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.     

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.     

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.     

Cost analysis of an electronic repairable redundant system with critical human errors

In this paper, an electronic system consisting of two subsystems connected in series has been considered. One subsystem consists of two identical units connected in parallel while the other subsystem has only one unit. The system is to be in any of the three states: good, degraded and failed. The system suffers two types of failures, viz; unit failure and failure due to critical human error. The system can be repaired when it fails due to the failure of the units in the subsystems and cannot be repaired when it fails due to critical human errors. The repair for the system in any state follows general distribution. To make the system more applicable to practical life problems, time dependent probabilities have been evaluated so as to forecast the expected profit and the operational availability of the system at any time.     

Two 1-Server n-Unit Systems with Preventive Maintenance and Repair

This paper deals with the availability and reliability analysis of two different 1-server n-unit systems with preventive maintenance and repair. Initially, one unit operates and the remaining n - 1 units are kept as cold standbys. In the first system the time to failure and the time to preventive maintenance of a unit are arbitrarily distributed. In the second system, each unit consists of 2 components connected in series. When a unit fails, the failed component is taken up for repair while the other waits for preventive maintenance. Explicit expressions for the Laplace transform of the mean down-time of the system in [0, t] and for the mean time to system failure are obtained. Steady-state availability of the system is also discussed. A few special cases have been studied.     

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.     

Availability analysis of a repairable system with common-cause failure and one standby unit

This paper investigates the mathematical model of a system consisting of two non-identical parallel redundant active units, with common-cause failure, and a cold standby unit. The failed units are repaired one at a time or are repaired together, if they fail due to common cause failure. All repair time distributions are arbitrary and different. The analysis is carried out under the assumption of having a single service facility for repair and replacement.Applying the supplementary variable technique, Laplace transforms of the various state probabilities are developed. Explicit expressions for the steady state probabilities and the steady state availability are derived.Some well known results are obtained as special cases. A numerical example is given to illustrate the effect of the repair policy on the steady state probabilities and the availability of the system.     

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 k-out-of-N:G redundant system with cold standby units and common-cause failures

This paper presents a k-out-of N:G redundant system with M cold standby units, r repair facilities and common-cause failures. The constant failure rates of the operating and cold standby units are different. Failed system repair times are arbitrarily distributed. The system is in a failed state when (N+M?k+1) units failed or a common-cause occurred. Laplace transforms of the state probabilities, the availability of the system and the system steady-state availability are derived.     

Availability analysis of steam and power generation systems in the thermal power plant

The paper discusses the availability analysis of a steam generation system consisting of three subsystems A, B and D and a power generation system consisting of four subsystems E, F, G and H arranged in series, with three states viz., good, reduced and failed. Taking constant failure and repair rates for each working unit, the mathematical formulation is done using the Birth-Death process. Expressions for steady state availability and the MTBF (mean time between failure) are derived. The graphs are given, depicting the effect of failure and repair rates on the system availability. The results are supplied to the plant personnel, to plan the policies for failure free running of the systems for a long duration.     

Reliability consideration on a compound redundant system with repair

This paper considers a standby-redundant system consisting of 2 systems, in which one is main and the other is its standby-redundant system. These systems also consist of 2 subsystems connected in series.A feature of this system is that the system has 2 switching devices connecting subsystems, in addition to one connecting main and standby systems, in order to utilize surviving subsystem. In this consideration it is assumed that all the units are repairable.We shall obtain the system reliability, the mean time to system failure, the steady state availability, and examine numerically the effects of this model to the usual one without particular switching devices.     

Analyses of Two Different 1-Server Systems

In this paper, the availability and the reliability of two 1-server systems with redundancy have been obtained. System 1 consists of n subsystems in series; each subsystem consists of two redundant i.i.d. components in `parallel' (cold standby) and one server. The times to failure of the components are exponentially distributed; their repair time distributions are arbitrary and different. System 2 consists of n dissimilar units and one server. The times to failure of the units are arbitrarily distributed; the repair rates are constant but all different. Explicit expressions for the Laplace transform of the mean down-time of the system in (0, t) and for the mean time to system failure have been obtained. A few particular cases are discussed.     

On a compound redundant system without repair

This paper deals with the reliability considerations on a redundant system consist of two subsystems connected in series, in which they have a similar warm-standby subsystem, respectively. And these four subsystems are composed of several identical units in parallel redundancy, respectively and are connected with switching devices each other.The purpose of this paper is to attain the following two subjects; (1) to utilize the surviving units at any switch-over point of time, as many as possible, making use of the switching devices as mensioned above, and (2) to deal with various complex redundant systems with or without switching devices, simultaneously.In these considerations we have obtained the reliability function and mean time to system failure (MTSF) of this system.     

A two unit series system with correlated failures and repairs

This paper investigates a stochastic model of a system having two identical units, each with two components, arranged in series configuration. Upon failure of a component of the unit, the standby unit replaces the failed unit instantaneously. It is assumed that the joint distribution of the repair and failure times of a component are bivariate exponential. Several reliability characteristics of interest to system designers as well as operations managers have been evaluated and relevant results obtained earlier are verified as a particular case. The MTSF and availability have also been studied through graphs.     

Stochastic analysis of systems with primary and secondary failures

This paper presents the stochastic analysis of repairable systems involving primary as well as secondary failures. To this end, two models are considered. The first model represents a system with two identical warm standbys. The failure rates of units and the system are constant and independent while the repair times are arbitrarily distributed. The second system modeled consists of three repairable regions. The system operates normally if all three regions are operating, otherwise it operates at a derated level unless all three regions fail. The failure rates and repair times of the regions are constant and independent. The first model is analyzed using the supplemental variable technique while the second model is analyzed using the regenerative point technique in the Markov renewal process. Various expressions including system availability, system reliability and mean time to system failure are obtained.     

Stochastic analysis of a 2-unit standby system with two failure modes and slow switch

This paper considers the cost-benefit analysis of a one-server two unit system subject to two different failure modes and slow switch. The failure rates of the units are constant. The repair times and the switchover time are assumed to be arbitrarily distributed. The server repairs the units and puts the standby unit into operation. Detailed analysis of the system is done by using regenerating point technique and results are obtained for mean time to system failure, steady state availability, busy period of a repair man, expected number of visits by the repair man and expected profit earned by the system.     

Reliability of a Repairable Multicomponent System with Redundancy in Parallel

Consider a multicomponent system consisting of two series subsystems. One contains identical components connected in parallel, while the other has nonalike components connected in series. Each component has constant hazard rate, while the subsequent repairs follow some general distributions. The supplementary variable technique developed by Kielson and Kooharian [1] and the phase technique are used to obtain the various time-dependent and steady-state solutions for the system. A numerical illustration compares the effect of two repair policies on the behavior of the system. The optimum number of components connected in parallel is obtained.     

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.     

MTTF and availability evaluation of a two-unit, two-state, parallel redundant complex system with constant human failure

This paper deals with MTTF and availability analysis of a two-state complex general repairable system consisting of two units arranged in parallel. Single service facility is available for the service of unit failure. The failure and repair times for the system follow exponential and general distributions respectively. Laplace-transforms of the various state probabilities have been derived and steady state behaviour of the system has also been examined. Availability at any time is obtained by the inversion process. To make the system more compatible with the physical situation, MTTF for the system has also been evaluated and various graphs have been plotted to highlight the utility of the model.