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Statistical Thinking to Improve Quality
This blog examines the use of data analyses and statistical tools in a framework of statistical thinking to improve quality. The following principles form the basis for statistical thinking:

* All work occurs in a system of interconnected processes,
* Variation exists in all processes, and
* Understanding and reducing variation are keys to success.

Statistical thinking significantly improves the effectiveness of data analyses and statistical tools.
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Process Capability Indices
Posted by: Gordon Clark on October 29, 2009 at 6:02PM CST
This posting discusses the use of process capability indices in fifth step, Evaluate Capability, of the Hoerl-Snee Process Improvement Strategy.   Refer to the figure in the April 4 posting for an overview of the process.    See Hare (2007) or Breyfogle (2003) for references.

The following figures illustrate two problems with the Cpk index.
1.     In the first figure, two processes with identical Cpk values (1.5) have significantly different means and standard deviations.  Possibly changing the mean is easier to accomplish than the standard deviation.
2.     In the second figure, two processes with identical Cpk values (1.0) have different distributions.   One is normal and the other lognormal.  For the normal distribution, the probability of being below the lower spec limit is .00135, and the probability of exceeding the upper spec limit has the same value.   For the normal distribution, the total probability of not meeting the spec limit is .0027.   For the lognormal distribution, the probability of the quality measure being below the lower spec limit is approximately zero, while the probability of being greater than the upper spec limit is .007915.   For the lognormal, the probability of not meeting the spec limits is almost three times the corresponding value for the normal distribution.

For the above reasons and others, Breyfogle (2003) recommends the use of estimated parts per million (ppm) beyond specification limits rather than process capability estimates.

Due to sampling variability, Hare (2007) recommends estimating process capability indices using at least 100 values.

Reference

  1. Hare, Lynne B. (2007).  “The Ubiquitous Cpk”, Quality Progress, pp. 72-73.
  2. Breyfogle III, Forrest W. (2003). Implementing Six Sigma – Smarter Solutionsâ Using Statistical Methods, John Wiley & Sons, Inc., pp 296-299.
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