Determination of optimum target values for a tool wear process based on a surrogate variable

In this research, we present a profit model for determining the initial process mean, the length of resetting cycle, and the screening limits for a tool wear process where its mean shifts linearly as its operating time elapses. Each outgoing item is inspected with a surrogate variable which is correlated with the quality characteristic of interest. A profit model is constructed which involves selling price, costs of resetting, production, inspection, scrap, and losses due to the type I and II errors. Assuming that the quality characteristics of interest and the surrogate variable are jointly normally distributed, the initial process mean, length of resetting cycle, and screening limits are obtained by maximizing expected profit function using a numerical search method. An illustrative example of the automotive end-body parts manufacturing process is provided with numerical studies.