EFFECTS OF ESTIMATORS OF PROCESS STANDARD DEVIATION ON THE DETECTIVE CAPACITY OF X-BAR CHARTS
The effect of the biased and unbiased estimators of process standard deviation on the performance of X charts is studied, with reference to false alarm rates. The false alarm rate function of X-bar charts is derived on the subgroup and the effect of the coefficients of the process standard deviation (denoted as k/) on X control charts is studied. The probability that a subgroup mean falls outside the control limits approaches its theoretical value as the number of subgroups m exceeds 500, with sample sizes n = 5.The conclusion of this study is that the traditional estimators, such as R/d2 n) andS/c4n), are better than biased ones in constructing X chart limits because of their ease of use and their lower false alarm rates. This study also presents an example of the wire pull strength of the BGA product to demonstrate the application of these estimators in the statistical process control (SPC) arena. It provides suggestions on the choice of suitable estimators for practical use. , number=1, journal=International Journal of Industrial Engineering: Theory, Applications and Practice, author=Ho, Chuanching and Kao, Shih-Chou and Case, Kenneth, year=2022, month=Feb., pages=28–40