Even a stable process can show variation when measurements are recorded in sufficient detail. Variation describes how observations differ. Some measurements, such as heights within a suitable population, may cluster around a mean, but a symmetric, bell-shaped distribution must be checked rather than assumed.
Insights from International Six Sigma Institute™
The Ultimate Revelation Of Six Sigma Variation
Standard deviation measures the spread of observations around a process mean, in the same units as the measurements. Reducing standard deviation reduces that spread. A sigma level instead compares the distance from the mean to a specification limit with the process standard deviation. Five, six or seven sigma describe such a distance, not the standard deviation between sequential outputs.
The familiar Six Sigma target of about 3.4 defects per million opportunities uses the conventional assumption of a 1.5-standard-deviation shift in the process mean. It is not an unconditional prediction for every process. For a stable, approximately normal process centered between specification limits that are six standard deviations from the mean, Cp and Cpk equal 2 before any shift. If the mean moves 1.5 standard deviations toward one limit while the spread stays the same, Cpk becomes 1.5 and that limit is 4.5 standard deviations from the mean.
To reduce variation, measure process performance, investigate the causes of variation, implement improvements and monitor the results. Lower variation can reduce defect risk, but the relationship also depends on the process mean, the specification limits and the distribution. Estimate defect rates from a suitable, checked model or from observed data with a clearly defined defect opportunity; reducing spread alone does not guarantee zero defects.
Further improvement can require sustained management focus, designed experiments, capability analysis and empowered teams. A normal, or Gaussian, distribution is symmetric and bell-shaped, but process data are not always normal. Check stability and distributional assumptions before applying normal-based capability indices or predicting tail probabilities. For nonnormal data, choose an appropriate alternative analysis. Compare outputs with the Lower Specification Limit and Upper Specification Limit, and select tools such as control charts, scatter diagrams, run charts and capability studies according to the question being investigated.
