Two-non-identical unit-system with priority-based repair and inspection

The present paper deals with the analysis of a system consisting of two non-identical parallel units, in which the first type of unit has priority over the second type for repair, inspection and post repair. The failure rates, and the repair, inspection and post repair time distributions for both types of units are assumed to be different. Using the regenerative point technique in the Markov-renewal process, several reliability measures are obtained.     

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.     

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.     

Two models for two-dissimilar-unit cold standby redundant system with partial failure and two types of repairs

This paper deals with the availability function and the mean time to the first failure for two models of a cold standby redundant system with two different types of repair. Each model consists of two dissimilar units. In the first model, the operative unit has two modes of operation, normal mode and partial failure mode. The standby unit has one mode of operation, normal mode. In the second model, each unit has three modes of operation, normal mode, failure mode and total failure mode. Both models are analyzed by the semi-Markov process technique, assuming that the failure time and repair time distributions are general and arbitrary. Some reliability measures of interest to system designers as well as operations managers have been obtained. Moreover, we give computer programs for calculating the MTSF for each model (see Appendix).     

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.     

Profit analysis of two-unit priority standby system with rest period of the operator

This paper deals with profit analysis of a single-server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. The priority unit gets preference both for operation and repair. After working a random amount of time, the operator of the system needs rest for a random amount of time and during the rest period of the operator the system becomes down but not failed. the system failure occurs when both the units are in total failure mode. Identifying the system at suitable regenerative epochs, the integral equations are set up for the probabilities of system being in the ‘up’, ‘down’ or ‘failed’ state and to solve these equations Laplace transform technique is adopted. Various reliability characteristics are obtained to carry out the cost-benefit analysis and numerical results pertaining to particular cases are also presented.     

Analysis of a system having super-priority, priority and ordinary units with arbitrary distributions

This paper deals with the analysis of a three non-identical unit cold standby system model. A single repairman is available to repair a failed unit. The priority in respect of operation and repair is being given to the units in order. All failure and repair time distributions are assumed to be general having different p.d.f.'s. Several measures of system effectiveness are obtained by using a regenerative point technique.     

Behaviour of a priority standby redundant system with different types of repair facilities

This paper discusses the stochastic behaviour of a two unit priority standby redundant system, in which priority units gets priority for all operations, with different types of repair facilities. Failure time distributions of Unit are exponential, whereas other distributions are arbitrary.     

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.     

Analysis of two-unit redundant system under partial failure and two types of repairs

In this paper we consider a redundant system with two identical units, providing for partial failure mode and two types of repairs for a failed unit. Failure and repair time are assumed to follow general distribution. Applying the regenerative theory in Markov-renewal process, several reliability characteristics of interest to system designers are obtained.     

Cost analysis of a two unit priority standby system with imperfect switch and arbitrary distributions

This paper deals with cost analysis of a single server two-unit (one priority and the other ordinary) cold standby system with two modes—normal and total failure. A switch is used to operate the standby unit (ordinary) and it works successfully with known probability p( = 1 ? q). Priority unit gets preference both for operation and repair. Failure and repair time distributions are arbitrary. System fails when switch or both the units fail totally. The system is observed at suitable regenerative epochs in order to obtain reliability characteristics of interest to system designers and operations managers. Explicit results for the exponential time distributions have been obtained in particular cases.     

Using system reliability to determine supportability turnaroundtime at a repair depot

This paper uses an expression for system reliability at a repair depot to construct a nonlinear, nonpolynomial function which is amenable to numerical analysis and has a zero equal to the supportability turnaround time (STAT) for a failed unit. System reliability is in terms of the constant failure rate for all units, number of spares on-hand at the time a unit fails, and projected repair completion dates for up to four unrepaired units. In this context, STAT represents the longest repair time (for a failed unit) which assures a given reliability level; system reliability is the probability that spares are ready to replace failed units during the STAT period. The ability to calculate STAT-values is important for two reasons: (1) subtraction of the repair time for a failed unit from its STAT-value yields the latest repair start-time (for this unit) which assures a desired reliability, and (2) the earlier the latest repair start-time, the higher the priority for starting the repair of this unit. Theorems show the location of STAT with respect to the list of repair completion dates, and form the foundation of the root-finding-based algorithm for computing STAT-values. Numerical examples illustrate the algorithm     

Reliability and maintainability of a multicomponent series-parallel system under several repair disciplines

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. Initially all the units are operating. 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 under several repair disciplines are obtained simultaneously. We use a suitable transformation to deduce the reliability from the availability function. Explict expressions for the steady-state availability of the system and the mean time to system failure under several repair disciplines are obtained. Finally some properties of the steady-state availability for each repair discipline are given.     

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.     

Cost benefit analysis of a complex system with correlated failures and repairs

This paper studies the cost benefit analysis of a complex system consisting of two subsystems, say A and B, connected in series. Subsystem A consists of two identical units, whereas subsystem B has only one unit. The system operates if one of the two units of subsystem A and the subsystem B are operative. Assuming a bivariate exponential density for the joint distribution of failure and repair times of the units, some reliability characteristics useful to system managers have been obtained. Explicit results have also been obtained for the case when failure and repair times are uncorrelated.     

Reliability analysis of an (N+1)-unit standby system with ‘preemptive priority’ rule

This paper deals with a repairable standby system consisting of N+1 units and a single repair facility, in which unit 1 has preemptive priority both in getting operation and in getting repaired. Under the general assumptions that life time and repair time of unit 1 have general continuous distributions, we discuss the system's stochastic behavior and obtain the explicit expressions, both in transient state and in steady state, of some main interesting reliability indices of the system.     

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.     

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.     

Availability, MTTF and cost analysis of a three-state parallel redundant multi-component system under critical human failures

This paper deals with the availability, MTTF and the cost analysis of a single server complex system consisting of two classes A and B with three possible states, viz. good, degraded, failed and suffers two types of failure, viz. unit failure and failure due to critical human errors.Sub-system A has two dissimilar units arranged in parallel whereas sub-system B has three non-identical units arranged in series. Failure and repair times have exponential and general distributions respectively. There is only one repair facility when the system is in failed state due to failure of sub-system B. Several parameters of interest are obtained using the supplementary variable method. A numerical example has been appended. Five graphs have also been given in the end.     

A Time-Dependent Complex System With Preemptive Priority Repairs

A repair system is analyzed that has three kinds of components, each with a different repair priority. Type 1 is essential to system operation and has the highest priority of repair; there is only one such component. Type 2 is nonessential (its failure degrades the system) and has an intermediate priority of repair. Type 3 is similar to type 2 except that it has the lowest priority of repair. There are many types 2 and 3 components. The differential equations for system state probabilities are solved by Laplace transforms, but only in implicit form.