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

KPMG, the public accounting firm, recently published a survey of outsourcing. Nearly three out of four companies in the survey do not measure the value of their outsourcing arrangements. Yet paradoxically, KPMG concludes outsourcing is working because 89% of their survey participants plan to maintain or increase their use of outsourcing.

There are software tools that run on the desktop (and SDKs that enable you to create custom web applications) that automate well-established quantitative techniques for *a priori* and *a posteriori* analyses of the outsourcing process. And, there are qualitative techniques that human beings use to "brainstorm," when reports generated by these tools indicate that there is an opportunity for improvement in the process.

Six Sigma is a set of practices to systematically improve processes by reducing process variation and thereby limiting failures. In this article, you'll apply Six Sigma methods in a model of the outsourcing process. You'll decide which vendor(s) to select after determining the true cost of doing business with each one.

Imagine that your company is launching a new product. During the implementation phase of product launch, your company predicts selling 25,000 units per month. A critical component of the product is outsourced for precision machining. That is, this component must meet very specific requirements to be used in your product. In particular, the length of this component must be 66.6 mm, with a tolerance of only +/- .1 mm.

Three vendors currently supply the critical component. You have negotiated a different unit price for the component with each vendor. However, the quality of the component varies with each vendor. Some of the supplied components are not within the specified length. With two of the vendors, you must inspect all incoming components to verify they are within specification. This adds labor and scrap cost to the process. The third vendor is certified, and guarantees 100% of the components will be within specification, eliminating the need for inspection and scrap. However, the unit price from this vendor is highest of the three.

You will always need multiple vendors in case one goes down. However, you want to know which vendor has the highest real cost per unit so that you can develop a more efficient strategy for sourcing your components.

### Variation

Too many Six Sigma practitioners rely on static models that don't account for inherent uncertainty and variability in their processes or designs. However, in the quest to maximize quality, it's vital to consider as many scenarios as possible.

That's where a risk analysis and simulation add-in for Microsoft Excel like @RISK can help. @RISK uses Monte Carlo simulation to analyze thousands of different possible outcomes, showing you the likelihood of each occurring. Uncertain factors can be defined using over 35 probability distribution functions, which describe the possible range of values your inputs could take. What's more, @RISK allows you to define Upper and Lower Specification Limits and Target values for each output, and comes complete with a wide range of Six Sigma statistics and capability metrics, some of which are discussed below, on those outputs.

Six Sigma focuses on identifying and controlling variation in input variables to maximize quality and minimize variation in output variables, as shown in Figure 1.

*Click here for a larger image.*

**Figure 1:** Monte Carlo simulation to analyze thousands of different possible outcomes

Six Sigma refers to having six standard deviations between the average of the process center and the closest specification limit or service level. That translates to fewer than 3.4 failures per one million opportunities, as explained in Appendix 1.

Now, look at how you might go about using Six Sigma with Monte Carlo simulation in the outsourcing of a critical component for precision machining.

### The Model

Component length for each vendor is described by @RISK distribution functions. These cells also are defined as @RISK outputs with RiskSixSigma functions to enable you to calculate Cpm, an index that measures a process's ability to conform to a target length, for each vendor as well as generate distribution graphs of the component lengths with specification markers. The RiskSixSigma functions contain the USL, LSL, and Target value of 66.6 mm, with a tolerance of only +/- .1 mm.

Appendix 2 contains a discussion of *RiskOutput*and *RiskSixSigma*.

**Table 1:** Component specifications

In this model, the component length for Vendor 1 is described by a Pert distribution:

= *RiskOutput(,,,RiskSixSigma(B30,D30,C30,0,6))+RiskPert(66.4,66.6,66.7),*

the component length for Vendor 2 is described by a Normal distribution:

*=RiskOutput(,,,RiskSixSigma(B30,D30,C30,0,6))+RiskNormal(66.6,0.0706)*

and the component length for Vendor 3 is described by a Truncated Normal distribution:

*=RiskOutput(,,,RiskSixSigma(B30,D30,C30,0,6))+RiskNormal(66.58,0.05,RiskTruncate(66.5,66.7))*.

Each output contains RiskSixSigma properties and B30, D30, and C30 reference cells in Table 1, as shown in the upper-left corner of Figure 2.

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