Anyone 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 (


Martha is a production supervisor for a company that makes a variety of dessert cakes and cookies. One product is the cookie part of an ice cream sandwich. These cookies are made on Line 6 several times per week. The customer has specifications for weight, taste, size and visual characteristics that include missing corners, broken cookies, and upturned or curled edges.

Most of these characteristics are monitored electronically and process behavior charts are visible to the line operators. Recently, the process behavior chart on visual defects for this product has shown erratic behavior with points far outside the control limits. Martha is puzzled and determined to find the root cause or causes.

Available data

The erratic behavior first appeared two weeks ago. Martha decided to concentrate on the visual-defects chart beginning two days before the erratic behavior and continuing to the present. She also collected additional data, such as Crew and Batch Number, which was not usually displayed on the chart that is seen by the operators. The data are recorded in number of defects per batch and are summarized in the table, "Visual Defects for Ice Cream Sandwich Cookies." Martha was also able to identify the types of defects, which are summarized in the table, "Defects by Type."


1. What was the average number of defects per batch of cookies prior to the onset of the erratic behavior?

2. What types of defects are likely associated with the erratic behavior?

3. How can the available information be used to investigate the cause of the erratic behavior?

4. What are possible causes of the most likely defect types?

Answers to May Brain Teaser

For his Six Sigma project, Greg and his team improved first-pass yield of one type of wiring harness from 68% to almost 97% on average. After three months of steady first-pass yields at the improved average, first-pass yield suffered a setback. In only a few days, first-pass yield began to drop as seen on the process behavior charts kept by the operators. Greg was convinced that something critical had changed and was determined to discover the cause.

Q: What is the current behavior of first-pass yield for Wiring Harness Type A?

A: Based on the data provided, first-pass yield shows a decrease in the past five days. The evidence includes a moving range outside the upper control limit and two individual values below the lower limit. See the graph, "First-Pass Yield for Wiring Harness Type A."

Q: Is there evidence in the data that shows the drop-off occurred at the same time as the change in materials supplier?

A: The moving range value above the upper control limit coincides with the information about the new supply of material reported by the operator.

Q: How can Greg determine if the decrease in first-pass yield is definitely associated with the change in supplier?

A: The easiest way to determine cause and effect is to switch between the two suppliers and capture the results on the process-behavior chart. A pattern that coincides with the supplier change indicates a connection between the supplier and first-pass yield. Greg needs to set up a more extensive experiment if he needs additional evidence.

Q: If the change in supplier did cause the lower yield, how can Greg use the data to convince the purchasing department that it is better to change back to the original supplier?

A: The most powerful case is based on economics. Greg needs to determine the cost of production under two different conditions: (1) using material from the original supplier with the improved first-pass yield and (2) using material from the new supplier with the reduction in first-pass yield. All costs must be included such as rework, labor, additional production required and any shipping delays. If total costs are lower with the original supplier and the higher first-pass yield, Greg has a powerful case to switch back to the original supplier.