As most readers know, statistical tests calculate a mean and confidence intervals on the mean. We are all familiar with the fact that as our sample size decreases, our knowledge of the “true” mean becomes less and less certain. This is important for tests that use the mean, such as the t-test and ANOVA.

FIGURE 1 is an example of two data sets: “apples” and “oranges.” In the first experiment we had 15 samples of apples and 15 samples of oranges. Plotting the means with their calculated confidence intervals shows we cannot differentiate between apples and oranges. (Since the confidence intervals overlap, we cannot be certain both means are not equal.)

Mixed-technology designs are prime for waste elimination. Here’s how.

Taiichi Ohno developed the concept of the seven wastes (muda) in manufacturing as part of the Toyota Production System (TPS), the foundation for Lean manufacturing philosophy. They are:

1. Waste of overproducing (no immediate need for product being produced).
2. Waste of waiting (idle time between operations).
3. Waste of transport (product moving more than necessary).
4. Waste of processing (doing more than what has been agreed upon).
5. Waste of inventory (excess above what was required).
6. Waste of motion (any motion not necessary outside of production).
7. Waste of defects (producing defects requiring rework).

The challenge created by system variation is sometimes best solved by moving test operations offline.

A paced assembly line with inline functional test balanced through careful application of Lean manufacturing principles is a model of efficiency. Achieving that level of efficiency requires careful coordination among engineering and production personnel.

Paced lines that integrate functional testers deal with several challenges, including:

• Length of test time vs. standard time per assembly station.
• Accommodation of system variation.
• Determining the best mix of automation and human interaction.
• Fixture reliability in a high-volume environment.
• Fail-safing the process from operator error.

Data distribution, explained.

In my December column I listed three items to watch out for when evaluating capability study results: Cp versus Pp, the distribution of data, and sample size. I hopefully cast some light on the differences between the two measures of capability, Cp and Pp.

In this column I will dive deep into the distribution of data. The thing to remember is the standard capability study assumes the data are normally distributed. This assumption of normality, while not so critical in other statistical tools, is very important in capability studies.

Cp and Pp give us predictions based on a sample of how our population will behave in the far tails of the normal curve. These measures use mean and standard deviation to create a normal distribution, and, from this, predict how many of our parts, over the entire population of parts, will fall outside the tolerance limits.