Cost Measures and Setup Determination for Manufacturing Processes under Multi-state Performance Deterioration

摘要

This paper considers a problem of cost measures and setup determination for a manufacturing process under performance deterioration. Traditionally, to evaluate the manufacturing process reliability and performance, a binary states model, a working (success) state or a failure state, is used to classify the manufacturing process conditions. However, in many cases the manufacturing process is deteriorating over time providing that a multiple states model could be a more realistic model to capture the process deterioration conditions. Hence, the manufacturing process under performance deterioration is modeled as a nonhomo-geneous continuous-time Markov process (NHCTMP), the length of time of this deterioration process staying in some state depends not only on its current state, but also on how long it has been in the current state. We present a state-by-state integration method to find the probability function of this deterioration process being in each state at some point in time. With these states probability functions, we integrate a general class of loss functions to construct a number of performance and cost measures for assessing how severe this process deterioration causes losses at some point in time as well as over the entire deterioration process. To minimize total expected cost over the manufacturing period, the optimal setup time is also determined.