Εκτίμηση της τυπικής απόκλισης στο στατιστικό έλεγχο ποιότητας
Estimation of standard deviation in statistical quality control
Statistical Quality Control is a method to control the production processes which aims at the conservation and in improving the quality of the derived product line. Control charts are a technique used in Statistical Quality Control. In this MSc dissertation we deal with various estimators of the standard deviation of the plotted statistic on the chart which is one of the major problems in the construction of control charts. The effectiveness of a control chart is mainly determined by the estimator to be selected. The research includes both the case of the individual observations and the case of rational subgroups. In the case of individual observations we study six estimators ( , , , , , ), unbiased and biased. The comparison of the estimators was based on their relative efficiency. The results obtained from the relative efficiency study show that the estimators based on the range of the samples range are less efficient. Moreover, the same seems to be true for the unbiased estimators. Finally among the non-unbiased estimators ( , , ), which are based on the sample standard deviation, estimator is slightly more efficient. Similarly in the case of rational subgroups we study six estimators ( , , , , , ), unbiased and biased. Based on the relative efficiency results, we observed that the estimators based on the sample range are not recommended for the estimation of standard deviation. Generally, it appears that the estimators that are based on the pooled sample statndard deviation outperfom the other estimators. It also appears that the non-unbiased estimators are superior in comparison with the biased estimators. Finally there is a slight superiority of estimator among the three more efficient estimators ( , , ).