Dynamic performance and cost measures with setup determination under state-age-dependent deterioration

Abstract

Many manufacturing processes and production systems suffer from progressive degradation with usage and age and are subject to random failures resulting from such deterioration. Traditional models for evaluating the reliability and performance of a process/system use binary-state models, with working success or failure, to classify the states of the process/system that are unrealistic. This article proposes the classification of discrete multiple states of the deterioration process. A nonhomogeneous continuous-time Markov process is employed for modelling the process deterioration because we assume that the time for which a process stays in certain state depends not only on the current state but also on the time for which the process has been in the current state. For major and minor deteriorations, we present symbolic solutions of several differential equations by using MATLAB to estimate the probability of the process being in each state at time t. We contribute dynamic performance and cost measures for the state-age-dependent process deterioration to assess the severity of the deterioration at some point in time as well as the total severity that it causes over the entire process. The optimal setup time is determined in order to estimate the minimum total expected cost during the production period. A practical application of the proposed methodology is illustrated throughout this article.

Keywords:

• deterioration process
• nonhomogeneous continuous-time Markov process
• general loss function
• dynamic cost measure
• setup determination

Acknowledgement

This work was partially supported by National Science Council of Taiwan under the grant no. NSC98-2221-E-151-030-MY3.