Two-unit redundant system with random shocks and inspection

The present paper deals with a two unit cold standby system, in which the failure of an operating unit is subject to random shock and internal stress. 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 regenerative point technique several effective measures of reliability are obtained.     

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.     

Two-unit standby reliability system subject to effective and non-effective random shocks

This paper considers a system consisting of two units. The system experiences shocks after certain random intervals. These random intervals are independently and identically distributed each with a general probability density function. Further, the shocks are classified into three types according to the effect of the shocks on the system: Type I, the shock that has no effects on the system, Type II, the shock increases the failure rate and Type III, the shock that fails the system. The system can fail either due to a shock of Type III or due to the internal stress and strain of the operation of the unit or due to two successive shocks, the first shock being of Type II. The repair times of the units are assumed to be exponentially distributed. The mean time to system failure (MTSF), steady state availability of the system and expected number of times the repairman is required are investigated. Finally, MTSF-shock rate and steady state availability-shock rate figures are drawn for special cases and certain interesting results are observed therefrom.     

Stochastic behavior of a two-unit cold standby redundant system subject to random failure

The present paper deals with a stochastic model of a two-unit cold standby redundant system subject to random failure. The random failure occurs at random times which follow an exponential distribution. Using a regenerative point technique in the Markov-renewal process, several reliability characteristics are obtained. The mean time to system failure function is studied graphically.     

Two-unit redundant system with inspection and adjustable rates

A two-unit redundant system is studied, in which one unit is operative and the other is a warm standby which replaces the operative failed unit instantaneously. To increase system availability, the failure rate of the operative unit and the repair rate of the failed unit adjust automatically according to the state of the standby unit. Also, after repair of the operative failed unit it is sent for inspection to decide whether the repaired unit is perfect or not. If the repaired unit is found to be imperfect, it is sent for post repair. Using a regenerative point technique in the Markov renewal process, several reliability characteristics of interest to system designers and operation managers 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.     

One unit reliability system subject to random shocks and preventive maintenance

In this paper we consider two systems each consisting of one unit. The operating unit is subject to random shocks which occur at random times. Due to the shock the following may happen: (i) The unit is not at all affected by the shock; (ii) the failure rate of the unit increases from λ₀ to λ₁; (iii) the unit fails. The failure time of the unit is exponentially distributed. The repair, shock and preventive maintenance times follow general distributions. In System 2 there is provision of preventive maintenance, whereas in System 1 there is no provision of preventive maintenance. There is one repair man available in each system. In this paper the mean time to system failure, steady state availablities and the impact of shocks on these are studied. In System 2 the effect of the preventive maintenance on MTSF and steady-state availabilities is investigated.     

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.     

Reliability analysis of a two state repairable parallel redundant system under human failure

In this paper, the investigations have been carried out for the MTTF and reliability analysis of a repairable two-unit redundant electronic equipment having two states under human failures. The two-unit repairable parallel redundant system suffers two types of failures; viz; unit failure and human failure. Human failure brings the system to a complete failure stage. There is only one server who is always available. Laplace transforms of the probabilities of the complex system being in up and down states have been derived and have been inverted to obtain time dependent probabilities. Two graphs have also been given in the end.     

Cost analysis of a two unit repairable system subject to on-line preventive maintenance and/or repair

The purpose of this paper is to carry out the cost analysis of a two-unit repairable system subject to on-line preventive maintenance(PM) and repair. The policy adopted here is that the on-line PM work of the operating unit is undertaken followed by repair work of the failed unit(if any). All the random variables that. arise in the analysis are assumed to be independently and arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and system of integral equations satisfied by various state probabilities corresponding to various initial conditions are obtained. An iterative numerical method is used to solve the system of integral equations. A cost function is built based on the expected number of various jobs completed by the server in [0, t].     

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.     

Profit analysis of a one-server one-unit system with partial failure subject to random inspection

This paper deals with the cost-benefit analysis of a single-server one-unit system with partial failure, which is subject to random inspection. An inspection policy model is considered in which the partial failure of the unit is detected only by inspection, but complete failure of the unit is detected instantaneously without inspection. The system is observed at suitable regenerative epochs in order to obtain several economics-related system characteristics. Explicit results are obtained in a few particular cases. Graphs are also given.     

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.     

Single-unit system with corrective maintenance at random checks governed by probabilities in a geometric progression

A system which comprises only one unit and a single server is considered. While the unit is in operation, at random intervals it is subjected to checks for corrective maintenance (CM). While the unit is under CM, it is also working and thus may fail. The probabilities that the unit will not undergo CM at random checks are in geometric progression (p, p², p³,…), whereas the probabilities that the unit will undergo CM are (1 − p, 1 − p²,…). We consider three models, and obtain the mean time to system failure and steady-state availability of the system for these models.     

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.     

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.