Detecting the Process' 1.5 SIGMA Shift: A Quantitative Study

Process behavior can change with time. In this study an attempt was made to discover whether the Six Sigma(TM) claim of changes in the process mean stayed within +/- 1.5 sigma units.

Several process groups were examined for a particular firm that made metal castings, machined parts, tested major components and assembled these into a vehicle that was a product sold to the customer.

As the assembly progressed, deficiencies were identified and recorded.

Analyses employed cumulative sum (CUSUM) sequence charts, Autoregressive Integrated Moving Average (ARIMA) time series analyses, minimum mean square error (MMSE) exponentially weighted moving average (EWMA), Shewhart control charts and Analysis of Variance (ANOVA) to identify the shift in the process mean, M/sw, the duration of the shift, lambdaB, and the proper choice of EWMA smoothing coefficient, lambdaEWMA.

Kruskal-Wallis analysis of the relationship of these measures to process group (assembly, foundry, heat treatment, machining, shaving, test machine, grinding, turning, warranty and yield) was also performed.

The method used was generally applicable for all these processes.

The process group and the ARIMA type also influenced the measurement of M/sw, lambdaB, and lambda EWMA.