On the use of sampling costs in quality control to select an estimator for the variance and standard deviation

In R and S-charts in quality control applied to a normal population one mostly uses a linear transformation of the range or the sample deviation as unbiased estimators of the unknown process standard deviation. In this paper, we propose related statistics as alternative estimators of the unknown standard deviation and variance having a smaller mean squared error. At the same time, we give a theoretical explanation for the rules of thumb recommended in quality control which unbiased estimators to use. Since obtaining samples from different independent subgroups is costly, we propose a mathematical model for selecting these samples to satisfy the budget constraint. The used estimator for the variance or standard deviation has a minimal mean squared error within a certain class of estimators. It is shown that selecting the whole sample from one particular chosen subgroup is a good strategy for linear sampling costs.

کلیدواژه ها:

‎Mean squared error ، Pooled statistics ، Quality control ، R-estimator ، S-estimator‎