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Departments: SPC Guide

Photo: Michael J. Cleary, Ph.D.

  
   

The Heat Is On
Hy Sedrate searches for the best chart to analyze variables.

Michael J. Cleary, Ph.D.
mcleary@qualitydigest.com

 

Hy Sedrate, a quality assurance specialist for St. Recover in the Long Run Hospital, has noticed that the accuracy of his lab readings is higher in cool weather than it is on hot days, even though the lab is air-conditioned and doesn’t have an appreciable difference in temperature from the rest of the hospital. Nonetheless, the data are dramatic, and Sedrate wants to demonstrate the pattern he’s observed so his boss and the entire quality team can analyze the situation.

Sedrate collects data relating to defective lab readings while tracking the daily high temperatures recorded by the National Weather Service for his area. Without complex analysis, he can see even from the raw data that the higher the temperature, the greater the number of errors. In order to illustrate the pattern that he’s observed, he decides to create an individual moving range chart from the data.

After he’s produced the charts and examined them for patterns, another quality specialist, Hap N. Stance, insists that Sedrate has used the wrong statistical method. Nevertheless, Stance can’t suggest an approach that might be better. Is Sedrate correct in using an individual moving range chart, or is there a better way to analyze this data?

a. Sedrate should abandon his chart and take an Alka Seltzer. It’s too hot outside to think.

b. An individual moving range chart provides insights about the data that no other method can give.

c. Stance is on the right track but the wrong train. He should advise Sedrate to use a scatter diagram to get the best analysis of the data.

d. Because he already knows that there’s a relationship between defects and temperature, Sedrate should select the chart that will be most dramatic so he can impress the quality team with his statistical prowess.

 

Answer c is the correct response.

A scatter diagram will indicate whether two variables--in this case, temperature and inaccurate lab reports--are related to each other, or whether there’s a correlation between the two. If one of the variables appears to have an effect on the other, then regression analysis will be appropriate. Because Sedrate wants to establish whether there’s a correlation, an individual moving range chart won’t be of any help. (See Practical Tools for Continuous Improvement Vol. I, Statistical Tools, by Jacqueline D. Graham, Ph.D., and Michael J. Cleary, Ph.D., pp. 298–311).

The same data is shown within the chart on page 20.

Because Sedrate assumes that temperature affects the number of defects (rather than the other way around), temperature becomes the independent variable, represented on the horizontal axis. The number of defects becomes the dependent variable, on the vertical axis. The line of best fit shows the relationship:

y = 13.44 + 1.66x

This means that as the temperature goes up, so does the number of defects. A correlation coefficient of 0.93 suggests a rather strong relationship between the two variables. In addition, the t value of 8.969 suggests that there’s indeed a statistical relationship between the number of defects and temperature. But Sedrate should be encouraged to study a little more statistics before approaching his next challenge.

About the author

Michael J. Cleary, Ph.D., founder and president of PQ Systems Inc., is a professor emeritus of management science at Wright State University in Dayton, Ohio. A 29-year professorship in management science has enabled him to conduct extensive research in expanding quality management methods. He’s the author of several articles on quality management and statistical process control. Letters to the editor regarding this column can be sent to letters@qualitydigest.com.