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
Nelson works for a paper mill that fabricates a variety of products for numerous customers. One product is the paper bags that are supplied to a food company. The bags are used to package microwave popcorn. Not long after becoming supervisor for production of these bags, Nelson was barraged with complaints from the food company about the quality of the bags. The bags were exploding during the microwave process. This breakage caused a mess and the food company's customers were switching brands. Nelson's company was on the verge of losing a valuable customer.

At a production meeting, Nelson's boss, Connie, gave him two days to get to the bottom of the problem. A technical team and production operators from the paper and fabrication departments met and immediately focused on the critical characteristics of fiber length and basis weight of the paper used for the bags. A sub-team of technicians and operators set out to discover any anomalies with fiber length. Nelson headed the group to gather and analyze any available data.

Available data
Both fiber length and basis weight data were available. Paper machine operators had reported that fiber length of recent shipments of raw material appeared to be shorter than the norm. However, the basis weight was still in specification, so the process engineers told them to continue making paper. Nelson decided to analyze the data to see if further insights could come to light. Three weeks of data are shown in the table, "Basis Weight Machine Direction." The data begins one week prior to the time the operators noticed the short fibers.

Questions
1. Do these data confirm that the basis weight is meeting specifications?
2. Has basis weight changed during the three-week period?
3. How could the paper meet specification for a critical characteristic and still cause problems for consumers using the bags?
4. Is there a need for a target in the case of a one-sided specification?

Answers to July Brain Teaser
Q: Do these data values meet the angle specifications?
A: An analysis of the data on left and right angles shows that both angles are predictable but have different averages and different amounts of variation. This is shown in the chart, "Average and Range Chart for Left and Right Angles." The capability analyses for each angle separately indicate that both angles are meeting the specifications, but both angles are on the low side of 45 degrees. These results are shown in the chart, "Capability Analysis for Left Angles," (p. 20) and the chart, "Capability Analysis for Right Angles," on the Web at www.qualitymag.com.

Q: What is the root cause of the assembly problem?
A: The angles must be centered at 45 degrees in order for the frames to fit together correctly. In these frame sections, the angles on both ends are centered on the low side of 45 degrees. This causes the assembly problems. If the end cuts are held together, the frame corner will not form a 90-degree angle. If the frame corner is held to 90 degrees, the end cuts will not meet.

Q: What actions are needed to correct the problem?
A: Immediate action is required to center the angles at 45 degrees. Because the variation in angles on both the left and right sides is small, there should be no problem in meeting the specification.

Q: What do you suggest Jeff include in his report to Miranda?
A: Jeff should include the analysis that shows the angle cutting process is predictable for both the left and right ends of each frame section. Also, he should include the capability analyses to show that even with the average off tar-get, all angles are meeting specification. He then should emphasize that just being in specification is not enough. Centering the angle cutting process at 45 degrees is critical to the assembly of the frames.