Optimal Ordering and Replacement for a 1-Unit System

A problem of ordering and replacement for a unit which degrades is discussed. The optimal age for ordering and for preventive replacement, which minimizes the total s-expected cost per unit time in an infinite time span, is obtained. Some numerical examples are presented.     

Optimum Preventive Maintenance Policies for a 2-Unit Redundant System

Optimum preventive maintenance policies are discussed to maximize the availability for a 2-unit standby redundant system. The Laplace-Stieltjes transform of the pointwise availability and the steady-state availability are derived by applying a unique modification of the regeneration point techniques under the assumptions that all the distributions are arbitrary. A theorem gives the optimum preventive maintenance time which is a unique and finite solution of the equation under certain conditions. A numerical example is presented.     

Replacement Policies for a Unit with Random and Wearout Failures

This paper considers three replacement models with random and wearout failures; a) the unit is replaced at failure, b) the unit undergoes minimal repair at failure, and c) the unit is replaced at failure only in a wearout failure period. Optimum replacement policies which minimize the s-expected cost rate for each model are discussed.     

Stabilization of Wearout?Replacement Rate

It is known that a perfectly maintained complex system of identical components, will, after an initial transient period, behave like a Poisson renewal process. In the present paper we present the results of a specific simulation which was carried out to find out how long the transient period lasts.     

Mission Reliability for a 1-Unit System with Allowed Down-Time

This paper considers a 1-unit system; the unit is repaired upon failure. The failure and repair rates need not be constant. The system fails if the unit is not repaired within a fixed time, or if the number of failures during the mission exceeds a fixed number. As a special case, that number is allowed to be ``infinite.' The Laplace transforms of the reliability and mean time to system failure are derived; they are not easily solved. The special case of constant failure and repair rates is treated. The results are compared with those of Calabro.     

Reliability of a 2-Unit Standby Redundant System with Constrained Repair Time

This paper considers a 2-unit warm-standby redundant system with repair. The repair of a failed unit is constrained as follows: Associated with each failure of a unit is a random variable termed the Maximum-Repair-Time (MRT) of the failure. If the repair of a failed unit is not completed within the MRT, the unit is rejected for further use. Two types of failure stituations for the system are considered: 1) No allowed down time, and 2) Some allowed down time. Expressions for the Cdf of the Time to System Failure (TSF) and the mean TSF are derived by using Markov renewal processes.     

Probabilistic Analysis of a 2-Unit Cold-Standby System with a Single Repair Facility

The reliability and the availability characteristics of a 2-unit cold standby system with a single repair facility are analyzed under the assumption that the failure and the repair times are both generally distributed. System breakdown occurs when the operating unit fails while the other unit is undergoing repair. The system is characterized by the probability of being up or down. Integral equations corresponding to different initial conditions are set up by identifying suitable regenerative stochastic processes. The probability of the first passage to the down-state starting from specified initial conditions is obtained by the same method. An explicit expression for a Laplace Transform of the probability density function (pdf) of the downtime during an arbitrary time interval is obtained when the repair time is exponentially distributed. A general method is suggested for the calculation of the moments of the downtime when the repair time is arbitrarily distributed.     

Reliability of a 2-Unit Priority-Standby Redundant System with Finite Repair Capability

This paper analyses the reliability of a 2-unit standby redundant system consisting of two dissimilar units. Unit 1 performs the desired system function whenever available for use. Unit 2 operates only during those periods when unit 1 is undergoing repair. Unit 1 can be repaired at most N times. Expressions for the Laplace-Stieltjes transform of the distribution of the Time to System Failure (TSF) and the mean TSF are derived.     

Stochastic Behavior of a 2-Unit Parallel Fuel Charging System

In a contribution to this TRANSACTIONS, Buzacott (1973) discussed a fuel charge/discharge system for a nuclear reactor. We consider the same parallel fuel charging system and derive more detailed results by making use of Markov renewal processes and renewal-type equations.     

A 2-Unit Repairable Redundant System with Switching Failure

The switch has two different failure modes: It switches an operating unit out of operation when it should not, and does not switch the standby in when it should. We consider a 2-unit warm-standby redundant system with two switching failure modes, and derive the stochastic behavior of system failure. Several reliability models are shown as special cases.     

An Optimal Maintenance Policy for a 2-Unit Parallel System with Degraded States

The system consists of two identical units in parallel with good, degraded, and failed states. We discuss a maintenance policy that maximizes the expected net profit-rate from the system over an infinite time span. General equations which describe the system behavior under a certain maintenance policy are derived. The optimal maintenance policy can be determined by solving those equations.     

Bayes Reliability Assessment of a 2-Unit Hot-Standby Redundant System

This study assesses the reliability of a 2-unit hot-standby redundant system with an imperfect switch. The prior knowledge of experts is used in the assessment through Bayes theorem. Bayes interval limits for the system reliability are presented. The predictive distribution of the first failure time of the system is formulated.     

Mean Time to System Failure for a 4-Unit Redundant Repairable System

The mean time-to-system-failure is derived for a system with 4-identical components, each of which has a constant failure rate and unspecified repair rate.     

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.     

Reliability Considerations for a 2-Unit Redundant System with Erlang-Failure and General Repair Distributions

This paper considers the case of a 2-identical-unit redundant system with Erlang-failure and general repair distributions. Two cases are considered: 1) the failure of each unit is independent of the other; 2) when one unit fails, the failure distribution in the other unit changes. The Laplace transforms of the distribution of time to system failure and the explicit formula for the mean time to system failure are derived.     

Reliability of a 2-Unit Standby Redundant System with Repair, Maintenance and Standby Failure

A repairable 2-unit warm-standby system with repair and preventive maintenance is discussed. Two models are presented. In each of the models the mean time to system failure and the steady state availability are calculated. Some numerical calculations illustrate the results.     

基于Gamma过程的单部件系统预防维修与更换策略

针对一类伽马(Gamma)劣化失效的单部件系统,提出了一种预防维修和预防更换策略.用伽马分布描述了系统的劣化过程,部件为不完全维修,系统维修效果假定服从正态分布.所建立的模型以部件生命周期单位时间内期望费用作为优化目标,通过求解模型可以确定预防性维修的次数、预防维修和预防更换的阈值.最后通过对一个伽马退化部件进行案例分析,验证了模型的可操作性.     

Reliability Analysis of a Two-Unit Standby-Redundant System with Preventive Maintenance

We consider a standby-redundant model of two units, where we assume that one unit is operative and the other unit is in standby at time t = 0. If the operative unit fails, a unit in standby is put into preventive maintenance policy of the operative unit to maintain our the preventive maintenance policy of the operative unit to maintain our system with high reliability. Our concern for the system is the time to the first system-down. The Laplace-Stieltjes transform of the time distribution to the first system-down and the mean time to the first system-down are derived by applying the relationship between Markov renewal processes and signal flow graph. Further, the behavior after the system-down is investigated by using the results of Markov renewal processes. Finally, numerical examples are presented for the k-Erlang failure time distributions. The optimal preventive maintenance time is discussed.     

Optimum Preventive Maintenance Policies for a Computer System with Restart

This paper considers a computer system where an operation is restarted when the system stops on some faults. The restart does not succeed every time. Three preventive maintenance (pm) models are considered: A) The pm is made at the scheduled time T. B) The pm is made at the K-th successful restart. C) The pm is made at the next scheduled time if the total number of successes of restart exceeds K. The availabilities of each model are obtained and the optimum pm policies are discussed.