Right up front in our discussion, let us recognize that the 1.5 sigma shift can be attributable solely to the influence of random error. In this context, the 1.5 sigma shift is a statistically based correction for scientifically compensating or otherwise adjusting a postulated model of instantaneous reproducibility (short-term capability) for the inevitable consequences associated with long-term random sampling variation. Naturally, such an adjustment (1.5 sigma shift) is only considered and instituted at the opportunity level of a product configuration. Thus, the model performance distribution of a given critical to quality characteristic (CTQ) can be affectively attenuated for many of the operational uncertainties associated with a design-process qualification (DPQ).
Based on this quasi-definition, it should fairly evident that the 1.5 sigma shift factor can often be treated as a statistical correction, but only under certain engineering conditions that would generally be considered typical. By all means, the shift factor (1.5 sigma) does not constitute a literal shift in the mean of a performance distribution – as many quality practitioners and process engineers falsely believe or try to postulate through uniformed speculation and conjecture. However, its judicious application during the course of designing a system, product, service, event, or activity can greatly facilitate the analysis and optimization of configuration repeatability.
By the conscientious application of the 1.5 sigma shift factor (during the course of product configuration), an engineer can meaningfully “design in” the statistical and pragmatic confidence necessary to ensure or otherwise assure that related performance safety margins are not violated by unknown (but anticipated) process variations. Also of interest, its existence and conscientious application has many pragmatic implications (and benefits) for reliability engineering. Furthermore, it can be used to normalize certain types and forms of benchmarking data in the interests of assuring a level playing field when considering heterogeneous products, services and processes.
In summary, the 1.5 sigma shift factor should only be viewed as a mathematical construct of a theoretical nature. When treated as a statistical correction, its origin can be mathematically derived as an equivalent quantity representing or otherwise reflecting the worst-case error inherent to an estimate of short-term process capability. As can be demonstrated, the shift factor is merely an algebraic byproduct of the chi-square distribution that will vary depending on the accepted level of risk and prevailing degrees-of-freedom. However, when typical application circumstances are postulated and rationally evaluated, the resulting shift will prove to be approximately equivalent to 1.5 sigma.