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.


As a process engineer, Wilma manufactures gel capsules for a variety of vitamins. She recently received information from the customer that their gel caps are performing poorly in the customer's capsule filling machine. Specifically, the capsules are sticking in the filling chute. Her team of engineers has agreed to assist the customer in locating the cause of the problem. Capsules were sticking to the chutes on the production line and the throughput was severely compromised.

Their initial investigations focused on the filling machines that the customer uses. When they could not find a cause in the filling machine, they started looking at the gel caps themselves. No specific cause was immediately apparent to Wilma's team. Finally, one person suggested that maybe the cause of the sticking was the smoothness of the gel capsule surface. Wilma was skeptical because her engineers had recently improved the surface smoothness.

Available data

Data on smoothness of the gel capsule were available in the QC database. Wilma obtained data on smoothness from the time period prior to the improvements through current production. Selected data are summarized in the table, "Surface Smoothness of Gel Capsules."


1. Is there evidence in the data that the recent efforts to improve the gel cap smoothness did result in a change for surface smoothness?

2. What statistical techniques can be used to determine if a difference exists in the smoothness of these two versions of gel capsule?

3. Is there evidence in the data to indicate that the new gel caps are too smooth?

4. How can Wilma's team determine the optimal surface smoothness for the gel caps?

Answers to November Brain Teaser

As production superintendent of polished chrome castings, Bernie has been asked for documentation on process yield to accompany each shipment of chrome castings to a particular customer. To keep things simple, Bernie decided to use the yield from all three machines on the process behavior chart, even though the customer's product is run only on polishing machine 3.

Q: How does the total yield for all three machines behave for the 12 days?

A: Total yield for all three machines combined behaves predictably as shown on the process behavior chart, "Aggregated Yield for All Three Polishing Machines." The average yield is 89.12% with natural process limits of 80.96% and 97.29%.

Q: What problems might be encountered by using the total yield for all three machines on the process behavior chart that Bernie sends to this customer?

A: One problem or issue that arises with aggregated data, such as the total yield for all three machines, is the inability to determine how each machine itself behaves. The three machines may have different averages and may or may not be predictable. Often unpredictable processes will show a predictable behavior for the aggregated measure. For Bernie's customer, the total yield chart will not reveal the behavior of polishing machine 3.

Q: What is the behavior of each separate polishing machine for the 12 days?

A: Polishing machines 1 and 3 have a predictable behavior as shown by separate process behavior charts while polishing machine 2 has one signal on the moving range chart indicating that an exceptional cause of variation did occur. However, the averages and amount of variation are not the same. See the table, "Average and Limits for Each Polishing Machine."

Average and Limits for Each Polishing Machine

Polishing Machine 1 2 3

Average 92.08 90.27 85.5

Lower Limit 84.61 80.35 71.32

Upper Limit 99.55 100.19 99.67

Q: Are there any additional actions that Bernie may want to consider?

A: First, Bernie needs to provide the customer with the chart for polishing machine 3. This chart shows the yield of the process that polishes the customer's product. Any additional actions should be directed to improving the yield for each polishing machine. This will require finding answers to questions posed by the charts for the individual polishing machines. To start, what is the cause of the exceptional variation for polishing machine 2? Why is the behavior for each machine predictable and yet different? What are the differences in the three machines as to the types of chrome parts polished on each one? Is the polishing material the same for all three machines? Are the requirements for the polished chrome parts the same from all customers? Once Bernie has answers to these and other questions that identify specific sources of variation, he can start making changes to increase the yield on all three polishing machines.

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