Everyone 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).


Samuel is the production manager of a food processing plant. For one particular product, cut pieces of a food product are chilled before shipping. During the chilling process, the pieces must be chilled sufficiently for safety and shelf life. However, pieces that are excessively chilled may suffer damage.

Some customers have complained about “freezer burn” on the pieces while others have complained about product that spoiled before the expiration date. Samuel and Beth, the quality control managers, decided to investigate the chilling process to ensure that the cut pieces have been chilled to the proper temperature.

Available Data

Rather than rely on already available information, Samuel and Beth decided to gather additional data. Beth collected two cut pieces of product as they exited the chiller every half-hour for one shift. These data are in the table, “Temperature of Chilled Pieces.” Specifications for the chilled pieces are 36 F ±4 F.


1. Is there evidence to support the complaints?

2. What is the behavior of the temperature of chilled pieces from the chilling process?

3. Is this process capable of meeting the chill-temperature specifications?

4. What actions should Samuel and Beth focus on based on the information from these data?

Answers to May Brain Teaser

Wilma supervises a machining center where holes are drilled into a 3-inch-thick casting. Difficulties in assembling these castings with other parts led to a question about the entrance and exit diameters of the hole. Wilma asked the operators who drill the holes to collect data to find out how to handle the problem.

Q: What is the behavior of the entrance and exit diameters?

A: The entrance diameter has a predictable behavior with an average of 0.5021 inch and natural process limits of 0.4919 to 0.5123 inch, as shown in the “Chart for Entrance Diameters.” The exit diameter has a predictable behavior with an average of 0.4999 inch and natural process limits of 0.4910 to 0.5087 inch, as shown in the “Chart for Exit Diameters.”

Q: Are the entrance and exit diameters capable of meeting specifications?

A: The entrance diameter is not capable of meeting the specifications. The chart, “Capability Analysis for Entrance Diameters,” shows that the Cp is 0.92 and the Cpk is 0.67. The exit diameter is capable of meeting the specifications. Cp is 1.13 and Cpk is 1.1 as shown in the chart, “Capability Analysis for Exit Diameters.”

Q: Wilma wants to study the difference between the entrance and exit diameters. What is the best approach to analyze the difference?

A: She can make an individuals and moving range chart of the difference between the entrance and exit diameters, as shown in the chart, “Chart for Entrance Minus Exit Diameters.” This chart shows that the difference between the two diameters is predictable with an average of 0.003 inch. The upper natural process limit is 0.0112, while the lower natural process limit is

-0.005. None of the observed differences are less than zero and the histogram has an appearance of a boundary at zero. See the Histogram for Entrance Minus Exit Diameters. Practically speaking, it would be difficult to find an exit diameter larger than the entrance diameter. At an extreme, Wilma can expect to find entrance diameters as much as 0.0112 inch larger than the exit diameters.

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.