Single Repair Facility Research Articles

Generalized reliability results for 1-out-of-n:G repairable systems

The author examines a class of 1-out-of-n:G systems consisting of n nominally identical units in parallel redundancy serviced by a single repair facility. Assuming constant failure rates and general repair distributions permits the problem of finding the Laplace transform of the time-to-system-failure distribution and the mean time-to-system-failure to be reduced to solving a closed-form system of (n-1) by (n-1) linear equations, for n at least 4. Numerical results are presented using a model of a satellite maintenance service. >

A study of a 2-unit system with ‘random breakdown’ of the repair facility

A two-unit cold standby system supported by a single repair facility is considered. The units after each repair do not behave as new and a unit can be repaired exactly k ( k < ∞) times. The failure time distribution of either unit is different after each repair. The repair facility is subjected to random breakdown with exponential lifetime and exponential repair time distributions. The availability and reliability measures and the MTBF are provided for the model.

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.

Reliability analysis of a k-out-of- N: F repairable system with dependent units

This paper deals with reliability analysis of a k-out-of- N: F system with dependent units, having a standby unit and a single repair facility. The failure rate λ n of an operating unit at any given instant of time depends on the number n of operating units at that instant. The repair times of an operating unit and of a standby unit are arbitrary and different. Applying regeneration point technique, explicit expressions for Laplace transforms of first passage time distribution and of system reliability are derived. The mean time to first system failure is also obtained. The mean time to first system failure is calculated for some special values of k and N in cases of the presence and absence of a standby unit.

A priority multi-component system with spares

A system with n similar components in series with constant failure rates and m spares in warm standby supported by a single repair facility is studied. The repair time distributions of on-line and standby failures are taken to be different and arbitrary. Two models, one with pre-emptive repeat priority and another with non-pre-emptive priority are discussed. Equations for the reliability and availability functions are obtained for both cases and earlier results are recovered as special cases of the non-pre-emptive model.

Two-unit standby systems with non-instantaneous switchover and imperfect switch

Four models of two-unit warm standby redundant systems with non-instantaneous switchover and imperfect switching device are studied. The units and the switching device share a single repair facility. Identifying suitable regeneration points, the availability and the reliability of the systems are obtained. A numerical example illustrates the results.

A reliability physics model for one-unit and two-unit standby systems with single repair facility

In this paper, the reliability and availability analysis of repairable one-unit and two-unit standby systems is carried out using a stress-strength failure model. Only single repair facility is considered and the time taken to repair a unit is assumed to be a random variable. The analysis is carried out for general stress, strength and repair distributions. Also, two particular cases of repair distribution are considered. Finally, a few numerical results are presented.

Reliability and maintainability of a multicomponent series-parallel system with simultaneous failure under preemptive repeat repair discipline

This paper considers a system consisting of two subsystems connected in series with a single repair facility. One sybsystem is K-out-of-N:G system consisting of N identical units, while the other consists of M different units connected in series. The life-times of the active units depend on each other in having simultaneous failure of all the operating units and repair times are distributed quite generally. The system breaks down if more than (N−K+1) units in parallel group are simultaneously in the failed states or if any failure occurs in the series group or if simultaneous failure occurs. The availability and reliability function of the system are obtained simultaneously. Explict expressions for the steady state availability of the system and the mean time to the first system failure are obtained.

A generalization of Freund's model for a repairable paired component based on a bivariate Geiger Muller (G.M.) counter : Suddhendu Biswas and Gurprit Nair. Microelectron. Reliab.24 (4) 671 (1984)

A two-unit cold standby system supported by a single repair facility is considered. The units after each repair do not behave as new and a unit can be repaired exactly k (k < ∞) times. The failure time distribution of either unit is different after each repair. The repair facility is subjected to random breakdown with exponential lifetime and exponential repair time distributions. The availability and reliability measures and the MTBF are provided for the model.

A fast algorithm to formulate Markov system equations : J. Luis Roca. Microelectron. Reliab.24 (5) 897 (1984)

A two-unit cold standby system supported by a single repair facility is considered. The units after each repair do not behave as new and a unit can be repaired exactly k (k < ∞) times. The failure time distribution of either unit is different after each repair. The repair facility is subjected to random breakdown with exponential lifetime and exponential repair time distributions. The availability and reliability measures and the MTBF are provided for the model.

