the inclusion of general waiting time distributions for failed system while examining its behavior with regard to dependability. The probabilities that the system is operable, waiting for repair and under repair are obtained. Some particular cases are also discussed in details. The behavior of the complex system under steady state has also been examined. It may be noted that in the particular case when the simple system is put under repair instantaneously the results correspond to those obtained by Hosford [1].     

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.     

The reliability function and the availability of a duplication redundant system with a single service facility for preventive maintenance and repair

This paper concerns a two-unit system with a cold standby and a single service facility for the performance of preventive maintenance and repair. Explicit expressions for the Laplace transforms of the availability of the system, the reliability, the mean down time during (0, t) and for the mean time to system failure have been obtained under the assumption that the failure times, the inspection times, the repair times and the preventive maintenance times of the two units are governed by distinct arbitrary general distributions. The results obtained by Srinivasan and Gopalan and by Gopalan and d'Souza are derived from the present results as special cases.     

Repairable consecutive-k-out-of-n: G systems with r repairmen

In this paper, we study repairable consecutive-k-out-of-n: G systems with r repairmen. The systems are either circular or linear. It is assumed that the working time, and the repair time of each component in the system are both exponentially distributed; and every component after repair is 'as good as new'. Each component is classified as either a key component, or an ordinary one according to its priority role to the system's repair. By using the definition of generalized transition probability, the state transition probabilities of the system are derived. Some important indices related to repairmen are obtained, and some reliability indices are derived by using the Laplace transform technique. Numerical examples are then studied in detail to demonstrate the theoretical results developed in the paper. The proposed method, and its numerical illustrations for the examples verify the validity & generality of the studied system.     

Analysis of a two-unit system subject to repair and preventive maintenance with non-linear revenue and costs

The cost-benefit analysis of a one-server two-identical-unit cold standby system subject to repair and preventive maintenance (PM) with non-linear revenue and costs is presented in this paper. Initially, one unit is in operation and the other is cold standby. When a unit fails, it is taken up for repair or waits for repair if the server is busy. The latter results in a system breakdown. If a unit returns from service (repair or PM) and the other unit is operating, the operating unit is taken up for PM. The revenue obtained by operating a unit for an uninterrupted interval of time is some function of the length of the interval. Similarly, the cost of a repair or PM action is a function of the length of the repair or PM time, respectively, for that action. With the help of regeneration point technique, the expected net revenue over an interval (0,t] is obtained. It is shown that the results for the special case when the revenue and cost function are linear agree with previously obtained results.     

Some characteristics of a man-machine system operating subject to different weather conditions

This paper deals with some characteristics of a single unit of a man-machine system operating under different weather conditions. It is assumed that the failure, repair and change of weather conditions (normal-stormy) 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, pointwise availability and steady-state availability of the system are obtained. Several important results have been 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.     

Some characteristics of a two-dissimilar-unit cold standby redundant system with three modes

This paper deals with the stochastic behaviour of a two-dissimilar-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure. It is assumed that the failure and repair 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-Stiektjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady state availability of the system are obtained. Certain important results have been derived as particular cases.     

A renewable single-server queueing system with priorities

A single-server queue with a triple priority system is considered in this paper. The server can fail during its occupation time and is sent for repair immediately.The stationary probabilities of the different states of the system are studied, under the assumption that the arrival time and the service time for the three kinds of customers, and the repair time, all have Poisson distributions with different parameters. The results obtained before, in [Mokaddis et al., Eighth International Congress for Statistics, Computer Science, Social and Demographic Research, Vol. 4, pp. 31–58 (1983)] in the case of a double priority, are derived from the present results as special cases. Moreover the mathematical expectation of the number of customers and the average waiting time of both kinds of customers and more characteristics of the system, in the case of double priority, are obtained. Also, in this paper, we study the system without priority, in the cases of both a triple priority system and a double priority system.     

A single unit multicomponent system subject to various types of failures

This paper investigates the mathematical model of a reparable system with several possible states of operation, failure and repair. There is also an inspection facility for deciding whether on failure, the system needs minor repair or overhaul. Repair rates are arbitrary functions of the time spent. All other transition rates are constant. Several reliability characteristics of interest to system designers as well as operations managers have been computed and results obtained earlier are verified as particular cases.     

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

The object of this paper is to carry out the availability and the reliability analysis of a two-unit system with a warm standby having a single service facility for the performance of preventive maintenance and repair. The failure times, the repair times, the inspection times and the preventive maintenance times of the main unit and of the standby one are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. Explicit expressions for the mean down time of the system and for the mean time to system failure are obtained. Some previous results are derived from this work as special cases.     

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.     

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.     

On a two-unit standby redundant system subject to repair and preventive maintenance

This paper derives the mean life and the Laplace-Stieltjes transform of the distribution of the first time to system-down for two dissimilar units standby redundant system with repair and preventive maintenance.Further, special cases of the results obtained here coincide with earlier results for the two-unit standby redundant system. The case when the system is not subject to preventive maintenance is considered as a particular case.     

Three-phase queueing servicing system with renewable servers

A three-phase queueing servicing system is considered in this paper. The servers can fail during their occupation time. A failed server is sent to be repaired immediately. The stationary probabilities of the different states of the system are studied under the assumption that the arrival time, service time, failure time and repair time of the servers all have a Poisson distribution with diferent parameters. Also the mathematical expectation of the number of customers in each phase is obtained. Finally, the results in Mokaddis et al., Ninth International Congress for Statistics, Computer Science, Social and Demographic Research, Ain Shams University, 31 March–10 April, 1984, are obtained as special cases from the results in this paper.     

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.