Summary. We propose a new and simple continuous Markov monotone stochastic process and use it to make inference on a partially observed monotone stochastic process. The process is piecewise linear, based on additive independent gamma increments arriving in a Poisson fashion. An independent increments variation allows very simple conditional simulation of sample paths given known values of the process. We take advantage of a reparameterization involving the Tweedie distribution to provide efficient computation. The motivating problem is the establishment of a chronology for samples taken from lake sediment cores, i.e. the attribution of a set of dates to samples of the core given their depths, knowing that the age–depth relationship is monotone. The chronological information arises from radiocarbon (14C) dating at a subset of depths. We use the process to model the stochastically varying rate of sedimentation.

A simple monotone process with application to radiocarbon-dated depth chronologies

Many systems are required to perform a series of missions with finite breaks between any two consecutive missions. In such a case, one of the most widely used maintenance policies is a selective maintenance in which a subset of feasible maintenance actions is chosen to be performed with the aim at achieving the subsequent mission success under limited maintenance resources. Traditional selective maintenance optimization reported in the literature only focuses on binary state systems. Most systems in industrial applications, however, have more than two states in the deterioration process. In this work, a selective maintenance policy for multi-state systems (MSS) consisting of binary state elements is investigated. Taking the imperfect maintenance quality into consideration, the Kijima model is reviewed, and a cost-maintenance quality relationship which considers the age reduction factor as a function in terms of maintenance cost is established. Moreover, with the assistance of the universal generating function (UGF) method, the probability of the repaired MSS successfully completing the subsequent mission is formulated. In place of enumerative methods, a genetic algorithm (GA) is employed to solve the complicated optimization problem where both multi-state systems, and imperfect maintenance models are taken into account. The effectiveness of the proposed method is demonstrated via a case study of a power station coal transportation system. Finally, a comparative analysis between the strategies with and without considering imperfect maintenance is conducted, and it is concluded that incorporating imperfect maintenance quality into selective maintenance achieves better outcomes.

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Optimal Selective Maintenance Strategy for Multi-State Systems Under Imperfect Maintenance

A review on maintenance optimization

A multi-state system (MSS) has more than two discrete states corresponding to different performance rates. Usually, MSS is viewed as in a failure state once its performance rate falls below user demand, and maintenance is carried out immediately. Generally, the repaired system cannot be regarded as good as new, and oftentimes the system restoration is stochastic. We introduce an optimal replacement policy for MSSs, called policy N. Under this policy, a MSS is replaced whenever its failure number reaches N . We assess the dynamic element state probabilities of each aging multi-state element (MSE) using a stochastic process model which is identified as a non-homogeneous continuous time Markov model (NHCTMM), and we evaluate the state distribution of the entire MSS via the combination of the stochastic process, and the universal generating function (UGF). To quantify the quality of imperfect maintenance, a quasi-renewal process is used to describe the stochastic behavior of each individual MSE after repair. Moreover, we derive an explicit expression of the long-run expected profit per unit time, and determine the optimal failure number N* to replace the entire system. The proposed models are demonstrated via an illustrative case, followed by some comparative studies.

/pdf/optimal-replacement-policy-for-multi-state-system-under-4wf5irynsl.pdf

Optimal Replacement Policy for Multi-State System Under Imperfect Maintenance

A deteriorating cold standby repairable system with priority in use

A shock model for the maintenance problem of a repairable system

This paper studies a geometric-process maintenance-model for a deteriorating system under a random environment. Assume that the number of random shocks, up to time t, produced by the random environment forms a counting process. Whenever a random shock arrives, the system operating time is reduced. The successive reductions in the system operating time are statistically independent and identically distributed random variables. Assume that the consecutive repair times of the system after failures, form an increasing geometric process; under the condition that the system suffers no random shock, the successive operating times of the system after repairs constitute a decreasing geometric process. A replacement policy N, by which the system is replaced at the time of the failure N, is adopted. An explicit expression for the average cost rate (long-run average cost per unit time) is derived. Then, an optimal replacement policy is determined analytically. As a particular case, a compound Poisson process model is also studied.

/pdf/a-geometric-process-maintenance-model-for-a-deteriorating-ynphgm8q8k.pdf

A geometric-process maintenance model for a deteriorating system under a random environment

In this paper, a repairable system consisting of one component and a single repairman (i.e. a simple repairable system) with delayed repair is studied. Assume that the working time distribution, the repair time distribution and the delayed repair time distribution of the system are all exponential. After repair, the system is not ''as good as new''. Under these assumptions, by using the geometrical process and the supplementary variable technique, we derive some important reliability indices such as the system availability, rate of occurrence of failures (ROCOF), reliability and mean time to first failure (MTTFF). A repair replacement policy N under which the system is replaced when the number of failures of the system reaches N is also studied. The explicit expression for the average cost rate (i.e. the long-run average cost per unit time) of the system is derived, and the corresponding optimal replacement policy N^* can be found analytically or numerically. Finally, a numerical example for policy N is given.

Yuan Lin Zhang

Papers

A deteriorating cold standby repairable system with priority in use

A shock model for the maintenance problem of a repairable system

A geometric-process maintenance model for a deteriorating system under a random environment

A geometrical process repair model for a repairable system with delayed repair

A geometric process equivalent model for a multistate degenerative system