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).

In the May Brain Teaser, Felix and his Six Sigma Project team began working on a project to address customer complaints. Parts had been returned because they could not be assembled correctly. After mapping the process, Felix discovered problems with the data that were collected when the length of pieces at the sawing step were measured. In particular, the operators were using a gage that measured lengths to the nearest 32nd of an inch, but specifications were written to I0.015 inch. With a different gage, Felix collected data and discovered that the sawing process produced piece lengths that were predictable, but not capable of meeting the customer's specifications.

Felix and his team started working on an experiment to determine how to reduce the variation in the process. One team member suggested that before doing an experiment on the sawing process, they needed to determine if the gage now in use is adequate for the job. Felix agreed and a measurement process study was conducted.

Available data
In Felix's Six Sigma training class, which he took in part to solve this particular customer's problem, he studied lesson plans and case exercises that taught him how to analyze a measurement process. This led him to ask two questions:

Is the resolution of the new gage adequate to understand the data collected on the sawing process?

Do operators on the different shifts take measurements in the same way? The saw is run on two shifts and two operators per shift take measurements; Cindy and Barry work the first shift while Jesse and Jay work the second shift.

Felix referred to his notes to set up the evaluation of the measurement process using the new gage. Ten pieces were selected at the sawing process to use in the study. The data are summarized in the table, "Measurement Study of Piece Length."

1. Has Felix set up the data collection correctly to do a measurement process study? Can he answer the questions listed below with these data? If yes, proceed to answer the questions; if no, how should data be collected to study this measurement process with the four operators?

2. Is the measurement process variation repeatable? What is the standard deviation of the measurement process?

3. Do operators on different shifts measure the pieces differently?

4. Is the new gage adequate for measuring the lengths of pieces from the sawing operation?

Answers to April Brain Teaser
Q: From the data Felix and his team collected, what is the behavior of the saw operation with respect to the length of the pieces?
A: When analyzed on an average and range chart, the initial data show that the process is predictable at an average of 20.009 inches with an average range of 0.016 inch. This behavior is illustrated in the chart, "Length of Pieces After Sawing." However, there is a problem. While the process behavior is predictable, the pieces do not meet the specifications for length. A histogram, "Capability Analysis of Piece Lengths After Sawing," compares the individual piece lengths to the specifications. The natural process limits are 19.986 and 20.032 inches. About 27% of the parts measured have lengths outside the specifications.

Q: What insights can be gained from the data that can help answer the customer complaints?
A: Felix now understands the difference between a predictable process and one that always meets specifications. Just because a process is predictable does not mean that it is acceptable. In this case, the use of the gage that measured to the nearest 32nd of an inch may have partially masked the problem. This could happen if the operators were not using the gage correctly. Changing to a different gage gave Felix and his team data they could analyze to understand the process.

Q: What should Felix and his team do next?
A: As part of his Six Sigma project, Felix needs to determine what changes to make in the process that will reduce the common cause or routine variability in this process. They need to design one or more experiments to determine how to reduce the variation from one or more causes. Some options are discussed in this month's brain teasers.