Statistical Reason for the 1.5σShift

Abstract

Ever since Motorola, Inc. introduced its Six Sigma quality initiative, quality practitioners have questioned why followers of this philosophy add a 1.5σ shift to the average before estimating process capability. Six Sigma advocates claim such an adjustment is necessary but offer only empirical studies as justification for this decision. By examining the sensitivity of control charts to detect changes of various magnitudes, this article provides a statistically based reason for including such a shift in the process average. A new capability index, called dynamic C pk , incorporating this shift is introduced.

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