Volume 40, Issue 3 (May 2012)
Performance Evaluation and Loss Measures for the Deterioration Process
This paper considers a problem of loss measures and setup determination for a process under performance deterioration. Traditionally, to evaluate reliability and performance of the process, a binary-state model, a working (success) state or a failure state, is used to classify its conditions. However, in many cases, the process is deterioration over time, providing that a multiple-state model could be a more realistic model to capture the process deterioration conditions. Hence, the process under performance deterioration is considered as a general Markovian model, which means that its length of time staying in some state depends not only on its present state, but also on how long it has been in the present state. We present an integration method to find the probability function sojourning in each state at some point in time for this deterioration process. Based on probability functions of states, we first present a number of performance-evaluation methods. Then, we integrate a general class of loss functions to construct loss measures for assessing how severe the cost is that this process of deterioration causes at some point in time, as well as the cost over the entire deterioration process. With this measure, the setup time can be determined by the total expected cost over the operation period exceeding a preset threshold value. A tool-wear problem of the friction-drilling process is illustrated throughout the paper.