We can use many Process Performance Metrics to measure our processes’ current and future value.

Before we look at the metrics, let’s review some of the terms we’ll use. It’s important that you understand these terms as they’re used in Six Sigma.

Terminology

  • Defect: An end result (often a product) that doesn’t fall within a pre-defined acceptable range of values. These values might be a physical product’s strength and/or size measurements. For a service, these values might be KPIs like turnaround time. Generally, a defect is a failure to meet customer quality expectations.
  • Opportunity: A chance to add value for a customer. This applies to any situation in which your company can improve the perceived value of a product or service. For example, if you’re manufacturing a product to customer specifications, your opportunities might be:
    • Matching customer’s physical requirements
    • Meeting deadlines
    • Providing a free courier service straight to the customer.
  • Unit: A tangible result to a customer: a single service or product. For example, a customer’s phone call to your service department is a unit.
  • Yield: The yield is the percentage of opportunities that were successfully met. Another way to look at yield is the percentage of defect-free processes.
    Yield = (Opportunities - Defects) / Opportunities

Opportunity vs. Unit

It’s easy to get opportunities and units mixed up. The simplest way to differentiate them is to consider customer needs and requirements.

The item they need is the unit.

The specifications for that item (color, size, materials, time to delivery) are the opportunities.

You might have several opportunities per unit. For example, think about a customer calling a service line to get help with a piece of software. The unit, in this case, is the phone call. The opportunities could be:

  • Answering the phone call within an acceptable time range.
  • Having the phone call directed to an appropriate person.
  • Being able to help the customer with their problem.
  • Leaving the customer with a positive experience.

Process Performance Metrics – Defects per Opportunity (DPO)

DPO stands for Defects per Opportunity. This is a simple ratio. Take the number of defects you have in your process (usually found by sampling) and divide it by however many opportunities there are. Then, express the ratio as a percentage.

DPO = Defects / Opportunities

Complex processes and items often have many opportunities to add value. Hence, you might have several defects per process or item.

Example: A fast food drive-through order. The customer has a lot of criteria on which they’ll judge the experience as a whole:

  • Staff attitude
  • Speed of service
  • Accuracy (do the received items match the order?)
  • Presentation
  • Taste of the food
  • Freshness/heat of the food.

Each of these criteria is an opportunity to add value for the customer. A failure in any of these criteria detracts from value and counts as a defect. If the customer has to wait ten minutes (defect in the speed of service), receives the wrong burger (defect in accuracy), and their burger is lukewarm (defect in freshness/heat), three defects have each detracted value from the end result.

Potential gotcha: Ensure you use the same population’s defects and opportunities. For example, if you’re counting defects in a sample of 500 products, the number of opportunities must also apply only to that sample of 500 products.

Examples of Defects Per Opportunity

Let’s say Joe’s Burgers serves 1,000 customers a day. The company has identified its opportunity types as follows:

  • Accuracy
  • Speed
  • Freshness
  • Taste

For example, in a single day, 50 customers were given the wrong order, 75 felt they waited too long, 25 said their order was cold, and 50 more said their burgers just tasted bad.

Some of that feedback might have overlapped; customers might have received the wrong order and waited too long for it. That doesn’t matter for this metric because each order has multiple opportunities attached to it.

To calculate the number of opportunities, multiply the number of orders (1000) by the number of opportunity types (4) to get 4000.

DPO = number of defects / number of opportunities = 200/4000 = 0.05 = 5%

Process Performance Metrics – Defects per Unit (DPU)

Defects per unit is a similar calculation to DPO, but instead of looking at opportunities, we’re looking at units. See Opportunity vs. Unit above if you’re getting confused.

Let’s look at the Joe’s Burgers example again, but this time from a DPU viewpoint.

Examples of Defects Per Unit

Let’s say Joe’s Burgers serves 1,000 customers a day. In a single 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.

Some of that feedback might have overlapped; customers might have received the wrong order and waited too long for it. That doesn’t matter for this metric. We’re just looking for a basic ratio.

(Note: it would matter if we discussed defective units per 1000, for example.)

The number of units is the number of orders (1000).

DPU = number of defects / number of units
DPU = 200/1000 = 0.2
DPU = 20%

Process Performance Metrics – Defects per Million Opportunities (DPMO)

DPMO is based on DPO, but it uses real-world manufacturing-type numbers. This is an important metric because it’s used in Six Sigma to measure the performance of a process. For example, Joe’s Burgers would use DPMO to determine how successful their current serving process is and how it compares to other serving processes they might have tried.

Defects per Million Opportunities are typically extrapolated from a sample. In the work examples above, we looked at Joe’s Burgers using a single day’s orders as a sample–1000 units. If you’ve already worked out DPO for a sample, you can calculate DPMO by simply multiplying the decimal result (not the percentage) by one million.

DPMO = DPO * 1000000

Alternatively, you can use this equation:

DPMO = (Defects / Opportunities) * 1000000

Or:

DPMO = (Defects / (sample size * opportunities per unit)) *
1000000

Worked example of Defects Per Million Opportunities

Joe’s Burgers serves 1,000 customers in a day. The company has identified its opportunity types as follows:

  • Accuracy
  • Speed
  • Freshness
  • Taste.

In a single 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.

