Six Sigma Metrics

The point of most Six Sigma projects is to reduce costs. The use of the Six Sigma metrics provides a common way to measure all processes so both the baseline and post-project improvements can be
 established and validated.
First, some simple terms will be explained, followed by three examples of how Six Sigma metrics are measured.

A unit of product can be defective if it contains 1 or more defects. And, a unit of product can have more than 1 opportunity to have a defect. With Six Sigma, we measure the defects per opportunity so that both simple and complicated processes can have common metrics.

To determine the number of opportunities,

1. Determine all the possible opportunities for problems, then

2. Reduce the list by excluding the trivial and grouping similar defect types, and then

3. Define the opportunities consistently across different processes and locations.

The Proportion defective (p) is determined by the following formula:

p = no. of defective units/total no. of product units, Then the yield (Y 1st-pass, or Y final) can be determinedly = 1 - p

Rolled throughput yield, RTY, is the accumulation of i yields after multiple processes or process steps: RTY = Y 1 x Y 2 x Y 3 x Y 4 x Y i

RTY Example

If 10 processes each have a yield of 99%, then

RTY = Y i = .99^10 = 90.4%

It doesn’t take very long for RTYs to drop significantly when there are multiple process steps and/or individual process yields that are not at very low defect rates.

Note: Yield can be converted to a sigma value using the Area

under the Normal Curve (Z) tables, which are available in any statistics book. An example will follow later.

Some other relationships and metrics used in Six Sigma are defects per unit, defects per opportunity, and defects per million opportunities.

Defects per Unit (DPU, or u in SPC): DPU = no. of defects/total no. of product units

Defects per Opportunity (DPO): DPO = no. of defects/ (no. of units x no. of defect

opportunities per unit)

Defects per Million Opportunities (DPMO, or ppm (parts per million): DPMO = DPO x 1,000,000

Since processes that have been improved can reach very low defect rates, a measure that conveniently reflects rates below 100 defects per million opportunities is needed. The DPMO can be then converted to sigma & equivalent C P values (see third example and the table at end of article).

Calculating DPMO Example

If there are 9 defects among 150 invoices, and there are 8 opportunities for errors for every invoice, what is the DPMO?

DPU = 9/150 = .06 DPU

DPO = 9/ (150 X 8) = .0075 DPO

DPMO = .0075 X 1,000,000 = 7,500 DPMO

The CP index, used as a measure of process capability in manufacturing, is a ratio of the product characteristic’s upper specification limit (USL) minus the lower specification limit (LSL), divided by six standard deviations ( s ). The specification limits are established by the design engineer, and the standard deviation is a calculated measure of the actual variation of the process.

CP = (USL – LSL)/6 s

CP is a ratio of the engineering spread over the process spread. The Six Sigma method of converting yield to sigma and CP metrics provides a common way to measure both manufacturing and transactional (business) processes.

Converting Yield to Sigma and CP Metrics Example

1. Yield = 1 - p = .990

2. Z Table value for .990 = 2.32 s (This means that 1%

of the area under the normal distribution curve lies more than 2.32 standard deviations, s, to the right of the mean).

3. Estimate process capability by adding 1.5 s to reflect the typical “real-world” shift in the process mean over time:2.32 s + 1.5 s = 3.82 s

4. This s value can be converted to an equivalent CP process capability index by dividing it by 3 s: CP = 3.82/3 s = 1.27