Traditionally, brain teasers are thought of as puzzles to solve using logical thought process in a sequential manner. Everyone who is faced with using the current data available in their organization will relate to this notion of a brain teaser. The brain teasers are based on real-world situations that are encountered by workers in a manufacturing environment. The brain teaser has three parts: (1) the situation -- a description of a process or problem, (2) available data or other supporting information and (3) questions that various workers want answered for continual improvement. Recommended solutions will 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.

Production downtime is an ongoing problem for many companies. In response to the problem, the corporate office of one company decided to track downtime in order to quantify the lost productivity. Patrick was asked to develop a method to measure downtime and his results would be used throughout the organization. The production process is made up of three sequential steps, which are virtually identical in all locations. Patrick tracked the downtime and recorded the cause on paper for each step of the process. These values were added together to determine the total daily downtime, which were then expressed as a percent of the working day. The findings were reported to the plant manager.

Available data
In the table, "Data on Downtime," data was collected over a 10-day period, in accordance with Patrick's instructions. The downtime for each of the process' three steps is given along with the total. Also, the length of the work day is reported.

1. How should these data be analyzed before they are presented to the plant manager?

2. Is there anything unusual about these data?

3. What additional information is needed to be comfortable with the analysis?

Answers to January Brain Teaser
Q: Analyze these data and determine if Traci is correct in her assertion that audit net weights are lower than production net weights.
A: In deciding how to analyze these data, it is imperative to be clear on the structure of the data collection. The two methods, A and B, were used on the same bottles and each container has a value for both Method A and Method B. The containers were measured in four sets of three bottles each. A traditional hypothesis testing approach would be used to calculate a t-value for paired differences for Traci and for Carl. Using this technique, Traci had an average difference of 1.6 between the two methods with a standard deviation of 0.63 giving it a t-value of 8.78. Carl had an average difference of 1.8 with a standard deviation of 0.396 giving it a t-value of 15.65. In both cases, the t-value indicates that the difference is definitely real, or not zero, and that Method A gives results that are systematically higher than Method B.

However, be-cause the data are collected in repeated sets of three, it would be appropriate to make an average and range chart of these subgroups of size where n=3.

In all, there are a total of 8 subgroups, four each for Traci and Carl. The differences between the two methods, which are shown on the chart entitled "Difference Between Methods A and B" reveal a grand average of 1.696 with control limits of 0.673 and 2.719. No signals of assignable causes of variation are present. Thus, on average it is expected that Method A is 1.696 higher than Method B. The control chart shows that the results are consistent over time and provides a basis from which to make predictions.

From either analysis, we see that Method B, which is used for audits, gives lower values than Method A. Q: What should be done to closer align the two techniques?
A: When emptying containers, there is a chance that some of the fill will remain in the container. If Method B cannot be changed, then a constant of 1.7 can be added to the results for Method B to make them comparable.

Q: What additional questions need to be answered?
A: Would this same constant apply for heavier or lighter containers? Would the operators get the same results as Traci and Carl? Does the technique for Method B need to be changed? Will this difference of 1.7 hold over time?