THE SAMPLING DISTRIBUTION OF THE D STATISTIC

This paper presents new statistical results for the finite population sampling distribution of the D statistic. These results are of general application and are valid whatever the operator and inspector measurement methods. An expression for the sampling variance of the D statistic is derived without making any assumption about the cause (diversion, clerical error, measurement error) of the discrepancy. The sampling variance is the sum of two terms. The first represents the uncertainty due to the sampling of a finite population of discrepancies. The second term is the sampling average of the inspectors measurement uncertainty of the sample set of items. In a second result the paper shows how the sampling variance can be estimated using only the operators declared values, the inspectors measured values and the uncertainty of the inspectors measurements. This estimation theorem is valid for any inspector measurement method. The paper also provides a general discussion of the distinction between planning a verification and performing the data analysis after the verification has been carried out.