Mimi Zhang

Degradation-based maintenance decision using stochastic filtering for systems under imperfect maintenance

The notion of imperfect maintenance has spawned a large body of literature, and many imperfect maintenance models have been developed. However, there is very little work on developing suitable imperfect maintenance models for systems outfitted with sensors. Motivated by the practical need of such imperfect maintenance models, the broad objective of this paper is to propose an imperfect maintenance model that is applicable to systems whose sensor information can be modeled by stochastic processes. The proposed imperfect maintenance model is founded on the intuition that maintenance actions will change the rate of deterioration of a system, and that each maintenance action should have a different degree of impact on the rate of deterioration. The corresponding parameter-estimation problem can be divided into two parts: the estimation of fixed model parameters and the estimation of the impact of each maintenance action on the rate of deterioration. The quasi-Monte Carlo method is utilized for estimating fixed model parameters, and the filtering technique is utilized for dynamically estimating the impact from each maintenance action. The competence and robustness of the developed methods are evidenced via simulated data, and the utility of the proposed imperfect maintenance model is revealed via a real data set.

A condition-based maintenance strategy for heterogeneous populations

Heterogeneous population.Cost criterion.Reliability criterion.Comparative analysis. This paper develops a maintenance strategy, called inspection-replacement policy, to cope with heterogeneous populations. Burn-in is the procedure by which most of the defective products in a heterogeneous population can be identified and removed prior to being placed in service. However, modern manufacturing is so well developed that a defective product is able to function for a long period of time even under aggravated operational conditions. Instead of weeding defective products out via costly burn-in tests, use can be made of them in field operation where maintaining actions will be performed to prevent early in-use failures. The inspection-replacement policy consists of an inspection, conducted in an early stage with the purpose of identifying and replacing defective products, and a preventive replacement, carried out at a later stage to prevent wear-out failures. The preventive-replacement time is dynamically determined, depending on the information obtained by the inspection. The inspection-replacement policy is compared with a joint burn-in and age-based-replacement policy to show its practicability and competence.

A Bivariate Maintenance Policy for Multi-State Repairable Systems With Monotone Process

This paper proposes a sequential failure limit maintenance policy for a repairable system. The objective system is assumed to have k+1 states, including one working state and k failure states, and the multiple failure states are classified potentially by features such as failure severity or failure cause. The system deteriorates over time and will be replaced upon the Nth failure. Corrective maintenance is performed immediately upon each of the first (N-1) failures. To avoid the costly failure, preventive maintenance actions will be performed as soon as the systems reliability drops to a critical threshold R. Both preventive maintenance and corrective maintenance are assumed to be imperfect. Increasing and decreasing geometric processes are introduced to characterize the efficiency of preventive maintenance and corrective maintenance. The objective is to derive an optimal maintenance policy (R*,N*) such that the long-run expected cost per unit time is minimized. The analytical expression of the cost rate function is derived, and the corresponding optimal maintenance policy can be determined numerically. A numerical example is given to illustrate the theoretical results and the maintaining procedure. The decision model shows its adaptability to different possible characteristics of the maintained system.

An Ameliorated Improvement Factor Model for Imperfect Maintenance and Its Goodness of Fit.

ABSTRACT Maintenance actions can be classified, according to their efficiency, into three categories: perfect maintenance, imperfect maintenance, and minimal maintenance. To date, the literature on imperfect maintenance is voluminous, and many models have been developed to treat imperfect maintenance. Yet, there are two important problems in the community of maintenance that still remain wide open: how to give practical grounds for an imperfect-maintenance model, and how to test the fit of a real dataset to an imperfect-maintenance model. Motivated by these two pending problems, this work develops an imperfect-maintenance model by taking a physically meaningful approach. For the practical implementation of the developed model, we advance two methods, called QMI method and spacing-likelihood algorithm, to estimate involved unknown parameters. The two methods complete each other and are widely applicable. To offer a practical guide for testing fit to an imperfect-maintenance model, this work promotes a bootstrapping approach to approximating the distribution of a test statistic. The attractions and dilemmas of QMI method and spacing-likelihood algorithm are revealed via simulated data. The utility of the developed imperfect-maintenance model is evidenced via a real dataset. This article has a supplementary material online.

