Traditionally, brain teasers are thought of as puzzles to solve using logical thought processes in a sequential manner. Everyone who is faced with using the current data available in their organization can relate to this notion of a brain teaser. The brain teasers are based on real-world situations that are encountered by workers in manufacturing environments. The brain teaser has 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 ( At the site, you can discuss the current brain teasers, as well as how its principles apply to everyday manufacturers. Use the skills that you have previously learned in Wheeler's Workshop to solve these problems.

Virginia is an engineer at a silicon wafer company whose products are used in the semiconductor industry. She is responsible for a process that deposits a layer of material on the wafers according to customer requirements, such as resistance or thickness. The customers' requirements vary greatly and target values for resistance can range from 1 to 100 with a tolerance of + or - 5% of the target.

One difficulty that Virginia faces is short production runs. Most of the production runs are between one and two days. Adding to this difficulty, Virginia someArial must alternate between runs that have a target of around 1 or 2 to those with a target of 100. Because of the extremes in the target values and the knowledge that the variability is different for the different targets, Virginia is reluctant to use process behavior charts to study the process.

Available data
After talking with another engineer, Virginia decides to study the process with some short-run techniques. She collects data from Reactor 11 for a period of several days. Reactor 11 is one of many such reactors used to deposit a layer of material on the silicon wafers. Her approach is to adjust the data by charting the percent deviation from the target value. The data she has collected are given in the table "Data Values for Reactor 11." The target values for the different products are summarized in the table "Target Values."

1. If Virginia uses the percent deviation from the target value for the short runs produced on Reactor 11, what does the analysis of the data show with respect to the behavior of Reactor 11?

2. What assumption is made when using the percent deviation from target?

3. What would be a more appropriate way to analyze the data?

Answers to November Brain Teaser
Q: Is the process temperature for producing this chemical behaving in a predictable manner?
A: The individuals and moving range chart of temperature values, which is shown in the graph, "Temperature of Chemical Process," indicates that this process is predictable with an average of 831 F. Individual temperature values could range from 786 F to 875 F on any given day.

Q: Is the process temperature meeting the process specifications?
A: A capability analysis of the temperature values shows that the process is not capable of meeting the specifications of 840 F + or - 25 F. This analysis is summarized in the graph, "Capability Analysis for Temperature of Chemical Process."

Q: What evidence, if any, can be found in the data to explain an increase in the variability of the quality characteristics for the finished product?
A: While there is no "official" pattern in the data that would be detected by traditional runs tests, there is an interesting zig-zaggedness to the running record. On examination, some data values appear to be in pairs with the moving range chart periodically showing a saw-tooth pattern.

A close look at the data and the timing of the data collection suggests that the values for Monday, Wednesday and Friday might be different in some way from the values for Tuesday and Thursday. Two individuals and moving range charts of temperature values--one for Monday, Wednesday and Friday and the other for Tuesday and Thursday--are posted on the Web site ( The capability analyses for these days are posted as well.

These analyses show that on Monday, Wednesday and Friday, the temperature values are predictable with an average of 842 F with individual values possible from 817 F to 867 F. Currently, no values are outside specification. On Tuesday and Thursday, the process is also predictable, but the average is 814 F with individual values possible from 789 F to 840 F. Approximately 50% of the values are outside of specification on these days. Further investigation is required to determine why these two situations are different.