The reliability function and the availability of a duplication redundant system with a single service facility for preventive maintenance and repair

This paper concerns a two-unit system with a cold standby and a single service facility for the performance of preventive maintenance and repair. Explicit expressions for the Laplace transforms of the availability of the system, the reliability, the mean down time during (0, t) and for the mean time to system failure have been obtained under the assumption that the failure times, the inspection times, the repair times and the preventive maintenance times of the two units are governed by distinct arbitrary general distributions. The results obtained by Srinivasan and Gopalan and by Gopalan and d'Souza are derived from the present results as special cases.     

A two-unit duplicating standby system with correlated failure-repair/vbreplacement times

This paper considers the stochastic analysis of a two-unit (original and duplicate) cold standby system model with preventive maintenance and replacement of the failed duplicate unit. The failed duplicate unit is non-repairable but its replacement is considered with an identical duplicate unit which is available instantaneously. Joint distributions of failure and repair/replacement times of original/duplicate units are bivariate exponential with different parameters. Various reliability characteristics of the system model under study are obtained by using regenerative point technique. Mean time to system failure and steady state availability have also been studied through graphs.     

Analysis of a two-engine aeroplane model with two types of failure and preventive maintenance

This paper deals with an aeroplane model; namely, a two-unit (non-identical) parallel system with dual mode of failures—(1) failure due to change in operating characteristics and (2) failure due to common cause. The system goes for preventive maintenance at random epochs. We assume that the failure, repair and maintenance times are stochastically independent random variates each having an arbitrary distribution. Using the regenerative point technique several measures of reliability are obtained. Certain important results have been derived as particular cases.     

Probabilistic analysis of a two-unit system with a warm standby subject to preventive maintenance and a single service facility

The object of this paper is to carry out the availability and the reliability analysis of a two-unit system with a warm standby having a single service facility for the performance of preventive maintenance and repair. The failure times, the repair times, the inspection times and the preventive maintenance times of the main unit and of the standby one are assumed to be arbitrarily distributed. The system is characterized by the probability of its being in the up or the down state. Explicit expressions for the mean down time of the system and for the mean time to system failure are obtained. Some previous results are derived from this work as special cases.     

Parametric Analysis of 2-Unit Redundant Computer Systems With Corrective and Preventive Maintenance

This paper shows the span of results which can be obtained by modeling a system's behavior by stochastic processes and demonstrates practical rules for employing Markov and semi-Markov models. The introduction summarizes several methods for reliability analysis and gives the advantages and drawbacks of four methods: Markov processes, semi-Markov processes, supplementary variables, the method of stages. The remainder deals with reliability and availability modeling of a 2-unit redundant computer system. There are a) two types of maintenance: corrective (c. m.) and preventive (p. m.), and b) two system parameters: coverage, and an increased failure rate when one unit is under repair or inspection. Approximate expressions for reliability, mean time to failure, and asymptotic availability show the effects of the system parameters as well as of the shapes of the Cdf's of the times related to maintenance actions. For c.m., Markov modeling is a good approximation. For p.m., Markov modeling is a rough approximation; one can go to semi-Markov models or to the method of stages. Lastly, an approximate expression is given for the mean inspection interval which maximizes reliability and availability for p.m.     

Profit analysis of a two-unit standby system with two types of repair and preventive maintenance

This paper deals with the profit analysis of a two-unit cold standby system with two types of repairs—cheap and costly. Cheap repair becomes available after a random amount of time while costly is available instantaneously. The preventive maintenance (P.M.) of an operative unit starts at random epochs of time and is done only if the other unit is in standby. The distribution of time to accomplish P.M. is negative exponential while the distributions of failure time, repair times and time to commence P.M. are general. Various economic reliability measures of interest to system designers as well as operation managers have been obtained using regenerative point technique.     

Approximated reliability of r-out-of-n(F) system with common cause failure and maintenance

In modern industries very high reliability system are needed. To improve the reliability of system, the component redundancy and maintenance of component or system play an impotant role and must be studied. This paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or CCF(Common Cause Failure). Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By using the analyzed MTBF, we compute MTBF of r-out-of-n(F) system. The MTBF with CCF is saturable even if repair rate is large.Approximated reliability of the r-out-of-n(F) system with maintenance and Common Cause Failure O.SummaryThe paper presents a reliability model of a r-out-of-n(F) redundant system with maintenance and Common Cause Failure. Failed component repair times are arbitrarily distributed. The system is in a failed state when r units failed because of the combination of single element failure or Common Cause Failure. Laplace transformation of reliability is derived by using analysis of Markov state transition graph. By analyzing this mean visiting time equations, we compute MTBF and shows computational example. The MTBF with CCF is saturable even if repair rate is large. In general the maintenance overcomes MTBF bounds, But the repair method not overcome the MTBF saturation when the system has Common Cause Failure.     