Reliability of a complex system under pre-emptive repeat discipline

In this paper we investigate a system, composed of two parallel subsystems, connected in series with a single repair facility. The failure times are exponentially distributed, whereas the repair times are distributed quite generally. The repair discipline is of pre-emptive repeat type. We obtain the following results: Laplace transform (L-T) of the pointwise reliability, L-T of the pointwise availability, the mean time to system failure and the steady state availability.

Reliability analysis of a series-parallel system under different repair disciplines

In this paper we investigate a system composed of two subsystems connected in series with a single repair facility. One subsystem is K-out-of- N: G, while the other consist of several different units connected in series. The method of the supplementary variable in two models differing by the repair discipline is used to obtain the availability of the system. By making suitable transformation the reliability and the mean time to system failure (MTSF) can be deduced from the availability function.

A reliability physics model for dissimilar two-unit standby system with single repair facility

In this paper, the reliability and availability analysis of a repairable dissimilar two-unit standby system is carried out using stress-strength failure model. Single repair facility with the time taken to repair a unit being either deterministic or random has been considered. The analysis is carried out for arbitrary stress, strength and repair time distributions.

Busy period analysis of a two-unit warm standby system with imperfect switch

Busy period analysis of a two-unit warm standby system with two modes (normal and total failure) and imperfect switching device has been studied by considering the availability of a single repair facility. Failure time distributions of the units are negative exponential whereas repair time distributions of units and switch are arbitrary. Using the regeneration point technique several reliability characteristics have been obtained. Moreover, the present model employs switch failure in non-regenerative states, for the first time.

Reliability and maintainability of a multicomponent series-parallel system with simultaneous failure and repair priorities

This paper considers a system consisting of two subsystems connected in series with a single repair facility. One subsystem is K-out-of-N:G system consisting of N identical units, while the other consists of M different units connected in series. The life-times of the active units depend on each other in having simultaneous failure of all the operating units and repair times are distributed quite generally. The system breaks down if more than (N−K+1) units in the parallel group are simultaneously in the failed states or if any failure occures in the series group. The availability and reliability function of the system are obtained simultaneously. Explict expressions for the steady state availability of the system and the mean time to the first system failure are obtained.

Some applications of semi-regenerative processes to two-unit warm standby system

We deal with a two-unit warm standby system with a single repair facility; a failure of an operating unit can be detected immediately but a failure of a warm standby unit can not be observed until the system is inspected. According to whether the operation of the system is stopped or not during each inspection, we consider two models. We describe the stochastic behavior of the system as a semi-regenerative process, and the pointwise availability and the steady state availability of the system are derived applying the limit theorem of semi-regenerative processes. Further, we shall discuss the optimum interinspection time maximizing the steady state availability for Model 1.

Quasi-stationary distribution of a two-unit warm-standby redundant system

This paper establishes the existence of the limit ast→ ∞ of the distribution of the residual lifetime at timetof a two-unit warm-standby reliability system supported by a single repair facility, conditioned on the event that the system has not been down at any time in (0,t). The conditioned limit distribution is proved to be exponential irrespective of the distributions of the lifetimes and repair times of the individual units, provided that their Laplace transforms are rational functions of their arguments.

Quasi-stationary distribution of a two-unit warm-standby redundant system

This paper establishes the existence of the limit as t → ∞ of the distribution of the residual lifetime at time t of a two-unit warm-standby reliability system supported by a single repair facility, conditioned on the event that the system has not been down at any time in (0, t). The conditioned limit distribution is proved to be exponential irrespective of the distributions of the lifetimes and repair times of the individual units, provided that their Laplace transforms are rational functions of their arguments.

Analysis of a two-unit hot standby system with three modes

This paper discusses the stochastic behaviour of a two-unit hot standby redundant system having exponential failure and a single repair facility with general repair time distribution. Each unit of the system has three possible states—normal, partial failure and total failure. 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.

Analysis of a two-unit parallel redundancy with an imperfect switch

A parallel redundant system of two identical units is studied when the switchover from repair to on-line is defective. It is assumed that there is a single repair facility and that either unit has priority over the switching device while queuing for repair. The reliability and availability functions are obtained explicitly when the units have a constant failure rate. The method of extension to cover the case of dissimilar units with non-constant failure rates is also indicated.