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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]

To make effective use of a running system, this paper proposes that, when replacement times could be scheduled at a planned time T of operation, and at a number N of minimal repairs, the newly proposed approach of whichever occurs last should be employed into optimizations for policy consideration. The replacement policy with the classical approach of whichever occurs first is also used to make comparison with the approach of whichever occurs last. Further, using the overtime technique, a replacement scheduled at time T in this paper is modified to be done at the first failure after T has arrived, to avoid probable interruptions for running jobs. That is, the system is replaced at failure N before time T, or at the first failure after T has arrived, whichever occurs first, and last, respectively. The policies acting on the approaches of first and last with minimal repairs are analyzed in detail, and their expected cost rates are formulated. Optimal solutions for separate and bivariate T and N are obtained and compared analytically. [ABSTRACT FROM PUBLISHER]

This paper proposes age and periodic replacement last models with continuous, and discrete policies. That is, an operating unit is replaced preventively at time T of operation as a strategic policy, or at a number N of working cycles to satisfy successive job completion, whichever occurs last. Such policies are named as replacement last, and their expected cost rates and optimal policies are obtained. However, the focus of this paper is to compare replacement last with replacement first policies, which are formulated under the classical assumption of whichever occurs first. From the points of cost and performability, different comparative methods for continuous and discrete optimizations are demonstrated to determine in what cases we should adopt replacement last rather than replacement first. All theoretical discussions in this paper are made analytically, and are computed numerically. [ABSTRACT FROM AUTHOR]

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]