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).

Situation
Miranda is the production manager for a company that assembles large quantities of frames in various sizes for photographic studios. She recently experienced a high volume of customer complaints that the frames were not built correctly and included gaps between sections and warped frames. During her investigation, Miranda discovered that assembly workers had to force fit the individual frame sections. The operators were convinced that the angles were the problem, but every time they checked the angles, they were within specification.

At the next production meeting, Miranda raised the question of the frame angles and the current specification and suggested that the specifications needed to be tightened. The supervisor of the frame department, Jeff, said that he would look into the problem and report back.

Available data
Jeff's research began at the cutting operation. He set up a plan to collect data for both the left and right angles of two frame sections every 30 minutes for the rest of the shift. The data he collected are summarized in the table, "Data for Angles of Frame Sections."

Questions
1. Do these data values meet the angle specifications?

2. What is the root cause of the assembly problem?

3. What actions are needed to correct the problem?

4. What do you suggest Jeff include in his report to Miranda?

Answers to July Brain Teaser
Q: Is the measurement process variation repeatable? What is the standard deviation of the measurement process?
A: Two operators on two shifts measured 10 pieces twice. This gives 40 subgroups of size two. The average range represents measurement process variation. Two points are outside the limits on the range and both are on piece B for two Shift 1 operators. These two points represent an inconsistency in the measurement process and need to be investigated to determine the cause of this excessive variation.
The measurement process variation is not repeatable as shown in the charts, "Measurement Study for Piece Length, Shift 1" and "Measurement Study for Piece Length, Shift 2," which can be viewed at www.qualitymag.com. After these two range values have been deleted, and the calculations on the range chart redone, there are no signals from the remaining 38 subgroups. The average range now equals 0.0017 and the standard deviation of the measurement process is 0.0017/1.128 or 0.001507.

Q: Do operators on different shifts measure the pieces differently?
A: The chart for operator averages, "Measurement Study for Piece Length, Operator Averages," showed that Barry measured the pieces on the high side; his average is above the Upper Limit. Cindy and Jesse measured them on the low side; Cindy and Jesse's averages were below the Lower Limit. The limits on the chart are based on the standard deviation of the averages of 20 pieces. Immediate action is needed to get all operators to measure the pieces the same way. This is crucial in order to rely on values from any operator.

Q: Is the new gage adequate for measuring the lengths of pieces from the sawing operation?
A: The discrimination ratio for a measurement process used with a specific production process answers this question by determining how many distinct categories in which the measured values can be grouped. For these data, the standard deviation of the measurement process is 0.001507 and the standard deviation of the averages of the 10 pieces is 0.007896. From these values, the discrimination ratio, DR, equals 7.46. Because this ratio is greater than four, the gage is adequate for measuring the lengths of pieces from the sawing operation. Thus, any perceived problems from the measurement process are coming from the operator differences instead of the variability of the gage itself.