# Six Sigma, Monte Carlo Simulation, and Kaizen for Outsourcing

### Quantitative Methods Employed in Six Sigma

Assuming normal distributions, look at some quantitative methods employed in your use of Six Sigma. *A brief discussion of mean (µ) and standard deviation (σ) used in this section is given in Appendix 1.*

First, consider Process Capability (C_{p}):

C_{p} = _{} where

USL = An upper specification limit that is a value below which performance of a product or process is acceptable.

and

LSL = A lower specification limit that is a value above which performance of a product or process is acceptable.

*Click here for a larger image.*

**Figure 5a:** C_{p} for different USL-LSL to 6σ ratios

The capability index C_{p} measures the ratio of the width of a specification to the width of a process. This is useful in telling you your process's ability to meet specification, if you get the process output to average right in the center of the specification. If your natural tolerance is exactly equal to your specification width, C_{p} = 1 and the process is said to be "potentially minimally capable" of meeting specifications. "Potentially" because it might be terribly off target and making 100-percent scrap but with variation equal to the specification width. More usually, companies have a goal of getting all their capability indexes equal to 1.33.

Many processes will only have one limit: either an upper or lower control limit. These are sometimes called 'One Sided Specs'. A C_{p} cannot be calculated for one-sided specs.

**Figure 5b:** Normal (Gaussian) curve showing mean and standard deviation

**Figure 5c:** Small standard deviation does not guarantee conforming to specifications

Consider the possibilities of accuracy versus repeatability. Suppose you measure the offset error 10 times and plot the 10 points on a target chart (refer to Figure 5c). Case 1 in this diagram shows a highly repeatable machine because all measurements are tightly clustered and on target.

The average variation between each point, known as the standard deviation, is small. However, a small standard deviation does not guarantee an accurate machine. Case 2 shows a very repeatable machine that is not very accurate.

As the bulk of the measurements are clustered more closely around the target, the standard deviation becomes smaller and the bell curve will become narrower.

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*This article was originally published on June 11, 2008*