Anyone who has faced a production problem with a need to solve it by using production data can relate to the notion of a brain teaser. The brain teasers presented here are based on real-world situations 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 need answered for continual improvement. Recommended solutions follow in the next issue and on the Web at Quality Online (


Maxine operates a machine that seals sophisticated electronic components inside a small box. One critical characteristic of the final unit is that the leak rate be less than 10-6. These boxes are 100% inspected for leaks, and 15% of the boxes typically fail the leak test. Every box that fails the leak test is taken apart and rebuilt. The electronic components are expensive and cannot be scrapped. Maxine keeps careful records on all boxes that are taken apart but so far has not found a dominant cause or location of the failures.

After attending a course on statistical process control, Phil recommended that Maxine record the actual leak rate as well as the number of failures. Maxine laughed and said that the values were so small that they could hardly matter. Phil replied that it might be interesting to look at the information in a different way and that Maxine could get the values from the leak test equipment.

Available data

Twenty-four boxes are produced every day on one shift. Data were available for the past 20 work days on the number of boxes that failed the leak test. These values are in the table, "Leak Test Failures Out of 24 Boxes." Maxine also obtained the actual leak rate values for the 24 boxes produced on one day. These data are in the table, "Leak Test Rates" and are recorded as times 10-6.


What insight can be gained by analyzing the number of leak test failures out of the 24 produced each day?

In finding the causes of the failures, does it matter whether the process is predictable or unpredictable?

What additional insight can be gained by analyzing the actual leak rates? Does it matter that the data values are very small?

How do these analyses help Maxine understand the lack of a dominant cause or location of the leak failures?

Answers to February Brain Teaser

After completing a special assignment on an ISO initiative, Travis returned to production as the person responsible for monitoring all specifications for collapsible tents. Of the two production lines, Production Line 2 has trouble with the final assembly of the internal tent frames. Travis decided to find out if the lengths of frame sections for both production lines meet specifications at a Cpk of 1.33.

Q: Is Travis correct in stating that the tent frame sections from both production lines meet specification for length?

A: Yes, Travis is correct. All tent frame sections in the data collected do meet the specifications of 45±0.05 centimeters.

Q: What is the behavior of each production line for the length of the tent frame sections?

A: Both production lines have a predictable behavior. Production Line 1 has an average of 44.9999 centimeters with a standard deviation of 0.01748 centimeter, while Production Line 2 has an average of 45.0274 centimeters with a standard deviation of 0.00580 centimeter. See the charts, "Length of Tent Frame Sections for Production Line 1" and "Length of Tent Frame Sections for Production Line 2."

Q: Which production line is doing a better job of meeting specifications?

A: The Cpk for Production Line 1 is 0.95 and that for Production Line 2 is 1.30. Production Line 1 is centered in the middle of the specifications but has a standard deviation that is three times that of Production Line 2. However, even with a Cpk of 1.30, Production Line 2 has all of the frame lengths above the center of the specifications. The Cpk for Production Line 2 is higher than that for Production Line 1, but the tent frame sections from Production Line 1 appear to fit in assembly better. See the capability analyses for Production Lines 1 and 2.

Q: Why is production Line 2 having trouble with assembly?

A: Production Line 2 is running at an average that is 0.0274 millimeter above the middle of the specification, which may contribute to the problem in assembly. Because all frame sections are above the middle of the specifications in length, the assembly likely will not meet the criteria for assembly. The overall frame may be too large and the tent itself may be stretched to the point of tearing.

Dr. Sophronia Ward is a continual improvement specialist. Brain teasers are now incorporated in the new training programs, Six Sigma Training for Champions, Black Belts and Green Belts, offered by Dr. Ward and her associates at Pinnacle Partners Inc. For more information, call (865) 482-1362 or visit