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

Much more useful is Process Capability Index (C_{pk,}), which measures your ability to conform to specification. If the process happens to be one that follows the normal distribution, then

C_{pk} = min(C_{p}U,C_{p}L) where

C_{p}U = _{}

and

C_{p}L = _{}

You'll go out of business pretty quickly if you don't at least conform to specification most of the time.

A simple modification of the C_{p} formula allows you to penalize that index for being off target by the square of the deviation from *Target*, where *Target is customer defined.*

C_{pm} = _{}

The equation is based on the reduction of variation from the target value as the guiding principal to quality improvement, an approach championed by Taguchi.

C_{pm} is used when the target value is not the center of the specification spread. From this equation, note that variation from target is expressed as two components; namely, process variability (σ) and process centering (µ - T).

Whatever losses you incur due to variation will be at a minimum when your output is at the real target and probably not much more loss if you're fairly close to target.

C_{pm} is an index that measures a process's ability to conform to target. If the process is on target, and if the target is in the middle of the specification limits, Cp = Cpk = Cpm. But if this is not the case, Cp ≥ Cpk ≥ Cpm. If the process is off target, C_{pm} < 1.

### Six Sigma Statistics Functions

A set of @RISK statistics functions return a desired Six Sigma statistic on a simulation output. For example, the function *RiskCPM(A10)* returns the Cpm value for the simulation output in Cell A10. These functions are updated real-time as a simulation is running. These functions are similar to the standard @RISK statistics functions (such as RiskMean) in that they calculate statistics on simulation results; however, these @RISK functions calculate statistics commonly required in Six Sigma models. These functions, a few of which are given in Figure 6, can be used anywhere in spreadsheet cells and formulas in your model.

*Click here for a larger image.*

**Figure 6:** Six Sigma statistics functions (partial list) that are available for simulations such as the one depicted in Figure 2

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