There are many metrics that are valuable to measure current state and base improvements off of in future state in Six Sigma projects.

## Defects per Opportunity (DPO)

DPO stands for Defects per opportunity. This is a simple ratio and you can find it by division. Just take that number of defects you have in your process (usually found by sampling) and divide it by however many opportunities there are. Complex processes or complex items that the process produces may have many opportunities for a defect. For example, thing of a fast food drive through order. The customer judges the experience on many criteria; speed, accuracy, presentation, edibility, taste. If the order falls short on any of those criteria, it’s a defect.

Example: Let’s say Joe’s Burgers serves 1,000 customers a day. 50 customers had the wrong order, 75 felt they waited too long, 25 said their order was cold, and 50 more said their burgers just tasted bad. That’s 200 defects (assuming they are mutually exclusive.)

200 defects in 1,000 opportunities is 20%.

## Defects per Unit

Example

Defects per unit is slightly different than DPO. Let’s use the Joe’s burgers example from above. The client is judging the drive through order on 5 different scales. That means for each order there 5 chances to get something wrong – to introduce a defect.

In those 1,000 orders that Joe’s Burgers makes in drive through sales there are 5 * 1,000 opportunities for a defect. Or, 5,000. Now let’s say that there were orders that had multiple things wrong. For instance, the process took too long and the food was cold when it was done. That counts as 2 defects. In this case, the kinds of defects are not mutually exclusive. Let’s say that at the end of the day after 1000 orders 2000 defects were found. That would equate to 2 defects per burger order – or 2 DPU

## Defects per Million Opportunities (DPMO)

DPO X 1,000,000. DPO stands for Defects per opportunity. Just take that number and multiply by one million to determine DPMO – Defects per Million Opportunities.

Example

### Hit to Calculate 6 Sigma level based on DPMO.

- Look at an appendix table.
- Or use the equation: 6 Sigma Level = 0.8406 = SQRT(29.37 – 2.221*ln(DPMO))

## Rolled Throughput Yield (RTY)

Rollef Throughput Yield is a great way of seeing how healthy a process is. In short, you take the percent chance of successful completion at each process step and multiply it by all the other steps’ % chance rate to arrive at a total number. Obviously you will have had to have mapped the process and recorded data to obtain these numbers.

For example; A sequence of 3 operations has first pass yield (right first time) rates as follows: 93%, 87% and 92%.

In other words, the first step in a process has a 93% chance of completing correctly. The 2nd has only an 87% chance. And the third process step has a 92% chance.

The first pass yield rate for the whole process is the chance of each step multiplied. RTY = 93% * 87% * 92% = 74%

So, even though each substep had high percent chances of being acceptable, when you take a look at the entire system you see that the cumulative errors take a toll. In that example, any item that the process produced only had a 74% chance of passing through without error or rework.

### Rolled Throughput Yield to get to DPU.

DPU = -ln(RTY)

### Rates of Defect and Yield Video

### Key Process Input Variable, Key Process Output Variable

- http://www.six-sigma-material.com/defectsperunit.html (DPU)
- http://www.six-sigma-material.com/defectsperopportunity.html (DPO)
- http://www.six-sigma-material.com/defectspermillionopportunities.html (DPMO)
- http://en.wikipedia.org/wiki/First_pass_yield (FTY vs TPY)
- http://www.six-sigma-material.com/Final-Yield.html (FY)
- http://www.six-sigma-material.com/Throughput-Yield.html (TPY)
- http://www.six-sigma-material.com/Rolled-Throughput-Yield.html (RTY)
- http://lssacademy.com/2010/07/20/how-to-determine-cycle-time-takt-time-lead-time/(Cycle Time and Takt Time)
- http://www.managementstudyguide.com/what-are-metrics.htm (What are metrics)
- http://www.managementstudyguide.com/primary-metric.htm (Primary metrics)
- http://www.managementstudyguide.com/secondary-metric.htm (Secondary metrics)
- http://www.isixsigma.com/methodology/balanced-scorecard/develop-correct-six-sigma-project-metrics/

Emailed to me and attributed to Will Poats of the CEB.

