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 (www.qualitymag.com).

Situation

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Raoul is the new supplier quality manager for a company that sells and distributes dental equipment. As part of his job, he must verify that the equipment in its catalog meets the specified requirements. In the past several months, there has been an increase in complaints from dentists regarding the swivel angle on the lighting fixtures used during dental procedures. Some customers say the fixture does not swivel far enough while others complain that the fixture swivels too much. Because his company does not make the equipment, Raoul has requested data on critical characteristics of the lighting fixtures from all suppliers in his company’s catalog. One supplier of lighting fixtures immediately started providing data about the swivel angle of their newest lighting fixture, Model LFX88. Raoul was amazed at the quick response and he wants to analyze the data correctly.

Available Data

The first observation Raoul made just looking at the data was that the actual values all were very close to each other. The specifications require that the maximum swivel equal 270 dgerees so all of the data values met the specification. Swivel angle data are summarized in the table, “Swivel Angle Data for LFX88.” These data come from production reports and are the average angle for two production lines each shift.

Questions

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1. After observing that all data values did meet the requirement of a maximum of 270 degrees, Raoul was concerned that the data looked “too good.” How can these data help him respond to his customers? What additional data should he request?

2. The data that Raoul received were averages of the two production lines. He decided to request the individual values from each production line to see if this could help explain why the customers were complaining. These data appear in the table, “Swivel Angle Data for Lines 1 and 2.”

3. What analyses can Raoul do with these additional data to understand why his customers are complaining?

4. In his position, what actions can Raoul take to deal with the complaints?

Answers to March Brain Teaser

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Mandy’s company has challenged all of the plants to increase productivity 5% over the average for the previous fiscal year. Productivity values are summarized monthly and those plants that achieve a 5% increase are rewarded. Mandy is new as a plant manager and thinks that this approach may reward plants that don’t make sustained improvements.

Q: In a given month, if a plant achieves a productivity increase of 5% from the average of the last fiscal year, does this imply that the plant is definitely improving?
A: Plant A achieved a value of 105.5% in the fourth month, but has an average productivity through 11 months of 97.4% of the previous fiscal year. The best way to determine if an individual plant has truly achieved an increase in productivity of 5% or otherwise is to analyze the monthly values on an individuals and moving range process behavior chart. Use each plant’s own routine variation and a center line of 100% to determine if there is a signal of increased productivity. On the chart for Plant A, the monthly value of 105.5% is not a signal of an increase in productivity over the previous year. However, there is a signal—four out of five points more than 1 sigma below the center line—showing that Plant A’s productivity has actually decreased. Plant E achieved a 5% increase in months 2 and 10, but their overall average through 11 months is 100.5%. The process behavior chart for Plant E shows a predictable process around the center line of 100%. There is no indication of an increase in productivity for Plant E. With natural process limits of 87.8% to 112.2%, Plant E would need to have a single month greater than 112.2% or a long run of 8 values above the center line of 100% to indicate an increase in productivity.

Q: Plant D did not achieve a 5% increase in productivity for any of the first 11 months. Does this mean that Plant D has declined in productivity?
A: Plant D has an average of 99.4% through 11 months of the current fiscal year. The process behavior chart for Plant D using a center line of 100 and Plant D’s own routine variation shows a predictable process. There is no indication that Plant D has declined in productivity.

Q: Plant F had the highest month’s percent increase in productivity. Does this mean that Plant F has improved productivity the most so far this year?
A: Once again, the process behavior charts tell the story. While Plant F had the highest single month’s productivity increase, Plant C had all 11 monthly values above the center line of 100%. Plant C has a predictable increase in productivity for the 11 months of data available with an average of 105.1%. The average for Plant F over the same period is 103.8%, but the process behavior is not predictable. Plant F shows exceptional behavior on the high side in the fourth month but there is a signal on the low side for months 9 and 10.

Q: What technique could be used to determine how each plant compares to the others? What can be determined based on the data for the 11 months?
A: As indicated in the answers to the previous questions, the process behavior chart is the superior analysis technique for these data. Initially, using a center line of 100% with the routine variation for each plant, the chart can indicate if there is an increase in productivity that is more than can be attributed to routine variation alone. Also, it is possible to analyze each plant’s data to determine if a plant is predictable around a new average. This is true with Plants B and C. The 11 months of data for each plant are adequate for determining the routine variation in each plant and serve as the basis of finding signals.