Cold Standby System Research Articles

Stochastic analysis of a two-unit cold standby system subject to maximum operation and repair time

A two-unit standby system is considered under excess time stochastic behaviour, i.e. the failure and repair time of the on line (off line) unit is exceeding some prespecified value. Whenever an operating unit crosses a prespecified operation time, it is sent to preventive maintenance and when repair of a failed unit crosses a prespecified time, the unit is rejected and replaced by a new unit. Using the regeneration point technique, certain characteristics of the system are derived and the cost of the system is calculated. Particular cases of the system are also considered.

Stochastic analysis of a priority unit standby system with repair machine failure

Abstract This paper deals with the analysis of reliability characteristics of a two-unit (priority ‘p’ and ordinary V) cold standby system model under a very practicable assumption that the repair machine may also fail during the process of system effectiveness. The analysis is obtained by using a regenerative point technique.

The time-dependent availability of repairable m-out-of-n and cold standby systems by arbitrary distributions and repair facilities

In this paper we present a method to compute the time-dependent availability of repairable m-out-of-n redundant and cold standby systems by arbitrary distributed time to unit failure and time to unit repair and arbitrary number of repair facilities. The method allows us to consider systems with a large number of units. It is accurate in results and efficient in computations.

ANALYSIS OF COLD-STANDBY SYSTEMS — CUTTING AND CLUSTERING THE STATE SPACE

In this paper two methods, namely cutting and clustering the state space are discussed to find approximate solutions to n-unit cold-standby system with a single repair facility. It has been assumed that the failure rate is constant and the repair time is arbitrarily distributed. A mathematical model is developed using semi-regenerative phenomena and systems of convolution integral equations satisfied by various state probabilities corresponding to different initial conditions are obtained. Explicit expressions for the availability and the reliability of the system are obtained. An iterative method is used to solve the systems of integral equations obtained and a comparative study has been carried out between exact and approximate solutions.

Analysis of a two unit standby system with preparation time and correlated failures and repairs

This paper analyses a two-unit cold standby system with preparation time for the repair of a failed unit. The joint distribution of failure and repair times of each unit is taken as bivariate exponential. Regenerative point technique has been used to obtain various reliability characteristics of interest. The behaviour of MTSF and steady state availability have been studied through graphs.

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.

Probabilistic analysis of a three unit cold standby redundant system with repair

This paper deals with a three unit cold standby system where the lifetime of the unit and the repair time are random variables with arbitrary distributions. Integral equations are set up to obtain expressions for various quantities of interest to system designers. Special cases are also considered. Using the various system measures, a comprehensive cost function is constructed and its optimization studied.

Probabilistic analysis of a two-unit cold standby system with instructions at need

A two-unit cold standby system with an expert repairman and his assistant is examined. If the expert repairman is busy in repairing a failed unit and at that time the second unit fails, the assistant repairman repairs the latter unit. The assistant repairman needs or does not need instructions for doing repair with probability p and q respectively. Using a regenerative point technique, various measures of system effectiveness are obtained.

GERT analysis of a two-unit cold standby system with repair

This paper presents a GERT (Graphical Evaluation and Review Technique) analysis of a two-unit cold standby system. The various performance characteristics of the system have been derived analytically.

Probabilistic analysis of a n-unit cold-standby system with general failure and repair time distributions

In this paper, a n-unit cold-standby system with a single repair facility is analysed under the assumption that the failure and repair times are arbitrarily distributed. A mathematical model is developed using semi-regenerative processes. Systems of integral equations satisfied by various states probabilities corresponding to different initial conditions are obtained. Explicit expressions for the availability, reliability and the expected busy period of the service facility are obtained. Two special eases when either the failure or repair rate is constant are discussed. A particular ease with three units is analysed numerically by assuming Weibull distribution for failure time and normal distribution for repair time.

A cold standby system with arrival time of server and correlated failures and repairs

This paper presents the analysis of a two unit cold standby system with random arrival time of a server. The failure and repair times of each unit are assumed to be correlated and their joint density is taken as bivariate exponential. Using the regenerative point technique, various reliability characteristics of the system have been obtained. The behaviour of MTSF and steady state availability have also been studied through graphs.

