A Sort Of Cumulative Sum Control Charts For Multivariate Fuzzy Data

The Statistical process control (SPC) is an approach that uses statistical techniques to monitor the process in order to improve and assure the quality of products .The so-called statistical techniques are referred to the applied methods of mathematical statistics, which is mainly the theory of control chart. It has a widespread application in some kinds of processes especially in production and manufacture processes. In general, there are three traditional variable control charts to detect the shift of mean for the continuous test problems. There are Shewhart control chart,Cumulative Sum(CUSUM) control chart and Exponentially weighted moving average(EWMA).Considering the poor sensitivity of detection of small shifts by use of conventional control chart, and based on the average run length (ARL) ease of computation, CUSUM control charts in comparison with the EWMA control charts applied more widely. Since the uncertainty of the measurement system and the fuzziness of the quality attribute, in this context, fuzzy set theory (Zadeh, 1965) is used to handle such uncertainty and fuzziness. By combining the fuzzy transformation techniques, a fuzzy CUSUM control chart for trapezoidal fuzzy data is given.Control chart is based on hypothesis testing principles. When we use control chart to detect if the shift of mean has occurred, parameters in the population distribution are usually known, or we can based on the test statistics with the estimated parameters to construct control charts. However, the variability of parameter estimation will affect the performance of control chart. Furthermore, these conditions may not be met in reality. Therefore, we use nonparametric statistical methods to deal with this situation. Commonly we can use Mann-Whitney test and Wilcoxon rank sum test. Some of the information can not be measured with the specific data, or the observations are often a matter of degree of difference, such as color depth, intensity of the reactions, fuzzy set theory and fuzzy transformation techniques are definitely some good ways. With a variable point model, Mann-Whitney statistics and the sequence comparison relationship between the fuzzy numbers, I have constructed the non-parametric CUSUM control charts in the classical or fuzzy environment correspondingly. Usually, when we test whether a product is meet the needs of the users or not only according to judge from the qualification or disqualification, it has been out of work in the actual situation. Therefore, in the industrial production process, we must evaluate the color, appearance, softness and other quality-related attributes. We can use some univariate quality control charts to monitor, each quality control chart monitors a quality attribute. However, when a large number of attribute variables need to be monitored in the process, it is not easy to implement. In this case, it is necessary to construct a fuzzy control chart for multivariate qualities. Under the transformation technique, we have considered the design of a CUSUM control chart with multivariate fuzzy data.