Optimal Burn-in Policy for Highly Reliable Products Using Inverse Gaussian Degradation Process

Burn-in test is a manufacturing procedure implemented to identify and eliminate units with infant mortality before they are shipped to the customers. The traditional burn-in test, collecting event data over a short period of time, is rather inefficient. This problem can be solved if there is a suitable quality characteristic (QC) whose degradation over time can be related to the lifetime of the product. Optimal burn-in policies have been discussed in the literature assuming that the underlying degradation path follows a Wiener process or a gamma process. However, the degradation paths of many products may be more appropriately modeled by an inverse Gaussian process which exhibits a monotone increasing pattern. Here, motivated by the numerous merits of the inverse Gaussian process, we first propose a mixed inverse Gaussian process to describe the degradation paths of the products. Next, we present a decision rule for classifying a unit as typical or weak. A cost model is used to determine the optimal burn-in duration and the optimal cut-off level. A simulation study is carried out to illustrate the proposed procedure.

A Stochastic EM Algorithm for Progressively Censored Data Analysis

Progressivecensoringtechniqueisusefulinlifetimedataanalysis.Simpleapproachestoprogressivedataanalysisarecrucialforitswidespreadadoptionbyreliabilityengineers.Thisstudydevelopsanefficientyeteasy-to-implementframeworkforanalyzingprogressively censored data by making use of the stochastic EM algorithm. On the basis of this framework, we develop speci ficstochastic EM procedures for several popular lifetime models. These procedures are shown to be very simple. We thendemonstrate the applicability and efficiency of the stochastic EM algorithm by a fatigue life data set with proper modificationand by a progressively censored data set from a life test on hard disk drives. Copyright

Lower confidence limit for reliability based on grouped data using a quantile-filling algorithm

The aim of this paper is to propose an approach to constructing lower confidence limits for a reliability function and investigate the effect of a sampling scheme on the performance of the proposed approach. This is accomplished by using a data-completion algorithm and certain Monte Carlo methods. The data-completion algorithm fills in censored observations with pseudo-complete data while the Monte Carlo methods simulate observations for complicated pivotal quantities. The Birnbaum-Saunders distribution, the lognormal distribution and the Weibull distribution are employed for illustrative purpose. The results of three cases of data-analysis are presented to validate the applicability and effectiveness of the proposed methods. The first case is illustrated through simulated data, and the last two cases are illustrated through two real-data sets.

Vine copula approximation: a generic method for coping with conditional dependence

Pair-copula constructions (or vine copulas) are structured, in the layout of vines, with bivariate copulas and conditional bivariate copulas. The main contribution of the current work is an approach to the long-standing problem: how to cope with the dependence structure between the two conditioned variables indicated by an edge, acknowledging that the dependence structure changes with the values of the conditioning variables. The changeable dependence problem, though recognized as crucial in the field of multivariate modelling, remains widely unexplored due to its inherent complication and hence is the motivation of the current work. Rather than resorting to traditional parametric or nonparametric methods, we proceed from an innovative viewpoint: approximating a conditional copula, to any required degree of approximation, by utilizing a family of basis functions. We fully incorporate the impact of the conditioning variables on the functional form of a conditional copula by employing local learning methods. The attractions and dilemmas of the pair-copula approximating technique are revealed via simulated data, and its practical importance is evidenced via a real data set.

Continuous-Observation Partially Observable Semi-Markov Decision Processes for Machine Maintenance

Partially observable semi-Markov decision processes (POSMDPs) provide a rich framework for planning under both state transition uncertainty and observation uncertainty. In this paper, we widen the literature on POSMDP by studying discrete-state discrete-action yet continuous-observation POSMDPs. We prove that the resultant

Degradation Modeling Using Stochastic Filtering for Systems under Imperfect Maintenance

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