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 (


Reggie is the night shift production manager for a company that makes kits for model airplanes. Some of the parts are molded and then cut in half to form a right and left component. After complaints from the toy and craft businesses that the right and left components were not the same size, Reggie did some investigating into the cutting process. It was clear that the pieces were not being cut in the middle, but no one had set up a system to measure cutting accuracy for these pieces.

After consultation with the quality department and the people working in this area on both shifts, Reggie set up a measuring system to determine cutting accuracy. The exact mid-point where the cut should be made had a mark from the mold and this point was given a value of zero. Any deviation from this zero point was recorded in 0.1-millimeter increments with negative numbers indicating a cut into the left component and positive numbers indicating a cut into the right component.

Available data

Everyone involved agreed that the line operators should make the measurements, and after training in the new technique, they started collecting data. Every 30 minutes three sets of pieces (right and left after cutting) were selected immediately after the cutting operation and the distance from the center mark was measured. These data appear in the table, “Data for Cutting Accuracy of Airplane Components.”


1. Based on the data collected by the line operators, what is the process behavior of the cutting process?

2. Could the behavior of the cutting process explain why the customers are voicing complaints?

3. What are the major challenges in fixing the cutting process?

4. What should Reggie do as a next step toward fixing the cutting process?

Answers to July Brain Teaser

In her capacity as process engineer for supplier components, Julie tells suppliers about all issues with their components during production. A recent complaint from production is that the hole diameters on a specific component are too small. This occurs in about 450 of the 20,000 pieces used each month. Her first action is to send the pieces with holes that are too small back to the supplier. Next she decided to collect data on the hole diameter to support the complaints.

Q: Based on the data collected by the assembly engineers, what is the process behavior of the hole diameter?
A: The hole diameter is predictable with an average of 0.24707 and a standard deviation of 0.00109. See the average and range chart, “Diameter of Hole A.”

Q: What is the capability of the diameter of the hole for this component?
A: The capability of the diameter of the hole for this component is Cp = 1.53 and Cpk = 0.63. See the chart, “Capability Analysis for Hole A Diameter.”

Q: Is the current behavior consistent with the complaints from assembly and the presence of an average of 450 pieces per month with holes that have diameters too small?
A: The capability analysis reveals that the process average is 1.9 standard deviations from the lower specification which leads to the Cpk of 0.63. Without any reference to a specific distribution, the empirical rule suggests that 90% to 98% of all data will fall between ±2 standard deviations from the average of a set of data. This means that somewhere between 2% and 10% of all data will fall outside this range with approximately one-half on the low side and the rest on the high side. Thus, it can be expected that between 1% and 5% of all data values in a predictable process will fall more than two standard deviations below the average.

If the PPM is truly 22,500, then we would expect on average that one piece in the set of 44 used for the analysis of process behavior to be outside the lower specification. There are four pieces with diameters that are exactly equal to the lower specification. These results are consistent with the complaints from assembly.

Q: What actions should Julie take with the supplier to improve the problem with holes that are too small?
A: A combination of the pieces with holes too small and the analysis of the data collected in assembly should be presented to the appropriate representatives from the supplier company. Because the analysis of process behavior shows a predictable process with a Cp of 1.53, all the supplier has to do is involve production and engineering and get them to agree on how to increase the average diameter for this hole. The variation is small enough that an increase in the average diameter should be the solution to the issue of holes too small.