Normal approximation through data replication when estimating DisPMO, DePMO, left‐side and right‐side Sigma levels from non‐normal data

Abstract

Purpose

This paper seeks to present a way of estimating DisPMO, DePMO, left‐side and right‐side Sigma levels (as the “mutations” of DPMO and Sigma level when applied on customer satisfaction measurements), where all critical attributes (CTQs) contain data sets that are non‐normally distributed.

Design/methodology/approach

The calculation of DisPMO, DePMO, left‐side and right‐side Sigma levels is based on dynamic‐multiple CTQs without the need for assuming 1.5 Sigma shift from the mean. Using step‐wise multiple regression, CTQs are then the attributes that significantly influence overall customer satisfaction. This further developed method no longer takes normality assumption for granted, which means that, prior to calculating DisPMO, DePMO, left‐side and right‐side Sigma levels, the data should be proven as being normally distributed. To fulfil the assumption of normality, the primary data are being “replicated” by first generating random numbers that follow normal standard distribution and then adjusting (re‐calculating) these random numbers with the mean, standard deviation, and the skewness of the primary data. Simulation technique is then applied to generate a larger amount of secondary data as the basis for estimating DisPMO, DePMO, left‐side and right‐side Sigma levels.

Findings

The application of the method in a Swedish house‐building construction project suggests that: the use of multiple CTQs may reduce the risk for under‐/overestimation of Sigma levels, and DisPMO and DePMO are each other's “mirror” and both of them should be considered when calculating Sigma levels. The calculated Sigma levels suggest that the developer's performance is still quite far below Six Sigma level of performance.

Originality/value

Using the replica of the primary data as a way of approaching normality may be regarded as the main contribution of the paper in addressing one of the challenges in Six Sigma theory.

Citation

Setijono, D. (2010), "Normal approximation through data replication when estimating DisPMO, DePMO, left‐side and right‐side Sigma levels from non‐normal data", International Journal of Quality & Reliability Management, Vol. 27 No. 3, pp. 318-332. https://doi.org/10.1108/02656711011023302