October 19, 2018
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# Six Sigma, Monte Carlo Simulation, and Kaizen for Outsourcing

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

Cpk = min(CpU,CpL) where

CpU =

and

CpL =

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 Cp formula allows you to penalize that index for being off target by the square of the deviation from Target, where Target is customer defined.

Cpm =

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.

Cpm 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.

Cpm 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, Cpm < 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.

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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