Measuring and Achieving SIX-SIGMA PERFORMANCE

Manufacturing Engineering, Jul 2004 by Horst, Robert L

Graphing data points can visually present operations personnel with the sigma metric and the level-of-defectives actually achieved

Manufacturers cannot know when they've achieved six-sigma performance-or some lesser goal-without measuring the performance of individual production variables in sigma-level metrics. But conventional statistical tools don't readily provide that knowledge.

The gold standard to be achieved and certified is six-sigma performance. It's a realizable objective and a highly desirable performance goal for enterprise profitability, but sometimes appears not to be economically justifiable. Sigma is population standard deviation, and a measure of data dispersion or scatter.

"Six sigma" is a statistical measure of excellence in process performance as defined by Motorola in the 1980s, wherein process tolerance corresponds to ±6[sigma]. It's not a total quality management program, strategy, or method, although some consultancies are marketing their TQM, CQI (continuous quality improvement), and quality-team implementation systems under the Six Sigma moniker.

The Motorola model defines a 6[sigma] criterion for excellence, promising extremely high yields, with a maximum of 3.4 defectives per million (dpM). (Note that a defective is an error, faulty part or action, or out-of-tolerance variable.) A unique feature of the Motorola peak-yield ideal is that it acknowledges an acceptable degree of drift (process shift) of variables from target, and permits a defined zone of variation. No process adjustments need to be made when the collected data stay within the limits of ±1 ½ sigma, as long as manufacturing specs are consistent with a process tolerance of ±6[sigma]-corresponding to a process capability index (C^sub p^) of 2-or, alternatively ±4 ½[sigma].

A second unique feature of the Motorola-defined model is the relevance of short-term versus long-term data collection. To meet the 6[sigma] criterion, short-term data need to exhibit a standard deviation that fits with process tolerance. The focus is always on reducing data scatter represented by the spread of the bell curve.

The power of sigma-level performance analysis for the improvement of manufacturing processes kicks in where the usefulness of statistical process control (SPC) diminishes. SPC is a powerful analytical tool for out-of-control process/product variables, but it's inadequate for quantitative analysis of "in-control," high-yield processes.

All quality management regimens are extensions and expansions of the PDCA cycle (plan, do, check, act) originated by W.A. Shewhart in his book The Economic Control of Quality of a Manufactured Product (published in 1931), in combination with problem definition, data collection, analysis, and testing of hypotheses. The action step is the engineering (or re-engineering) that leads to improvement of quality in a manufacturing process and/or product. The work and writings of W.E. Deming and most contemporary quality consultants are founded upon Shewhart's teachings, including the principal analytical tools of SQC/SPC (statistical quality control/statistical process control).

Today, however, Shewhart's tables for estimating process standard deviation [sigma] are of little utility on the factory floor, because of the availability of handheld calculators and laptop computers that provide instant statistical calculations for collected data. In the October, 2003 issue of Manufacturing Engineering, Vivek Sharma states correctly that Six Sigma consultancies have "not introduced even one original tool to the quality field." (See Six Sigma: A Dissenting Opinion on page 16 ofthat issue.)

SPC practice always focuses on centering the mean value, on reducing process shift to a minimum. Standard deviation is used to establish upper and lower control limits of ±3[sigma] representing 99.7% yield for a perfectly incontrol, centered-on-target process.

Surprisingly-and perplexingly to some quality improvement practitioners-the long-term performance of a 6[sigma]-controlled process may have a centered process deviation that looks like a 4½[sigma] process (actually, 4.65[sigma]), and still meet the 3.4 defects per million requirement!

Multiple sets of short-term data will have central values (means) that scatter across the allowable ±1 ½[sigma] zone within which no correction is required. The data distribution for the subgroups may be systematic or irregular, but the distribution of the data over the long term will tend to be normal (Gaussian), with mean value centered at, or near, the specification target value. (Statisticians rely on something called the central-limit theorem to explain this outcome.)

In practice, short-term data are considered to be 10-30 consecutive data points per set, spanning a minimum of one to three or more process cycles, depending upon the dynamics of the given process. Long-term data are usually collected at regular intervals over the course of an extended factory run with a minimum of 10 data points per subgroup.