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This article revisits the optimization problems of age-based replacement models for exponential failure distributions. First, we show the steps how an age replacement time goes to an infinite value when the lifetime of a unit has an exponential distribution, and then, we give two discussions of possible replacement times, by introducing a new concept of cost named as deviation cost per unit of time between replacement and failure. Second, similar discussion is given for a random replacement model when the age replacement time is a random variable with a uniform distribution. Third, the models of age-based replacement first and last with deviation costs are discussed when a random replacement is taken into account for an age replacement model. Numerical examples are illustrated to show the results of the analytical discussions. Finally, necessary proofs are provided in the Appendixes. [ABSTRACT FROM AUTHOR]

This paper takes up managerial maintenance policies during different phases for mission executions. When a mission execution is divided into two phases and three phases respectively, replacement, minimal repair and keeping failure status become alternatives for managerial maintenance policies. Further, we give approximations of the above managerial maintenance policies to make the computations simple. In this paper, keeping failure status is considered as the last choice for the last phase of mission executions. We aim to minimize the expected maintenance costs for the total mission executions. All of the discussions are made analytically and their numerical examples are given. [ABSTRACT FROM AUTHOR]

This paper discusses preventive replacement policies for an independent damage process, in which successive shocks occur at random times, and the independent damages caused by shocks are random variables. It is assumed that a unit fails when the damage has exceeded a prespecified level K. We consider three models: Model 1: the unit is replaced at the M th shock for damage Z , at damage K , or at time T , whichever occurs first. Model 2: the unit is replaced at the M th shock for damage Z , at damage K or at shock N , whichever occurs first. Model 3: the unit is replaced at the M th shock for damage Z , at damage K , at shock N or at time T , whichever occurs first. We obtain the expected cost rates for each model and discuss analytical optimal T ∗ and N ∗ to minimize their expected cost rates. Numerical examples are given when the damage has an exponential distribution and shocks occur at a gamma distribution. [ABSTRACT FROM AUTHOR]

It is always difficult to discuss the analytical formulas, in which optimum solutions of replacement policies satisfy, due to the mathematical complexity. This paper proposes several approximate calculations for age-based random replacement policies, such that the unit is replaced at time T, at random time Y j (j = 1 , 2 , ...) over time T, and at random time YN for Y j (j = 1 , 2 , ... , N). We use the inequality properties of the formulas and the bounds of the extended failure rate functions to find the approximate calculations of replacement times in analytical ways. It is shown from numerical examples that these approximate calculations would become useful references for the optimum age-based random replacement times. [ABSTRACT FROM AUTHOR]

This paper takes up the reliability and preventive replacement problems for a K -out-of- n system, where K is a stochastic parameter provided. Firstly, we consider the case when K is predefined as constant numbers as is done with the traditional method, and obtain the system reliability R ( t ), mean time to failure (MTTF), and replacement policies, in which the number n of units for replacement and replacement time T of operation are, respectively, optimized. Secondly, we focus on the above discussions again when K cannot be predefined constantly, but it is a random variable with an estimated probability function. Furthermore, we give approximate computations in an easier way for MTTF, optimal number n * and replacement time T *, respectively. [ABSTRACT FROM AUTHOR]

It has been assumed for a standby unit that periodic inspection is performed more easily to detect failures, but such a strict periodic mode would be impractical if the unit is executing some procedures without stops. From the above viewpoint, this paper first optimises a random inspection policy in accordance with random procedure times, compares it with periodic inspection and computes a modified checking cost for random inspection to determine the case where such a random inspection would be adopted. Second, this paper proposes three new inspection models in which inspections with deterministic policies are scheduled strategically while their performances need to be limited by completion times of operation procedures. These policies are called inspection first, inspection last and inspection overtime. The total expected inspection and downtime costs of each model until failure detection are obtained, and optimal policies which minimise them are derived analytically. Furthermore, the three inspection policies are compared with periodic inspection, inspection first and last are compared with each other, and a modified checking cost for inspection overtime is discussed when the policy would be better than periodic inspection. [ABSTRACT FROM AUTHOR]

In some practical situations, it may be more economical to work a used system than do a new one. From this viewpoint, this article considers three basic preventive maintenance (PM) policies for a used system: the system with initial variable damage Y 0 begins to operate at time 0, and suffers damage due to shocks. It fails when the total damage exceeds a failure level K and corrective maintenance is made immediately. To prevent such failure, it undergoes PM at a planned time T, a shock number N and a damage level k, but maintenances are imperfect. However, failure rate of a used system maybe higher than that of a new one, so some maintenance is applied to the policies at each shock in the extended models. Using the theory of cumulative processes, expected cost rate models are obtained, optimal policies which minimise them are derived analytically and discussed numerically. [ABSTRACT FROM PUBLISHER]

This paper considers a parallel system with a random number of units according to a Poisson distribution. The fracture of an aircraft fuselage with multiple site damage serves as a real world application for this problem. The mean time to failure is obtained. Using this result, an optimal number of units and replacement time for the system which minimize the expected cost rates are derived analytically, and numerically, when the failure time has a Weibull distribution. It is of interest that these results also give good approximations to those of the system with a constant number of units. Further, similar discussions for a scheduling problem of a job with random working times are made, when a parallel system is provided. [ABSTRACT FROM AUTHOR]

This article considers an extended parallel system with cascading failure: Compared with the conventional parallel system with independent failure, the factor that cascading failure could reduce the reliability of the system due to redistribution of the workload. Reliability measures of the system are derived, using the theory of stochastic processes. To counteract the impact of cascading failure, a preventive maintenance policy is proposed. Further, this is applied to a dual active system. An optimal maintenance policy which minimizes the expected cost rate is derived. Finally, a numerical example is given and some discussions are made. [ABSTRACT FROM AUTHOR]