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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.


When the Chips Are Down
Cold, hard facts and p-charts

Michael J. Cleary, Ph.D.


Synk R. Swymm is learning to make charts for Deer Dairy Farms, a small firm that produces ice cream. When evaluating the quality of the finished product, the company insists on consistency for all the ice cream that’s shipped. For example, inspectors examine chocolate chip cookie dough ice cream content for the number of chocolate chips and the amount of cookie dough in sample containers of the product. In addition, inspectors evaluate creaminess factors and melt temperature for each sampled container and check the container label to be sure it accurately indicates contents, that it’s applied straight and that the printing is correct. This proofreading task was assigned after a shipment went out that proclaimed the company’s name as “Dear Diary,” so the firm is sensitive about its image.

Swymm understands attributes charts and decided to create a p-chart to reflect the proportion of nonconforming items in each day’s shipments, based on a batch of 10 cartons of ice cream. He explained p-charts to his inspectors and sent them on their way.

However, the inspectors returned, puzzled by the data they’d received. “We know how many are bad, but we don’t know why,” they explained. “We’re rejecting lots of ice cream, which our employees are taking home to their families. They never complain about the quality, so we don’t learn anything by rejecting the ice cream samples.” The inspectors wondered how p-charts could help the company improve the quality of its ice cream and reduce the rejection rate.

Swymm assured them that after enough data had been collected, it would be analyzed and the answer would be useful with respect to improving quality. But as he said this, he wasn’t sure it was the truth. How can Swymm improve the data analysis so that it will lead to better quality?

a) Create larger sample sizes.

b) Sample more frequently.

c) Use a u-chart instead of p-chart.


Answer c is the correct response.

Like p-charts, u-charts record attributes data. But the distinction lies in the difference between go/no-go situations, in which a product either has a defect or it doesn’t, and nonconforming products, which might have several defects in a single product. The p-charts show data relating to the proportion of rejected containers, whereas u-charts give information about how many individual defects are recorded in samples.

For example, manufactured parts that are the wrong dimension and tested with a go/no-go approach should be charted on a p-chart. Ice cream, on the other hand, might have too many chocolate chips, a sloppy label and insufficient fill--all in the same container. Instead of recording the ice cream container as good or bad, more useful information would be gathered by identifying the kinds and number of defects in each batch of containers. This could be charted with a u-chart and future analysis done by means of Pareto charts.

An example of a u-chart is illustrated here.

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 statistical process control in a variety of academic and professional journals. His Web site is www.pqsystems.com. Letters to the editor regarding this column can be e-mailed to letters@qualitydigest.com.