Tests of significance for the average square deviation from target in a finite lot

Abstract

Consider lots of discrete items 1, 2, …,N with quality characteristicsx ₁,x ₂, …,x _N . Leta be a target value for item quality. Lot quality is identified with the average square deviation$z = \mathop - \limits_N^1 \mathop \Sigma \limits_{i = 1}^N (x_1 - a)^2$ from target per item in the lot (lot average square deviation from target). Under economic considerations this is an appropriate lot quality indicator if the loss respectively the profit incurred from an item is a quadratic function ofx _i −a. The present paper investigates tests of significance on the lot average square deviationz under the following assumptions: The lot is a subsequence of a process of production, storage, transport; the random quality characteristics of items resulting from this process are i.i.d. with normal distributionN(μ, σ ²); the target valuea coincides with the process meanμ.