Anyone who has faced a production problem with a need to solve the problem by using production data can relate to the notion of a brain teaser. The brain teasers presented here are based on real-world situations that are encountered by workers in manufacturing environments. The brain teasers have three parts: (1) the situation, (2) available data or other supporting information and (3) questions that various workers want answered for continual improvement. Recommended solutions follow in the next issue and on the Web at Quality Online (www.qualitymag.com).

## Situation

Amy has just completed a four-month project to reduce the variation in electrical noise of a specialty circuit used in security cameras. The maximum specification for electrical noise is 80 units. When she started the project, the average value was 45 with a standard deviation of 10. None of the circuits she tested were above the maximum specification set by the customer. However, Amy's company set internal specifications that were even tighter than those of the customer. The internal maximum was set at 60, which led to some circuits failing the noise test.

At the end of the project, Amy had reduced the average to 30 with a standard deviation of 5. She put process behavior charts in place at the end of the assembly process as well as in testing to ensure that the process continued to produce circuits that met the specification for noise.

## Available Data

Production of the circuits takes place on two shifts-day and swing. Two circuits are tested every hour for electrical noise. Data for two days of production are given in the table "Electrical Noise for Specialty Circuits."

## Questions

1. Verify that Amy was successful in reducing the average and standard deviation to 30 and 5, respectively.

2. What is the Cpk for her improved process with respect to the internal specification? What is the Cpk for her improved process with respect to the customer's specification?

3. How high can the average value for electrical noise be if Amy is to maintain a Cpk of 1.33 from the customer's perspective?

4. If the standard deviation remains approximately 5, what would the average need to be for Amy to say she had a sigma level of 6.0 relative to the customer's specification?

## Answer to March Brain Teaser

To meet the minimum corner thickness specification for a plastic molded container, the engineer, Ian, has been adding an average of 50 grams of weight. Because the extra weight adds cost, Ian must now determine how to reduce the amount of extra weight but still meet the minimum corner thickness specification.

Q: Ian analyzed the data using all eight values for a single unit as a subgroup. He had a total of 24 subgroups on an average and range chart. With this approach, what is the behavior of corner thickness for product 2-GAP-HD?

A: Using Ian's approach to setting up the process behavior chart, the process appears to be predictable with an average corner thickness of 5.054 millimeters and an average range of 2.3 millimeters. See the chart, "Corner Thickness for Molded Container 2-GAP-HD." Because the process appears to be predictable, it is appropriate to calculate the upper and lower natural process limits (NPL). These are LNPL=2.635 millimeters and UNPL=7.473 millimeters.

Note: Putting all eight corner thickness values in a subgroup must be done with caution because Ian has not yet verified that all corners have the same average and same variability. If they don't, further analyses will be misleading. See the answers to the last two questions.

Q: Is corner thickness meeting the minimum specification?

A: For the data available, no values are below the minimum specification.

Q: As the process currently behaves, will a unit have a corner that is below the minimum specification?

A: Based on the capability analysis as shown in the graph "Capability Analysis for Corner Thickness of 2-GAP-HD," this process has a Cpk of 0.849. Because this value is less than 1, Ian should expect that there will be situations where the containers will not meet the minimum corner thickness specification even though none have been spotted.

Q: How can Ian use these data to learn a way to reduce weight and still meet the minimum corner specification?

A: Ian verified that the data values were entered in the table representing the eight corners in standard order. With this information, he can use separate individuals and moving range charts to determine the process behavior at each corner. All but one corner, number 5, is predictable for thickness. The average thickness ranges from 4.5 millimeters for corners 1 and 3 to almost 6 millimeters for corners 7 and 8. Also, the standard deviations for the various corners range from 0.312 to 0.871 millimeter. If Ian were to make changes in the process, such as a change in raw material or a design change to the mold, to get the average and standard deviation for every corner to behave like corners 1 and 2, then he could reduce the weight and still meet the minimum corner thickness.