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 (


In her job as the supplier quality manager, Carmen monitors critical characteristics of incoming components and materials. She would like to accept incoming materials based on data provided by the supplier for all critical characteristics, but first she wants to verify that the measurement systems used by her company and the supplier give the same results. To verify the measurement systems, she has selected three suppliers for a pilot program. For each supplier, she has identified the specific materials or components along with the critical characteristics. The next step is to set up measurement studies on the critical characteristics. For each measurement study, Carmen and the supplier will agree on a set of samples. Then both the supplier and Carmen’s company will measure the critical characteristics for these samples. When the results from both sides agree, she will set up a plan to receive the materials based on data from the supplier.

Available Data

Results from the first measurement study have been sent to Carmen. The component is a metal disk used in a subassembly and the critical characteristics are thickness and diameter. Each of 10 disks was measured twice by one technician from the supplier and by one technician at Carmen’s company. Data for the thickness values are summarized in the table, “Measurement Study Data for Thickness of a Metal Disk.”


1. Do both the supplier and Carmen’s company have predictable measurement techniques?

2. What is the standard deviation (repeatability) of each measurement process?

3. Do the two measurement processes give similar results on the thickness values?

4. What actions do you recommend Carmen take based on the results of this measurement study?

Answers to December Brain Teaser

The sales group from Isaac’s company assures its customers that the assemblies of custom components are specially matched during assembly for better performance during use. The matching process is somewhat time consuming and Isaac wanted to know if it was worth the cost. He gathered data from a set of 15 inserts and sockets. Data on the socket bore and pin inside diameters along with data on the insert bore and pin outside diameter were available in a database. Also, the matched pairs of components were identified for the assembly. All of the data appeared in the December 2008 issue ofQualityMagazine.

Q: What is the process behavior of each dimension for the 15 sockets and inserts? Consider the data are in time order as presented.
A:On the socket, both the bore and the pin inside diameters behave predictably. The insert bore and pin outside diameters also have predictable behaviors. As an example, see the graph, “Individuals and Moving Range Chart for Insert Bore Outside Diameter.” The averages and standard deviations of each dimension are in the table, “Average and Standard Deviation for Socket and Insert Dimensions.”

An analysis of capability shows that all dimensions are capable of meeting the specifications, but the average for the socket pin inside diameter is too high and the Cpk is 0.745. For the other dimensions, the Cpk values are at least 1.4. See the graph, “Capability Analysis for Socket Pin Inside Diameter.”

Q: What can you predict about the gaps for bore and pin if the components are assembled randomly? A:It is appropriate to use the technique of linear combinations for predicting the bore and pin gaps in the assembly because all of the individual dimensions are predictable. The average and standard deviation for each gap is based on the averages and standard deviations of the individual dimensions. For the bore gap, the average and standard deviations are estimated to be 0.00374 and 0.000237 respectively, while the pin gap average and standard deviations are estimated to be 0.00621 and 0.000377 respectively. Using these figures, the natural process limits for bore gap values are estimated to be 0.00303 and 0.00445. The natural process limits for pin gap values are estimated to be 0.00508 and 0.00734.

Q: What is the behavior of the gaps for bore and pin for the matched components?
A:For the matched components, the bore gap has an average of 0.00377 with a standard deviation of 0.00017 and the pin gap has an average of 0.00621 with a standard deviation of 0.00018.

Q: What is the benefit of the matching process?
A:Using the matching process, both the bore gap and pin gap have the same averages, but the standard deviations are smaller. The bore gaps for the matched components should fall between 0.00326 and 0.00429 while the pin gaps for the matched components should fall between 0.00568 and 0.00674. If the gaps were the cause of a high defect level in the assembled components, the matching process could reduce the defect rate over random assembly. However, if the capability of the socket pin inside diameter were improved, random assembly of the components could yield acceptable gap values.