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When we consider the improvement of the functional performances that are released by the new updates of the products, it is an interesting problem to revisit the existing replacement policies. For such a viewpoint, four replacement models with product update announcements, i.e., PUA for abbreviation, are given in this paper: Model 1, the unit is replaced at time T or at PUA over time T. Model 2, the unit is replaced at the Kth failure or at PUA over the Kth failure. By considering both time T and failure K, Models 3 and 4 are obtained based on the approaches of replacement first and last. We obtain the expected cost rates for four models and discuss analytically their optimal replacement policies Further, numerical examples are given when the time for PUA has an exponential distribution. [ABSTRACT FROM AUTHOR]

Periodic replacement policies modeled with the history of minimal repairs have been studied extensively. However, in the viewpoint of cost rate, there is no literature to compare replacement polices which are carried out at some periodic times and at a predetermined number of repairs. In this paper, we compare these two types of replacement policies analytically from the optimizations of the integrated models. It will be shown that there always exists a degradation model when any bivariate replacement policy is optimized and this is just the best choice of the comparisons. Not only that, the approaches of whichever occurs first and last are applied to model the above two types of policies, which are named as replacement first and replacement last, respectively, and their comparisons are also made. In addition, we delay the policy at repair to periodic time for easier replacement, and the modified replacement model, which is named as replacement overtime, is compared with the original ones. Numerical examples are also given and agree with all analytical discussions. [ABSTRACT FROM AUTHOR]

Age replacement models are fundamental to maintenance theory. This paper summarizes our new perspectives and hods in age replacement models: First, we optimize the expected cost rate for a required availability level and vice versa. Second, an asymptotic model with simple calculation is proposed by using the cumulative hazard function skillfully. Third, we challenge the established theory such that preventive replacement should be non-random and only corrective replacement should be made for the unit with exponential failure. Fourth, three replacement policies with random working cycles are discussed, which are called overtime replacement, replacement first, and replacement last, respectively. Fifth, the policies of replacement first and last are formulated with general models. Sixth, age replacement is modified for the situation when the economical life cycle of the unit is a random variable with probability distribution. Finally, models of a parallel system with constant and random number of units are taken into considerations. The models of expected cost rates are obtained and optimal replacement times to minimize them are discussed analytically and computed numerically. Further studies and potential applications are also indicated at the end of discussions of the above models. [ABSTRACT FROM AUTHOR]

When a unit is running successive works with cycle times, it would be uneconomical or impractical to do maintenances during any working cycle. This paper firstly reviews two replacement models proposed in literatures as follows: (1) replacement is done over a planned time $$T$$ at the completion of the working cycle, which is called over-time replacement, and (2) replacement is done over damage level $$Z$$ at the completion of the forthcoming working cycle, which is called over-level replacement. From the viewpoint of replacement cost savings, we secondly focus on comparisons of over-time replacement and its standard age-based policy, over-level replacement and its standard condition-based policy. Furthermore, modified over-time and over-level replacement costs are obtained to specify critical points at which these new replacements, rather than their standard polices, would save more replacement costs. Discussions in this paper are given analytically and computed numerically. [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]

It might be difficult sometimes to derive theoretical and numerical solutions for analytical maintenance modelings due to the computational complexity. This paper takes up several approximate models in maintenance theory, by using the cumulative hazard function H ( t ) and the newly proposed asymptotic MTTF (Mean Time to Failure) skilfully. We firstly denote by t x the time when the expected number of failures is x . Using H ( t x ) = x , we estimate failure times, model age and periodic replacements, and sequential imperfect maintenance. Motivated by the asymptotic method of computation of MTTF, we secondly model the expected cost rate for a parallel system when replacement is made at system failure, and give approximate computations for the sequential inspection policy. Optimizations of each model are obtained approximately in an easier way. When failure times have a Weibull distribution, it is shown from numerical examples that the obtained approximate optimal solutions have good approximations of the exact ones. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to observe where the classical assumption “whichever occurs first” holds for preventive maintenance (PM) modelings. We firstly take up a bivariate maintenance policy where “whichever occurs first” and the newly proposed “whichever occurs last” are respectively used. Modification of PM performance is introduced into modelings to avoid interruptions of job executions, that is, PMs are done only at the end of working cycles. From the points of performability and maintenance cost, we secondly compare the optimized “first” and “last” policies in detail and find two critical points of comparisons analytically. Further, by comparing the “first” and “last” policies with the standard maintenance, modified PM costs are obtained to observe whether it is easy to save PM cost for “whichever occurs first”. For a trivariate maintenance policy, we thirdly propose an entirely new assumption “whichever occurs middle” and give another one model that considers both assumptions of “first” and “last”. We analyze maintenance probabilities for each model and then obtain directly their expected maintenance cost rates for further studies. [ABSTRACT FROM AUTHOR]

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 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]

Effective maintenance policies can improve the production system performance by alleviating product quality degradation and increasing system reliability and availability. However, reliability, product quality degradation, and availability are conflicting optimization objectives and are rarely considered together in maintenance policy optimization. Aiming at optimizing these three objectives simultaneously, this paper proposes a joint model for opportunistic maintenance (OM), and product quality and availability improvement of a series multi-machine production system (MMPS). First, a condition index (CI) is developed to characterize the condition of individual machines based on monitoring data, and the corresponding threshold functions are developed to realize maintenance decision-making for individual machines. Then, considering maintenance dependence in the MMPS, based on the CI, the dual dynamic threshold functions are introduced: the preventive maintenance (PM) and the OM threshold functions, and a novel dual-dynamic-thresholds-based OM policy is developed. Whenever the CI of a machine reaches its PM threshold, all the other machines whose CI reaches the OM zone will be maintained together with this machine. Finally, a case study and comparisons are performed to show that the proposed model can simultaneously provide good production economic performance, high quality, and availability. • A joint model for a series multi-machine production system is developed. • A quantitative index is introduced to characterize the condition of the machines. • A hybrid performance factor is developed to evaluate the joint effect of maintenance. • Economic dependence and availability dependence are considered in the PM schedule. [ABSTRACT FROM AUTHOR]