Assignment of Priority in Improving System Reliability

In many maintenance situations for certain weapon systems, such as anti-aircraft systems, the problems confronted are: 1) which priority for repair is to be assigned, and 2) which type of component should be assigned priority for repair. This can be done on the basis of mean time to system failure. This paper discusses the reliability characteristics of a system of two paralleled radars working in conjunction with two paralleled computers. The system is in up stage even if one computer and/or one radar fails. The system failure takes place only when both the computers or both the radars are in failed condition. The distribution of time to system failure and its expectation have been derived assuming that the failures occur following Poisson distribution and the repair times follow the negative exponential distribution for these two types of subsystems imposing head-of-the-line priority and preemptive resume priority for the repair process. The results are discussed with reference to numerical examples. It has been observed that the mean time to system failure is higher when the head-of-the-line priority discipline is adopted for repair of components, especially when the repair times are shorter.     

Analysis of 7 Models for the 2-Dissimilar-Unit, Warm Standby, Redundant System

The paper is in 2 parts. In all models the failure rates are constant, but repair rates need not be constant. The method of supplementary variables is used for solving the models. Part I considers the effect of priorities on reliability and availability for 4 basic models; 1) priority in both repair and operation; 2) priority in repair; 3) priority in operation; 4) no priority. Models 1 and 2 treat 2 repair disciplines: a) preemptive-repeat, b) preemptive-resume. We obtain 1) Laplace transforms of availability and reliability and 2) explicit expressions for steady state availability and for mean time to system failure. The effect of priority assignment to maximize steady state availability is discussed. Part II considers the effect of having different repair rates, depending on whether the failure was from standby or from operation. We obtain 1) Laplace transforms of availability and reliability and 2) explicit expressions for mean time to system failure.     

Availability of Priority Standby Redundant Systems

A priority standby system consisting of two repairable units is considered. One unit, the priority unit, is always in service except when it is failed. The standby unit is in service only for the duration of repair of the priority unit. Expressions are derived for the availability of such a system for both preemptive and nonpreemptive repair. The results assume reasonably general failure-time and repair-time distributions of the priority and standby units. The preemptive priority results are relatively insensitive to the form of the distributions.     

A two unit priority redundant system with three modes and correlated failures and repairs

This paper considers a two dissimilar units priority redundant system with three modes. One of the units has a priority operative mode and the other has a priority repair mode. Assuming that the joint distribution of failure and repair times is exponentially bivariate, some reliability characteristics useful to system managers have been obtained. Results for a system with two similar units are obtained as a particular case.     

On optimal burn-in procedures - a generalized model

Burn-in is a manufacturing technique that is intended to eliminate early failures. In this paper, burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure), which can be removed by a minimal repair or a complete repair; and the other is Type II failure (catastrophic failure), which can be removed only by a complete repair. During the burn-in process, two types of burn-in procedures are considered. In Burn-In Procedure I, the failed component is repaired completely regardless of the type of failure; whereas, in Burn-In Procedure II, only minimal repair is done for the Type I failure, and a complete repair is performed for the Type II failure. Under the model, various additive cost functions are considered. It is assumed that the component before undergoing the burn-in process has a bathtub-shaped failure rate function with the first change point t/sub 1/, and the second change point t/sub 2/. The two burn-in procedures are compared in cases when both the procedures are applicable. It is shown that the optimal burn-in time b/sup */ minimizing the cost function is always before t/sub 1/. It is also shown that a large initial failure rate justifies burn-in, i.e., b/sup */>0. The obtained results are applied to some examples.     

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.     

Availability for 2/n: F and secondary subsystems with general repair-time distributions and shut-off rules

The model which main 2/n: F and secondary subsystems subject to shut-off rules is considered. In this model, the system has single repair facility. The repair discipline that the main subsystem has the preemptive repeat priority is considered. Constant failure rate and general repair-time distribution are assumed. The system availability is obtained by using linear ordinary differential equation method and supplymentary variable technique.     

Availability of a series system with warm spares

We discuss two models for the availability of a series system of components with warm spares, serviced by a single service facility. Replacement of failed components by a spare has pre-emptive priority over repair of the failed components; for the restart model, in which interrupted repairs restart from the beginning, we find the availability of the system; for the resume model, in which interrupted repairs resume from where they left off, we show how to obtain the availability of the system. Some numerical examples and the distributions of system downtime are given for both models.     

A two-unit priority standby system subject to random shocks and Releigh failure-time distribution

This paper deals with the cost-benifit analysis of a two-unit priority standby system subject to random shocks. The priority unit gets preference both for repair and operation over the ordinary unit and has three modes- Normal, Quasi-normal and Total-failure. The ordinary unit has only two-modes- Normal and Total-failure. The distributions of shock-time, repair-time of the ordinary unit and failure time of the priority unit are negative exponential. The distribution of the repair-time of the priority unit is taken to be general while the time to failure of ordinary unit follows Releigh distribution. Various characteristics related to system effectiveness have been obtained by using the regenerative point technique.     

