Incomplete-data analysis and optimal planning of inspection, maintenance and replacement


Student thesis: Doctoral Thesis

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  • Mimi ZHANG


Awarding Institution
Award date16 Feb 2015


To date, the literature on inspection, maintenance (or, interchangeably, repair) and replacement is quite large. Maintenance actions include preventive (planned) and corrective (unplanned) actions carried out to retain or restore a device in or to an acceptable operating condition. An optimal planning of inspection, maintenance and replacement aims to provide optimal reliability performance (or availability performance) at the lowest possible cost. To achieve that goal, one should in turn go through the following 3 steps. Data Analysis: Manipulate raw data, e.g., completing incomplete data, and fit a candidate model to the manipulated data. Model Selection: Select among several candidate models the “right” one for the manipulated data. Maintenance Scheduling: According to the selected model, develop and then optimize a favorable maintenance policy. Therefore, to develop an optimal maintenance policy for a particular device, this dissertation is composed of 3 parts corresponding to the above 3 consecutive steps: incomplete-data analysis, model selection and maintenance scheduling. A datum is complete in that the value of the datum is exactly known. A datum is incomplete in that the value of the datum is only partially known, e.g., a right censored lifetime datum. A data set is incomplete in that some of its elements are incomplete. When dealing with data, we will run into either complete data or incomplete data. Analyzing complete data is a no-brainer, while analyzing incomplete data is a challenge. Therefore, the first part is devoted to incomplete-data analysis: we developed a data-completion approach to dealing with incomplete data. Compared with existing incomplete data analyzing methods (e.g., the EM algorithm), our approach is much easier to implement and applicable to all kinds of incomplete data. The objective of model selection is to select among a set of candidate models the most appropriate model which is the best approximation of reality revealed in the collected data. In the second part, we developed a test statistic for model selection. It is motivated by the following practical need. The Wiener process, the gamma process and the inverse Gaussian process are the three most widely used stochastic processes in condition-based maintenance. Unlike the Wiener process whose path is continuous and non-monotonic, the gamma process and the inverse Gaussian process have a lot in common. They are both suitable for modelling gradual damage introduce by continuous use. A conventional method for selection between these two models is to compare maximized likelihoods. However, selecting model by comparing maximized likelihoods is inefficient, because maximized likelihoods do not contain enough information provided by the data. Therefore the broad objective of the second part is to promote an efficient test statistic which utilizes the structural information provided by the data. The proposed test statistic has two main advantages. Firstly, it is more efficient than selecting models based on maximized likelihoods. Secondly, the test statistic is also applicable to incomplete data. To evaluate the impact of maintenance actions on a maintained system’s condition, many imperfect maintenance models have been developed. The motivation of the third part is to address three fundamental problems in imperfect maintenance that still remain widely open. First, many imperfect maintenance models are confined to the realm of speculation. It is more desirable to develop imperfect maintenance models by taking a physically meaningful approach. Second, for most imperfect maintenance models, the parameters introduced for modeling the effect of maintenance actions are assumed constant. It is more realistic to assume that they are random. Third, though there have been many imperfect maintenance models, most of them are only concerned with age-based maintenance. The issue of treating imperfect maintenance in the context of condition-based maintenance has not received much attention and remains widely open. The broad objective of the third part is to develop practical imperfect maintenance models and suitable maintenance policies for different types of devices.

    Research areas

  • Maintainability (Engineering)