Brain Teasers: What Size Is It?

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 (


Fiona is a production manager for a company that makes specialized equipment for companies that sort product by weight into certain size categories. Individual units pass over a scale that captures the product weight and directs it to drop in a certain bin. One customer has been having problems getting the sorting process to work correctly. Two particular problems are: individual items go into the wrong bin during the sorting process and some items that are the correct weight do not fall into a bin, but go off the end of the belt.

Fiona has offered to provide a quality technician, Fred, to study the sizing machine in the customer’s location and determine how to fix it. At the first meeting at the customer’s facility, Fred asked for available data on the scale and also helped set up a measurement study of the scale in the sizing machine.

Available data

The first data available came from the daily calibration of the scale using a single standard weight. The most recent 50 data values are summarized in the table, “Scale Data from Daily Calibration.” For the measurement study of the scale, the team decided to use 10 different standard weights to cover the range on the sizing machine. Also, because the ability of the scale to operate correctly depends on how consistently the operator feeds the product to the machine, two operators were involved in the study. Data from the measurement study are summarized in the table, “Data for Scale Study on Sizing Machine.”


    What can be learned from an analysis of the 50 days of calibration data on the sizing scale?

    What do the data from the measurement study reveal about the scale and the operators?

    How do the results from the calibration data and the measurement study compare?

    How can Fred explain the results from these two sets of data to Fiona and the customer?

Answers to April Brain Teaser

After learning that some elevator component parts are failing more quickly than expected, Anton, a process engineer, recommended that the company conduct an experiment to determine what factors are most critical in impacting the durability of the component parts.

Q: Which of the three factors used in this experiment has an impact on the average value for durability?

A: Both heat treat and the process speed have an impact on the average value of durability. The average durability of the product at the high heat treat setting is 2.12 units lower than the durability at the low heat treat setting. For the process, the average durability is 1.9 units lower at the fast process speed than at the slow process speed. The average durability is not detectably different for the two types of steel. See the graph, “Average Durability for Factors in Experiment.”

Q: Which of the three factors has an impact on the variation of durability values?

A: The type of steel has an impact on the variability of the durability of the product. Specifically, the special steel has an average range that is almost one-fourth of the average range for the regular steel. This means that the standard deviation for the special steel will be much lower than the standard deviation for the regular steel. Heat treat and process speed do not detectably impact the variability of durability. See the graph, “Variation in Durability for Factors in Experiment.”

Q: Are there any other important findings from analysis of these data?

A: A complete analysis of variance of this factorial experiment shows that there is an interaction between steel and heat treat on the average durability. Specifically, when using the special steel, the average durability is approximately 4 units lower at the high heat treat vs. the low heat treat, while the average durability using the regular steel is only 0.29 unit lower at the high heat treat vs. the low heat treat.

Q: Recommend a combination of the three factors for production trials that would likely achieve the desired target of 16.

A: The combination of steel, heat treat and process speed in the experiment that comes closest to the desired target of 16 is special steel, low heat treat and fast process. This combination uses the special steel, which has the lower variability. Actual production trials using this combination of factors will reveal if this average near 16 and the low variability can be sustained.

Dr. Sophronia Ward is a continual improvement specialist and Six Sigma Senior Master Black Belt and coach. 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

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