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.

## Situation

Bernie is the production superintendent in charge of the production of polished chrome castings. These castings are sold to a large number of customers for automobiles, motorcycles and children's riding toys. In the polishing process, one operator runs three machines on each of two 8-hour shifts. Each operator keeps track of the part number, the number of parts in a run and the number of parts with flaws that can be seen after the polishing step. A final yield, percentage of good castings, is calculated for all three polishing machines together. The yield values for each shift are entered into the daily production report.

Recently one customer requested documentation in the form of process behavior charts for the yield of their chrome parts to accompany each shipment. Bernie has decided to construct a process behavior chart using the combined data from all machines for each shift even though he knows that this customer's product is run only on polishing machine 3.

## Available data

Data are available for all three machines for both shifts for a period of 12 days. The data are given in the table, "Yield for Polishing Machines 1, 2, 3 and the Combined Total Yield."

Questions

1. How does the total yield for all three machines behave for the 12 days?

2. What problems might be encountered by using the total yield for all three machines on the process behavior chart that Bernie sends to this customer?

3. What is the behavior of each separate polishing machine for the 12 days?

4. Are there any additional actions that Bernie may want to consider?

## Questions

1. How does the total yield for all three machines behave for the 12 days?

2. What problems might be encountered by using the total yield for all three machines on the process behavior chart that Bernie sends to this customer?

3. What is the behavior of each separate polishing machine for the 12 days?

4. Are there any additional actions that Bernie may want to consider?

## Answers to October Brain Teaser

Jay, the engineering manager for a motorcycle manufacturer, has been over budget for the past three months. In addition, parts have been late to assembly and overtime has increased. He has asked Rachel, the process improvement coordinator, to help him analyze data to determine if this situation is related to the adoption of a new just-in-time scheduling system. Data were available for the past 20 months on Deviation from Budget in Dollars, Percent Compliance to Schedule and Overtime Hours Worked.

Q: What analysis technique should Rachel use with Jay's data?

A: To detect a change in any process, Rachel should use a process behavior chart. She can analyze the process to detect a change associated with a particular event by calculating limits with the data preceding the event and then observing if the additional data show a signal of exceptional variation. Often, if an exception is strong, limits calculated for all the available data will show a signal.

Q: Is there evidence in these data of exceptional causes of variation?

A: For the three measures that Jay is using, only one-Overtime Hours Worked-shows a signal of an exceptional cause of variation in the past three months. See the process behavior chart, "Overtime Hours Worked." The other measures, Deviation from Budget in Dollars and Percent Compliance to Schedule, do not yet have a signal of exceptional variation.

Q: How can Jay justify to his boss that the new just-in-time scheduling system is causing an increase in budget, or reduction in the compliance to schedule or increasing the overtime hours worked?

A: The only clear signal that can be tied to the adoption of the just-in-time scheduling system three months prior is the increase in overtime hours worked. Both the deviation from budget and compliance to schedule appear to be going in the wrong direction, but only the most recent value in each case is more extreme than previous values. In light of previous behavior for these measures, there is no clear signal that either one has been impacted by the just-in-time scheduling system. Therefore, Jay cannot justify that the just-in-time scheduling system has caused an increase in budget or reduction in the compliance to schedule. He can, however, present compelling evidence that the overtime hours have been impacted. The adoption of the just-in-time system may be impacting all of these measures, but the evidence is not available in these data with the exception of overtime hours worked.

Q: Recommend a focus for Jay's meeting with his boss.

A: When Jay meets with his boss, he should show the process behavior charts and explain that the only signal appears on the chart for overtime hours worked. This appears to be connected with some event three months prior and it could likely be the just-in-time system. He should emphasize that the values for deviation from budget and percent compliance to schedule need to be watched carefully to see if a signal does appear. There is a lot of month-to-month variation in these two measures. In such situations, the evidence for process changes may take longer to appear. Jay may argue that the increase in overtime hours has prevented the compliance to schedule or the deviation from budget from getting even worse, but the evidence in the data is not certain after only three months.

Dr. Sophronia Ward is a continual improvement specialist. 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.