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Brain Teasers: Misusing Trend Lines
by Dr. Sophronia Ward
October 23, 2008

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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

As the global director of operations for her company, Amy attends a lot of meetings. Most of the business information—financial and marketing—presented in these meeting is summarized in graphs, such as bar charts or pie charts. From an operations perspective, Amy prefers to see the information displayed over time to connect company decisions with any noticeable changes in the information. Most of the charts presenting data over time include what the managers refer to as a “trend line” over the data. Amy finds these lines distracting and believes they can lead to incorrect interpretations of the data. The other managers are comfortable using these charts and disagree with Amy’s comments. She has decided to use some of the data on sales volume in dollars and present it with and without the trend line to illustrate the opportunity for misinterpretation.


Available Data

Amy found data on weekly sales volume in dollars. These data are summarized in the table, “Weekly Sales Volume.”

She put the data into time order and then added a “trend” line. See the chart, “Trend Chart of Sales Volume.”


Questions

1. What message is implied using the data in time order with a trend line?

2. How can the use of a trend line make it difficult to find important messages?

3. Analyze the data using a process behavior chart. What message is communicated using this analysis?

4. What business decisions are impacted by a misinterpretation of data using a trend line?


Answers to October Brain Teaser

As manager of continual improvement for his company, Sergio worked with customer service to identify quality and performance issues reported by customers. The number one issue based on complaints was container breakage. Using this information Sergio conferred with a team of process engineers and operators to select the critical process measures associated with container breakage. They started with raw material batch temperature for process monitoring and control.

Q: What is the behavior of the raw material batch temperature?
A: Based on the data provided and analyzed on an average and range process behavior chart, raw material batch temperature is predictable with an average of 93.81 degrees and average range of 2.84 degrees. See the chart,“Raw Material Batch Temperature.”

Q: What is the capability of batch temperature for this process based on the stated specifications?
A: For this process, Cp = 0.53 and Cpk = 0.37. The chart “Capability Analysis of Raw Material Batch Temperature” shows that the natural process limits of 86.3 degrees to 101.3 degrees are almost twice as wide as the specification limits. In addition, the average batch temperature is a little over one degree below the target of 95 degrees.

Q: If raw material batch temperature is a critical contributor to the breakage issue with customers, what should be the focus of improvement for this process by Sergio and the team?
A: Sergio and the team must first get the average temperature up to 95 degrees and then work to reduce the routine variation in batch temperature. The team should spend time watching how the raw material batches are made and transferred to the next step of the process, as well as observing how the measurements are made.

These observations should be organized on a cause-and-effect diagram. The cause-and-effect diagram can then be used to help the team identify what variables might be appropriate for experimenting on batch temperature. Using a cause-and-effect diagram ensures that all possible variables are visible and the team can prioritize them for an experiment. Experiments are critical to finding the causes of routine variation in any process as well as to ensuring that specifications are set correctly.


Dr. Sophronia Ward
Dr. Sophronia Ward is a continual improvement specialist and Six Sigma Senior Master Black Belt and Coach. Brain teasers are now incorporated in the new training programs, Six Sigma Training for Champions, Black Belts and Green Belts, offered by Dr. Ward and her associates at Pinnacle Partners Inc. For more information, call (865) 482-1362 or visit www.pinnaclepartnersinc.com.

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