The Role of Statistics in Red X® Problem Solving
By Richard D. Shainin
Dorian called his discipline Statistical Engineering. He didn’t mean that he was engineering statistics. Rather he saw his problem-solving approach as combining engineering insight with statistical thinking. As we look at the field of statistics, I think it’s useful to recognize three categories of statistical application: statistical estimates, diagnostic statistics and judgmental statistics. These terms are my terms. In the field of statistics everything we do falls under the heading of inferential statistics; meaning we are inferring things about populations beyond the sample data. In the field of statistics, descriptive statistics apply only to the sample data.
Statistical estimates are very familiar to us. They provide assessments of populations based upon sample data. In our everyday lives, we are informed of opinion polls, median incomes, median housing prices, economic growth and unemployment data. In our work, we use statistical estimates when we conduct an Isoplot® or a Tolerance Parallelogram™. Manufacturing and quality engineers rely on statistical estimates for process capability studies.
Using statistical estimates properly requires drawing random samples from the population of interest to estimate parameters such as population mean and standard deviation. Common errors are not getting representative samples or unintentionally drawing samples from multiple populations.
Diagnostic statistics reveal potential cause-effect relationships. Common techniques include regression analysis and screening designed experiments. In Red X® Problem Solving, we use diagnostic statistics to eliminate those parts of the system that don’t contain the Red X. Multi-Vari charts, Concentration diagrams, and Component Search™ are examples of diagnostic statistical tools that eliminate broad sections of a system. Proper use requires an understanding of system structure to ensure that samples are properly stratified. Strategy diagrams are an important tool for documenting our understanding of a system’s structure. Paired and group comparisons™ are diagnostic tools that eliminate detailed inputs and are best used after broad sections of the system have been eliminated.
Judgmental statistics are used to prove cause-effect relationships. In Red X® Problem Solving we call this taking the Red X to court. A B vs. W™ test proves the identity of the Red X. A six pack achieves that proof with a 5% risk that we’ve been fooled by the data. B vs. C™ tests assess if a proposed improvement is better than the current system. Full factorial experiments confirm suspected cause-effect relationships and reveal interactions. Proper use of judgmental statistics requires an understanding of alpha and beta risk and the proper use of p-values. Samples must be taken out of phase with trends, shifts or cycles which could lead to spurious associations. The new Red X® Problem Solving Journeyman class has extensive information on this topic.
At Shainin, we are engineers who use statistical tools in our everyday work. We must understand the field, the same way we understand algebra and calculus. We must be disciplined in our applications and able to explain what we are doing to our clients in a simple straight forward manner. We want to Keep It Statistically Simple and Statistically Sound.