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 Yeild Video

## 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.

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

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.

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?

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.