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 (


Charles is a process engineer who works for a company that manufactures platforms for security cameras. His assignment is to determine which processes can be converted from manual assembly to automation through the use of robots. One step Charles wants to automate is the insertion of a pin on a swivel frame into an opening on the platform. The pin must move freely in the opening so that the frame may rotate. However, if the pin is too loose, the swivel frame will not maintain the correct orientation. Specifications for this clearance are 0.5±0.3.

During assembly, operators insert

a pin in the opening and spin it to see if the pin is too tight or too loose. If the pin does not rotate to the satisfaction of the operator, the pin is replaced by another until the assembly "feels" right. In addition to the extra time taken at this step, there are parts left over that cannot be assembled. Before he can determine how to automate this process step, Charles has decided to collect data to study the individual components.

Available data

The platform is manufactured in house and the pin is purchased from a supplier. Charles collects data internally on the inside diameter (ID) of the opening periodically as the platform is produced. These data are shown in the table, "Inside Diameter of Opening." He also set up a data collection plan for the outside diameter (OD) of the pin as shipments are received from the supplier. These data are given in the table, "Outside Diameter of Pin."


1. Are all opening inside diameters and pin outside diameters in specification?

2. Can Charles predict that these dimensions will continue to meet their respective specifications?

3. Why are the operators having trouble getting the pins to fit the opening in the platform?

4. Is this process step ready for automation?

Answers to July Brain Teaser

In her role as operations manager for a company that produces a variety of motors, Suellen has worked diligently to reduce the unit cost of motors. One high-volume motor, Model MM400, has gone over the budgeted cost three months in a row while a similar motor, Model MM325, has not. Suellen and her boss are concerned about making the current budget.

Q: Looking at the data for Model MM400, does Suellen's boss have reason to be concerned?

A: During the past 17 months, the unit cost of Model MM400 has exceeded the budgeted value six times. The first three times occurred during 2004 and were not consecutive. The remaining three times were from the most recent three months. It seems reasonable to Suellen's boss that a trend is developing. But is this really true? See the answer to the next question.

Q: What can Suellen learn about the cost per unit for Models MM400 and MM325 using process behavior charts?

A: An individuals and moving range chart for the Model MM400 data shows that the process was predictable during 2004 with an average unit cost of $24.69. The natural process limits indicate that in any given month the unit cost can be as low as $23.39 or as high as $26.00 without anything changing in the process. Data for the first five months of 2005 are consistent with these limits. Therefore, the unit cost for Model MM400 is predictable at an average that is $0.21 below the budget value of $24.90, but there will be some monthly results above budget. See the chart, "Model MM400 Cost per Unit."

For Model MM325, an individuals and moving range chart shows a predictable behavior with an average of $22.21 during 2004 which is below the budgeted value of $23.45. However, the upper natural process limit of $23.71 for this motor shows that there can be individual monthly values that exceed the budgeted value with no change in the process. Up to this point in time, no individual monthly value has exceeded the budgeted value. See the chart, "Model MM325 Cost per Unit.'

Q: Based on the results of an analysis of the cost per unit for these two models of motors, what is the real issue for Suellen to address?

A: Both motors have a predictable cost per unit since January 2004. However, in both cases the upper natural process limit is greater than the respective budgeted values ensuring that there will be months where the unit cost is above budget. The real issue lies with the variation month to month. For each model, the average monthly cost per unit is under the budgeted cost, and as long as the process remains predictable for cost per unit, Suellen will meet budget for the year. The variation drives the individual values around the average, and in both cases, this variation guarantees that there can be months with unit costs above the budgeted value.

Q: How should Suellen address the situation based on the analyses?

A: First, Suellen needs to understand the implications of a predictable process. As long as the cost per unit for these motors is predictable, responding to a single monthly value as if the process has changed will only cause more variation. At a minimum, the result of such actions is wasted resources. Worst case, variation is added to the process. The only way to stay under the budgeted value every month is to enact fundamental process changes that would lower the average monthly cost per unit or reduce the month-to-month variation so that the upper natural process limit equals the budgeted value. Such changes would be based on an in-depth analysis of all costs as well as wastes associated with production.

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