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# As Easy as 1, 3, 9?

Summary: Weighted matrices appear in many contexts in Six Sigma. They appear, for example, when computing risk priority numbers (RPN) in a failure mode and effects analysis (FMEA). In this case, the RPNs are the products of three individual values. In other contexts, the important results are the products of two values. The values being multiplied are often integers from some range, perhaps one to 10. When working with weighted matrices, the analysis is often simplified by using a scaled set of values; instead of using one to 10, you may use only the values low, medium and high—perhaps represented numerically by one, three and nine. It is natural to wonder if one, three and nine are the best integer values for low, medium and high. Issues can arise when using scalings. A metric is defined that minimizes those issues, and enumeration is used to determine the best scalings: those that minimize this metric. In fact, a one-three-nine scaling is optimal. In addition, there’s a statistical technique that easily allows a way to determine whether the optimal one-three-nine scaling has been used correctly.

**Topics:**Six Sigma, Statistics**Keywords:**Failure mode and effects analysis (FMEA), Risk priority numbers (RPN), Six Sigma, Matrices, Matrix scores, Optimal scaling,**Author:**Zwillinger, Dan**Journal:**Six Sigma Forum Magazine