Cost optimal, parallel reliability systems with fixed repair sanction

Optimisation methods under varied criteria for different parameters in stochastic reliability systems are being increasingly developed and have been reported in recent literature. The large interest evinced in this fascinating area is primarily due to its applicational value and operational role in the decision making process. Recently a parallel system has been considered and the optimal number of units discussed, as well as optimal replacement times for the system based on acquisition and replacement costs.In this paper we consider an improved version of the model formulation, by bringing in additionally the maintenance and per unit repair time costs, and develop a procedure to obtain the optimal number of components in the system with the condition that the system is allowed to undergo a prefixed maximum number of repairs, after which the system is to be replaced.The applicational use of the results is illustrated through numerical work, specialising to some known laws governing the system parameters and corresponding to different fixed number of repair sanctions.     

定期检修系统的可靠性建模与仿真

定期检修情况下冗余系统的可靠性建模是目前可靠性工程领域的难点之一。针对定期检修系统现有可靠性评价方法的不足,推导了考虑故障检测率、故障隔离率、修复率等参数的定期检修冗余系统的可靠度计算公式,并设计了一种基于仿真的方法,解决了定期检修冗余系统的可靠性评价工程问题。验证了仿真方法的正确性。最后应用MATLAB开发了定期检修冗余系统的可靠性仿真工具,并给出了一个实例。     

Analysis of a k-out-of-n unit system with two types of failure and preventive maintenance

A k-out-of-n unit system is analysed with two types of failure: (1) failure due to change in operating characteristics and (2) catastrophic failure. Preventive maintenance of the system is allowed at random epochs. All transition rates are taken to be general. Several measures of reliability useful for system designers and operations managers have been obtained by using regenerative point technique with Markov renewal process. Some important results obtained earlier are shown as particular cases.     

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.     

A cold standby system with arrival time of server and correlated failures and repairs

This paper presents the analysis of a two unit cold standby system with random arrival time of a server. The failure and repair times of each unit are assumed to be correlated and their joint density is taken as bivariate exponential. Using the regenerative point technique, various reliability characteristics of the system have been obtained. The behaviour of MTSF and steady state availability have also been studied through graphs.     

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.     

A high power solid-state medium wave broadcast transmitter

The factors leading to the choice of an all-solid-state 50-kW medium-wave broadcast transmitter are examined, and its advantages over vacuum-tube-type transmitters of the same power are discussed. The installation and operation of the transmitter are described. The transmitter has demonstrated high levels of performance and reliability. Energy savings and reduction of maintenance times have been achieved     

Some characteristics of a two-dissimilar-unit cold standby redundant system with three modes

This paper deals with the stochastic behaviour of a two-dissimilar-unit cold standby redundant system in which each unit works in three different modes—normal, partial failure and total failure. It is assumed that the failure and repair times 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-Stiektjes 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. Certain important results have been derived as particular cases.     

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.     

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.     

Reliability and MTTF evaluation of a repairable complex system under waiting

This paper deals with the reliability and mean time to failure (MTTF) evaluation of a complex system under waiting incorporating the concept of hardware failure and human error. Failure rates of the complex system follow exponential time distributions, whereas repair follows a general repair time distribution. Laplace transforms of various state probabilities have been evaluated and then reliability is obtained by the inversion process. A formula for variance of time to failure has also been developed. A particular case is also given to highlight some important results. Moreover, various plots have been sketched at the end.     

Reliability of a 3-unit cold redundant system with Weibull failure

Redundancy technique is applied to increase the reliability of a system where maintenance or repair is either not possible or is too costly. Reliability of a cold redundant system is always higher than a hot one. Moreover the increase in reliability due to adding of a unit in sequence can always be exactly determined.Literature is full of derivation of reliability expressions of a cold redundant system whose units obey exponential failure density. Due to extreme difficulty in evaluation of integrals involving Weibull density function, few attempts on derivation of reliability of redundant systems have been made. We have here derived reliability of a simple case of a 3-unit cold standby system whose units obey Weibull failure density.     

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.