Accounting and Reporting teams are always looking to include the most relevant metrics in their management reports, so they should avoid the three following missteps when incorporating metrics: wrong metric selection, lack of process ownership, and ineffective reporting practices.

Below are 13 questions you can ask yourself and your team members when designing or strengthening your metrics program.

1. Have we chosen no more than 12 to 15 metrics for decision making among those suggested by the corporate finance leadership team and business partners?

2. Do we agree on the definition for each metric, the reason for tracking it, and the target we are aiming for?

3. Can we link each metric back to a business or corporate goal?

4. Have we tested the metrics with our stakeholders to ensure they understand the definition and have a clear sense of how they will use the metric to make decisions?

5. Have we incorporated both qualitative and quantitative metrics into our decision-making framework?

6. Do we know which drill-down options are most useful for each metric?

7. Do we know which styles of metrics presentation each stakeholder prefers?

8. Have we run each metric during a trial period to establish a baseline?

9. Have we agreed on refresh triggers or cycles for each metric to prevent them from becoming obsolete?

10. Do we have a metric that can predict future problems?

11. Do business partners feel comfortable alerting Finance when metrics need to change and adapt to the new environment?

12. Do we eliminate old metrics when new ones become more representative?

13. Do we update our business partners on metrics we will no longer be tracking when the dashboard changes?## Six Sigma Black Belt Certification Process Performance Questions:

Question:Which of the following performance measures is most appropriate for evaluating the tangible effects of a six sigma project? (Taken from ASQ sample Black Belt exam.)a) Cycle time

b) Team member absentee rate

C) Employee morale

D) Unsolicited compliments from customers

Answer:Cycle Time. Six sigma projects usually revolve around improving a process to the benefit of the client (and the corporate bottom line!) Cycle time can be found by analyzing a process. Making improvements to that process can make for a faster cycle time. You could use six sigma techniques in projects aiming to decrease absentee rates, increase employee morale, or gaining more unsolicited compliments, but the best answer is cycle time.

Question:Which of the following is the correct formula for DPMO?(A) D/TOP

(B) DPO X 1,000,000

(C) D X U XOP

(D) DPU/DPO

Answer:DPO X 1,000,000. DPO stands for Defects per opportunity. Just take that number and multiply by one million to determine DPMO – Defects per Million Opportunities.## ASQ Six Sigma Green Belt Process Performance Questions

Question:Which of the following measures is used to show the ratio of defects to units?

(A) DPU

(B) DPO

(C) DPMO

(D) PPM

Answer:(A) DPU stands for Defects per Unit. DPO is defects per opportunity, DPMO is defects per million opportunities, and PPM is parts per million. See Process Performance Measures.

Nwabueze Chibuoyi James Jnr says

The DPMO for a process is 860. What is the approximate 6sigma level of the process?

a. 4.2 b. 4.4 c 4.6 d 4.6

Six Sigma Study Guide says

860 dpmo is sigma level 4.64 – you can get this by using sigma calculator or reference tables or you can use MS Excel formula ‘NORMSINV(1 – (DPMO/1000000))+1.5 in Excel to find the sigma level of the process. NORMSINV() refers to the probability value (yield) in the Z distribution table to arrive at the sigma level based on the probability of the yield.

Divyansh says

Why have you added 1.5 in the formula?

Six Sigma Study Guide says

Sorry, Divyansh. Which formula?

Bernard Leung says

Divyansh, I think + 1.5 is representing 1.5 sigma shift over time.

Joe says

In your explanation of DPO, should the number of opportunities be 5,000 instead of 1,000 as there are 5 opportunities for a defect in each of the 1000 units?

Six Sigma Study Guide says

Good eye, Joe, but no. I’ll admit this example is a bad one. The key here is the wording ‘mutually exclusive.’ See the description for DPU for some disambiguation. I’ll update the example to something a bit clearer.