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 (


Anton is a process engineer for a company that makes component parts for elevators. One issue with these components is durability. It appears that some components are failing more quickly than expected, causing elevator performance to be compromised. Anton recommended that they conduct an experiment to determine what factors were most critical in impacting durability. His team decided to experiment with three factors at two levels each. These factors and levels are summarized in the table, “Designed Experiment for Component Durability.”

Available Data

The team decided to replicate the experiment five times for a total of 40 observations. Each team member participated in the experiment, ensuring that the order of experimental runs was maintained and preventing any deviations from the design. Data for the experiment are summarized in the table, “Data for Component Durability Experiment.” The data values are coded and no units are given. For the coded data, the desired target is 16.


1. Which of the three factors used in this experiment has an impact on the average value for durability?

2. Which of the three factors has an impact on the variation of durability values?

3. Are there any other important findings from analysis of these data?

4. Recommend a combination of the three factors for production trials that would likely achieve the desired target of 16.

Answers to March Brain Teaser

Denise is an engineer who switched careers from designing industrial equipment to designing toys. Her first assignment was to address customer complaints about the difficulties in assembling the frame for the goal in a child’s hockey set. Some parents cited injuries such as scrapes and cuts when inserting one piece into another. Denise formed a team to review data on specifications for the inside diameter (ID) of the elbow and the outside diameter (OD) of the tube in the hockey set goal frames.

Q: Do the data support the production worker’s statement that the outside diameters of the tube still meet specifications?

A: Yes, the data for both the ID of the elbow and the OD of the tube all meet specifications. However, there are several OD values that are close to or at the upper specification limit.

Q: What is the behavior of the OD of the tube? What is the behavior of the ID of the elbow?

A: An analysis of the data on a process behavior chart shows that the OD of the tube is predictable with an average of 1.25249 inch and a standard deviation of 0.00024 inch. A process behavior chart for the data on the ID of the elbow shows that one of the ranges is above the upper control limit, indicating that there is an exceptional cause for the increase in variation for the first subgroup during swing shift on January 25. The root cause of this exception needs to be identified and removed from the process to ensure that the ID can sustain a predictable behavior. See the process behavior charts for the OD of the tube and the ID of the elbow.

Q: What is the capability of the OD of the tube? What is the capability of the ID of the elbow?

A: The OD of the tube has a Cp of 1.4, but the Cpk is only 0.71 because the average OD is between the nominal and the upper specification limit. In fact, all of the data values are between the nominal and the upper specification limit. A capability analysis of the ID of the elbow will be misleading because of the exceptional variation associated with the range chart. However, Pp of 1.21 and Ppk of 1.19 give a worst-case scenario. The average of the ID data values is essentially at the nominal so the only issue is dealing with the cause of the exceptional variation previously mentioned.

Q: Based on the current behavior of the components, does it make sense that customers are having difficulty assembling the frame for the goal of this hockey set?

A: The current behavior of the components does confirm what the operator said about increasing the OD of the tube. This also explains why customers are having trouble assembling the hockey frame. With the ID averaging at the nominal and OD values all above the nominal, the pieces will be harder to assemble. Just meeting specifications does not guarantee a quality product that meets customer expectations.

Dr. Sophronia Ward is a continual improvement specialist and Six Sigma Senior Master Black Belt and coach. 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