Fuzzy Evaluation Models for Accuracy and Precision Indices

Abstract

The random variable X is used to represent the normal process containing two important parameters—the process average and the process standard deviation. The variable is transformed using Y = (X − T)/d, where T is the target value and d is the tolerance. The average of Y is then called the accuracy index, and the standard deviation is called the precision index. If only the values of the accuracy index and the process precision index are well controlled, the process quality level as well as the process yield are ensured. Based on this concept, this paper constructed a control chart for the accuracy index and the precision index and derived the confidence intervals of the accuracy index and the precision index using in-control data, as the process was stable. This paper aims to control process quality via monitoring the accuracy and precision of the process. At the same time, fuzzy tests are developed for the indicators of process accuracy and precision to evaluate whether the process quality can reach the k-sigma quality level, as well as offer suggestions about directions of improvement when it fails to reach the k-sigma quality level. Obviously, the model in this paper cannot only evaluate whether the process meets the requirements of the quality level; it can also provide a decision regarding whether the process should be improved. It is very helpful for the enhancement of enterprises’ process capabilities.

Keywords

• <i>k</i>-sigma
• accuracy index
• precision index
• membership function
• fuzzy evaluation model