Availability of the system with general repair time distributions and shut-off rules

A model which has main and secondary subsystems subject to shut-off rules is considered. In this model, the system has a single repair facility. The repair discipline that the main subsystem has the pre-emptive repeat priority is considered. Constant failure rate and general repair time distributions are assumed. The system availability is obtained by using the linear ordinary differential equation method and supplementary variable technique.     

A two dissimilar unit multi-component system with correlated failures and repairs

This paper investigates a two non-identical unit cold standby system model. Each unit is composed of n independent components arranged in a series configuration. A single repairman is available to repair a failed unit. The priority in operation is being given to the first unit, while in repair the priority is given to the second unit. The failure and repair times of the ith and jth component for the first and second unit, respectively, are jointly distributed as bivariate exponentials (B.V.E.) with different parameters. Using a regenerative point technique, various reliability characteristics have been analysed.     

Analysis of a two unit standby system with partial failure and two types of repairs

A two dissimiliar unit standby system is analysed. The priority unit can either be in normal or partial operative mode. When the unit fails from the partial mode, it undergoes minor repair and the unit becomes operative with different failure rate. If this unit fails again, it goes to major repair after which it works as good as new. The standby unit while in use is either operative or failed. This non priority unit fails without passing through the partial failure mode and undergoes only one type of repair with different repair time distribution. Failure and repair time distributions are negative exponential and general respectively. Regenerative technique in MRP is applied to obtain several reliability characteristics of interest to system designers.     

Stochastic behaviour of a two-unit (dissimilar) hot standby system with three modes

A hot standby system composed of two non-identical units is analysed under the assumption that each unit works in three possible modes—normal, partial failure and total failure. For each unit the failure time distribution is negative exponential and the repair time distribution is arbitrary. Breakdown of the system occurs when both the units are in total failure mode. There is only one repair service and when both the units are in the same mode, priority is given to the first unit in the matter of operation as well as repair. Several reliability characteristics of interest to system designers and operations managers have been evaluated.     

Availability and reliability of system with dependent componentsand time-varying failure and repair rates

System reliability depends not only on the reliabilities of components in the system but also on their interactions. Generally, in a system, not only s-independent failures but also s-dependent failures among components can occur; thus there are many studies where the s-dependencies among components are taken into account in system reliability and availability analysis, but in which the failure and repair rates were assumed constant. Whereas, from a practical viewpoint, the constant failure rate assumption for components has been, and is repeatedly challenged by knowledgeable reliability practitioners. Therefore, there are other studies which handled the problem of time-varying failure rates, among which all concerned repairable systems did not involve s-dependent failures. In most cases, however, to combine s-dependent failures and time-varying failure and repair rates in system reliability and availability analysis is the most appropriate for real systems. But it is very difficult to obtain the analytic solution and, in most cases, the closed-form solution for system reliability and availability does not exist, so that numerical or simulation methods must be used. This paper studies one kind of system that endures environmental shocks, and where one or more components can fail simultaneously due to a cumulative shock-damage process. An approach for reliability and availability analysis of such kinds of repairable systems is presented, where failure and repair rates of components can be varied with time. One type of special vehicle with such mechanical systems illustrates system reliability and availability solutions     

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.     

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.     

Analysis of a two-unit warm standby system subject to degradation

This paper deals with the reliability analysis and the mean time to system recovery of a single server, two-unit (priority and ordinary) warm standby subject to degradation. Initially the priority unit is operative and the ordinary unit is kept as a warm standby. The priority unit passes through three different operative stages (excellent, good and satisfactory) before it fails. The priority unit enters into the total failure mode only from the satisfactory stage, and after repair it enters into the normal mode with any of the ‘excellent’, ‘good’ and ‘satisfactory’ stages with different probabilities. The failure, repair and degradation time distributions are assumed to be general and arbitrary. The system is observed at suitable regenerative epochs in order to carry out the expected first passage time analysis. Moreover, three special cases have been considered. The results of Gupta [Int. J. Systems Sci.22 (11) 2329–2338 (1991)] are derived from the present results as a special case. A computer program for calculating the mean time to system failure and the mean time to system recovery is made.     

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.     

Repair Priority Effect on Availability of a 2-unit System

This paper is concerned with a 2-unit parallel system with priority repair. The priority rule is a mixture of several disciplines. The optimal priority rule minimizes the s-expected total discounted time in which the system is failed. The optimality of Late Preemption Rule is shown and the effect of the rule on the availability of the system is investigated.     

A complex system having four types of components with pre-emptive repeat priority repairs

A parallel redundant complex system having pre-emptive repeat repair discipline is considered in which the pre-empted unit of lower priority class joins the service only when all units of higher priority class in service or waiting have been served. The problem is solved with the use of Laplace transforms and generating function techniques.