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.

Situation
As part of a Six Sigma initiative, Felix and his team have been focusing on parts used in assemblies. Customers have complained and have sent some of these parts back. The team analyzed data from the process using a new gage and discovered that the length was predictable but did not meet specifications. To make certain that the new gage was good enough for measuring this process, Felix set up a measurement study. Unfortunately, Felix did not obtain at least two measured values for each operator on each part. Consequently, he could not get an estimate of the measurement process' standard deviation. Without this estimate, Felix could not answer the questions posed in the June brain teaser about the measurement process.

After Felix and his team reviewed the technique for analyzing the measurement process, they realized that they needed multiple data values for each combination of part and operator. They decided to bite the bullet and re-do the study.

Available data
After he re-did the measurement study, Felix summarized the data values in the table, "Measurement Study of Piece Length, Second Trial." Specifications on the length of these pieces are 20 + or - 0.015 inches.

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

2. Do operators on different shifts measure the pieces the same way?

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

Answers to June Brain Teaser
Q: 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?
A: After a review of the questions, it is clear that Felix did not grasp some of the critical requirements for a measurement study. The answers to the questions depend on having an estimate of the standard deviation, and the deviation's repeatability, of the measurement process. Such an estimate is calculated from repeated measurements of the same part by the same individual using the same process. Unfortunately, Felix did not specify that each person should measure each part at least twice. Therefore, Felix is unable to estimate the standard deviation of the measurement process and he cannot answer the following questions using the data he collected.

Q: Is the measurement process variation repeatable? What is the standard deviation of the measurement process?
A: Felix cannot answer this question because he did not collect multiple measurements for each part.

Q: Do operators on different shifts measure the pieces differently?
A: Again, an estimate of the standard deviation of the measurement process is required to answer this question.

Q: Is the new gage adequate for measuring the lengths of pieces from the sawing operation?
A: Two issues are important to determine if the gage is adequate. One issue is the resolution of the data values and the other is the ability to discriminate between parts. Both issues depend upon the standard deviation of the measurement process, and Felix cannot estimate this deviation with these data.