Analysis of a two unit redundant system with optimum interchangement time

By considering a two unit cold standby system with single repair facility, we in the present paper give an analytical approach for finding optimum interchangement time of units for giving rest to the operative unit. In this paper, for attaining increased reliability of the system, the operative and the standby units are interchanged after the optimum interchangement time.

Profit analysis of two-unit standby system with rest period for the operator and correlated failures and repairs

This paper analyses a two-unit cold standby system with the provision of rest for the operator. After working a random amount of time, the operator needs to rest for a random amount of time and during the rest period the system comes down, but does not fail. Also, the failure and repair times of each unit are assumed to be correlated, by taking their joint density as a bivariate exponential. The system is observed at suitable regenerative epochs to obtain various reliability characteristics of interest to system designers as well as operations managers. Numerical results pertaining to a particular case are also presented.

Reliability and availability analysis of cold standby system with repair and multiple non-critical and critical errors

Reliability and availability analysis of systems having k active, N cold standby identical units with repair facilities and multiple non-critical and critical errors is presented. Failed unit (active and/or any one of the multiple non-critical errors) will be repaired with same constant repair rate. The system is in a failed state when any one of the multiple critical errors has occurred or when (N+1) units (active and/or any one of the multiple non-critical errors) have failed. Failed system will be repaired with repair times which are arbitrarily distributed. The formulas for reliability and steady-state availability are given.

On the effect of weather condition in a two unit cold standby system

This paper investigates a two unit cold standby system in which operation is affected by the weather conditions. Weather conditions are subject to a Markov process with two states—normal and abnormal. These are independent of the system state. Using the regeneration point technique we obtain several characteristics of the system.

A two-unit system with allowed down time and random check of standby

This paper deals with the cost-benefit analysis of a two-unit (priority and ordinary) cold standby system under two very practicable assumptions: (i) the ordinary unit goes for a check at random epochs; (ii) the system remains down for a random time if, during the repair of ordinary unit, the priority unit also fails. The important measures of system effectiveness are obtained by using the regenerative point technique (R.P.T).

Cost-benefit analysis of a two-unit standby system with a proviso of repair-machine failure

This paper deals with the cost analysis of a two-unit (priority and ordinary) cold standby system model under a very practicable assumption that the repair machine (R.M.) may also fail during the repair of a failed unit. Some important measures of system effectiveness are obtained by using the regenerative point technique (R.P.T.).

Reliability analysis of a cold standby system with multiple critical errors

A reliability and availability analysis of k active and N cold standby identical units of r repair facilities with multiple critical errors is presented. The system is in a failed system when (N+1) units have failed or any one of the multiple errors has occurred. Failed units will be repaired with constant repair rate. Failed system will also be repaired with same repair rate. The expressions for reliability, availability and steady-state availability are given.

Profit analysis of a system with two-units having guarantee periods and delayed operation of standby

A single-server two-unit (one priority, p and the other ordinary, o) cold standby system model is investigated. The p-unit has four different modes—excellent (E), good (G), satisfactory (S) and total failure (F)—of which the first three are operative modes while the o-unit has only two modes—normal (N) and total failure (F). When the p-unit enters F-mode the repairman starts the operation of the o-unit. The time taken to start the operation of the o-unit is not negligible and is assumed to be a finite quantity T r. The failure time distributions of the o-unit and the p-unit in the E-mode are taken to be truncated exponential while all the other time distributions are negative exponential over the range 0 to ∞. By identifying the system at suitable regenerative epochs, the profit functions under two different policies are obtained.

An inspection policy for unrevealed failures in a two-unit cold standby system subject to correlated failures and repairs

Abstract This paper considers the stochastic analysis of a two-unit (dissimilar units) cold standby system subject to revealed and unrevealed failures. We assume that a revealed failure is detected as soon as it occurs but an unrevealed failure is detected by an inspection only. Failure and repair times are assumed to be correlated and their joint distributions are taken to be bivariate exponential (B.V.e.). Important reliability characteristics useful to system designers are obtained by using the regenerative point technique.