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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.


Crossroads or Crisis?
Simsack takes the low road to opportunity.

Michael J. Cleary, Ph.D.



Recurring ISO 9001 audits can be seen as challenges or opportunities. The Chinese characters for "crisis" include "opportunity," illustrating the two-edged sword that is "challenge."

To Hartford Simsack, his company's upcoming audit represents only an opportunity for a grand headache, no matter how many times he's reminded about what he might learn from it. Greer Grate & Gate's most recent audit reflected several major findings--all of which made Simsack look bad. Looking bad was what Simsack had wanted to avoid at all costs.

During the last audit, the auditor asked Simsack about a data set that showed how the company's defect rate increased as the plant temperature increased. Simsack didn't respond except with a mumble, so the auditor pressed him about analysis of the data.

Because Simsack knew only how to use X-bar and R charts, he insisted that the next step would be to use such charts to determine the relationship between defects and the temperature. When the auditor suggested that a scattergram would provide a clearer idea of the correlation, Simsack grudgingly mumbled that he would have his team look into scattergram usage. Secretly, however, he felt confident that an X-bar and R chart would serve him better--simply because he used this statistical analysis for everything else.

Checking with his mentor, Dr. Stan Deviation, at the local community college, Simsack was introduced to the concept of simple regression and immediately loved the way the term rolled off his tongue. Deviation pointed out that if one variable has an effect on a second variable, the appropriate model is simple regression. He drew an example depicting the relationship between tons of coal produced and total cost.

He went on to explain how to determine the regression line using "least squares." In this case, the regression line is defined as illustrated above.

Simsack could hardly wait to showcase his newfound knowledge in front of the auditor the following day and explain that in order to get a best fit line, all that's required is to square all the data and take the smallest (i.e., least) one.

Would Simsack's explanation be considered:

a) an opportunity for continued growth in understanding?

b) yet another crisis created by his ongoing incompetence?

Unfortunately, Simsack has apparently mastered only one aspect of the Chinese characters--that which pertains to crisis. His ear for statistical language doesn't match his understanding of computation.

The concept of least squares is best understood with the following diagram:

Consider the above figure with three data points that suggest a relationship between x and y of lower left to upper right. A line through these points minimizes the vertical deviations . This explains what the least squares method accomplishes. Mathematical formulas to determine the line are:

Formulas have their own language. Perhaps Simsack should go back to studying the richer possibilities of the concept expressed in the Chinese characters.

About the author

Michael J. Cleary, Ph.D., is a professor emeritus at Wright State University and founder of PQ Systems Inc. He has published articles on quality management and SPC in a variety of academic and professional journals. Visit his Web site at www.pqsystems.com. Letters to the editor regarding this column can be e-mailed to letters@qualitydigest.com.