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 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 characteristics of a man-machine system operating subject to different weather conditions

This paper deals with some characteristics of a single unit of a man-machine system operating under different weather conditions. It is assumed that the failure, repair and change of weather conditions (normal-stormy) are stochastically independent random variables, each having an arbitrary distribution. The system is analysed by the semi-Markov process technique. Some reliability measures of interest to system designers as well as operations managers have been obtained. Explicit expressions for the Laplace-Stieltjes transforms of the distribution function of the first passage time, mean time to system failure, pointwise availability and steady-state availability of the system are obtained. Several important results have been derived as particular cases.     

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.     

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.     

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.     

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.     

Profit analysis of the machine repair problem with cold standbys and two modes of failure

In this paper we deal with the cold-standby machine repair problem where machines have two failure modes under steady-state conditions. The two failure modes have equal probability of repair. Failure time of the machines and repair time of the repairmen are assumed to follow a negative exponential distribution. The failed machines are served by R repairment according to first-come, first served discipline. Profit model is developed in order to determine the optimal values of the number of cold standbys and the number of repairmen simultaneously, while maintaining a minimum specified level of system availability. Numerical results are presented in which several system characteristics are calculated under optimal operating conditions.     

Behavioural analysis of shell gasification and carbon recovery process in a urea fertilizer plant

The paper discusses the behavioural analysis for shell gasification and carbon recovery process in a urea fertilizer plant. The system consists of three subsystems D, E and F arranged in series, with three possible states good, reduced and failed. The subsystem D has three parallel operating units with two units in cold standby. Failure and repair rates for each subsystem are taken as constant. Formulation of the problem is carried out using simple probability consideration. The expression for steady-state availability is derived. Taking data from a medium size plant, the effect of each working unit on the system availability is tabulated. The results are supplied to the plant personnel for improvement in designing the system and planning the process for minimum failure.     

Human error analysis of a standby redundant system with arbitrarily distributed repair times

This paper presents human error analysis of a (two units working and one on standby) system with arbitrarily distributed repair times. The supplementary vairables method is used to develop the system availability expressions. A general formula for the system steady-state availability is developed when the failed system repair times are gamma distributed. Time-dependent availability, system reliability with repair, mean time to failure and variance of time to failure formulae are developed for some particular cases. Selective plots are shown to demonstrate the impact of critical human error on system availability and reliability.     

Behavioural analysis of a shell gasification and carbon recovery process in a urea fertilizer plant

The paper discusses the behavioural analysis for a shell gasification and carbon recovery process in a urea fertilizer plant. The system consists of three subsystems D, E and F arranged in series, with three possible states—good, reduced and failed. The subsystem D has three parallel operating units with two units in cold standby. Failure and repair rates for each subsystem are taken as constant. Formulation of the problem is carried out using simple probability consideration. An expression for steady-state availability is derived. Taking data from a medium sized plant, the effect of each working unit on the system availability is tabulated. The results are supplied to the plant personnel for improvement in designing the system and planning the process for minimum failure.     

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.     

A note on the statistical characteristics of a two-unit system

Expressions for the Laplace transforms of reliability and availability functions are obtained for a two-unit system, with different repair times for the units which have failed from online and standby states, and a dead time value for the repair facility by the use of regeneration point technique. The system consists of two-units with one repair facility. The repair facility is not available for a random time immediately after each repair completion. From the Laplace transforms of reliability and availability functions the steady state availability, reliability and mean time to system failure can be obtained.     

Reliability analysis of a three-unit system in a changing environment

Consider a parallel redundant repairable system consisting of three identical units and one repair facility, which operates in a changing environment subject to a Markov process with two states. Using Markov renewal processes we obtain the system availability, failure frequency and reliability 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.     

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.     

Optimal System Reliability Parameters with Minimum Costs

This paper gives a procedure for a repairable complex system which will determine the failure and repair rates as well as the number of redundant components to achieve minimum total s-expected cost for a given availability. The total s-expected cost is the s-expected investment and operating costs. The capital investment cost function is related to the steady-state availability of each component and the operating cost function to the steady-state probability of the system's being in a particular state.     

On a compound redundant system with the particular switching devices

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, in which each one is composed of several identical units connected in parallel.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 units as many as possible. In this consideration it is assumed that all the units are not repairable.We shall obtain the system reliability and the mean time to system failure, and examine numerically the effects of this model to the usual one without particular switching devices.     

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.     

Reliability analysis of a k-out-of-N:G redundant system in the presence of chance with multiple critical errors

A reliability analysis of a k-out-of-N: G redundant system with multiple critical errors and r repair facilities in the presence of chance, is dealt with in this paper. The system is in a failed state when k units have failed or one of any multiple critical errors has occurred. Failed system repair times are arbitrarily distributed. The formulae for reliability function in terms of a Laplace transform, steady-state availability and mean time to failure are derived.