Abstract
For a process in which a shift of the mean from the target appears to be less serious in one direction than in the other, the user should be able to impose only one tolerance. If the risk is considered k times less serious in the direction opposite to the tolerance, Grau suggests using the Cup(u, v) or C1p(u, v) indices. In this paper we study the links between these indices and process centering, as well as the links between these indices and the percentage of non-conforming items manufactured under the assumption of normality. These results are used to choose the pair (u, v) meeting the needs of the user as well as possible. We also develop a decision making rule based on the natural estimator which can be used to test whether the process is capable or not. We then present a study made on a polymer granulates manufacturing process to illustrate how this reasoning can be applied.
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