Fuzzy Xbar and S Control Charts Based on Confidence Intervals

Abstract

There have been changes since the companies have realized the important role of quality improvement in their success. If they are able to produce high quality products and satisfy demands, then they can survive in competitive global markets. Quality improvement applications aim to decrease variability, which leads to less cost, production time, number of defects, scrap, rework and more customer satisfaction. Quality can be improved by reducing product variability. On the other hand, uncertainty or subjectivity is a part of many engineering and real life problems. However, these problems cannot be solved by traditional methods. This study focuses on constructing Xbar and S control charts in fuzzy environment. The approach is developed by considering the theoretical structure of the Shewhart control charts. The core of the approach depends on the combination of parametric interval estimation and fuzzy statistics. Control limits and samples are presented by fuzzy numbers which ensures to maintain fuzziness in control charts. An important property of the approach is that the fuzzy charts can be reduced to Shewhart control charts. A simulation study was conducted for the performance evaluation of fuzzy Xbar and S control charts. The proposed fuzzy control chart is sensitive to process mean shifts and variance changes, and outperforms the traditional control charts under the changes of variance. In addition, an example from the literature shows that the approach is an effective way of presenting fuzziness in the quality characteristics, which enables the approach to have high applicability to the real life problems.