Number of defects: 50 + 75 + 25 + 50 = 200
Sample size: 1000
Opportunities per unit: 4
DPMO = (Defects / (sample size * opportunities per unit)) *
1000000
DPMO = (200/(1000 * 4)) * 1000000
DPMO = 50000

How to Calculate 6 Sigma level based on DPMO

There are two basic ways that you can determine the Six Sigma level from your DPMO figure:

  • Look at an appendix table.
  • Use the equation.
Process Performance Metrics

Six Sigma Level Equation

Use this equation to calculate your process’s Six Sigma Level based on its DPMO:

Level = 0.8406 + √(29.37 – (2.221 * ln(DPMO)))

Note: If you’re wondering where the numbers 0.8406, 29.37, and 2.221 come from, they are constants that help us calculate the DMPO or level.

Process Sigma = 0.8406 + SQRT(29.37 – 2.221 * (ln(DPMO))).
Reference: Breyfogle, F., 1999. Implementing Six Sigma: Smarter Solutions Using Statistical Methods. 2nd ed. John Wiley & Sons.

Worked example of calculating Six Sigma Level

Let’s start with the DPMO figure from Joe’s Burgers: 50000.

Firstly, if you haven’t come across ln before, it means that you need to find the natural logarithm of the number–in this case, the DPMO. Use a scientific calculator. In this case, the natural logarithm of 50000 to 4 decimal places is 10.8198.

Secondly, we need to plug that into the equation:

Level = 0.8406 + √(29.37 – (2.221 * ln(50000))) 
Level = 0.8406 + √(29.37 – (2.221 * 10.8198))
Level = 0.8406 + √(29.37 - 24.0307)
Level = 0.8406 + √(29.37 - 24.0307) 
Level = 0.8406 + √5.3392
Level = 0.8406 + 2.3106
Level = 3.1513

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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.

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Comments (31)

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.

This unit was a great introduction to the math that will be coming. The examples were easy to follow and the explanation of what the different measures tell you were simple and to the point. A great confidence builder for what is ahead.

Re: Question #19: XYZ company paying $2 per form and there are 30 fields in each form. Customer reported 1,600 defects in the 6,000 forms filled by the supplier. Calculate the DPMO and process sigma level.

I understand how we can lookup the DPMO using the chart you provided, but will this table be on the exam?

And I can only assume we will be allowed to use a scientific calculator (embedded in the online test) in order to derive the DPMO via log calculation?

Different exams have different stipulations. For example, some exams allow you to bring your own reference material while others do not. Some allow for scientific calculators, while others do not.

DPMO is a simple division. Looking up Sigma level is usually done by chart. It would be unreasonable for organizations to ask you to memorize the chart (however, do enough practice questions and you’ll get close!), so for the exams that provide reference sheets they will have that material or not ask you the question. For the exams that let you bring your own material, I would certainly add this to your must-have references.

Hi Ted,
Trust you are doing well,
I would like to thank you for your guidance and support to help us learn and properly understand the material of lean six sigma,
Moreover, I would like to ask you with regards to the worked example of calculating Rolled Throughput Yield
Let’s go back to Joe’s Burgers. They have 1000 customers in a day – 1000 instances of the food delivery process. We can break their process down into four steps:

Take the order.
Make the ordered items.
Assemble the order.
Take payment and deliver the order.
Now, we said that in the day we’re using as our sample data, they received the following complaints:

50 customers had the wrong order (problem in step 1)
75 felt they waited too long (problem in step 4)
25 said their order was cold (problem in step 3)
50 said their burgers just tasted bad (problem in step 2)

My understanding is that I need to follow the sequence of processes and multiply the defect free % in each step as per the following:
RTY= ((1000-50)/1000) * ((950-50)/950) * ((900-25)/900) *((875-75)/875)*100
Hence, can you please clarify why the problem was resolved by multiplying the defect free for every sequence starting from 1000 as initial input for every sequence?

Good observation, Mayssa. You’re essentially asking what is the difference between First Pass Yield and Rolled Throughput Yield.

I really should clean this part up so it’s more clear. I fear that I was too ambitious putting all of this on one page. I’ll try to disambiguate with help from this article on the same.

RTY

Rolled throughput yield is the probability of passing all in-process criteria for each step in a process, as well as all end process criteria. RTY is defect sensitive, meaning that instead of being based on the yield on produced units, it uses the number of defects found at each process step.

FPY

First time yield, the most common way to calculate process yield, is the probability of a defect-free output from a process. This metric considers only the criteria at the end of the process. FTY is unit sensitive, meaning it does not take into account whether the output unit is defective, and is calculated by dividing the number of units produced from a process by its inputs. It does not capture how many defects were found and corrected within a single unit.

Does that help?

Hello Mr. TED,
Thank you very much for your explanation.
Talking about RTY and FPY, they are a little bit tricky for me. When we talk about RTY, do we consider that all the parts will continue all the processes even though they are defective (scrap or rework) ? If it’s not the case, wouldn’t it be incorrect to calculate the middle processes yields while taking in consideration the total number of parts ?
The same for FPY, do we consider that all the defective parts (rework or scrap) would be taken from the process thus we would only produce free-defects parts ? If it’s not the case, wouldn’t it be incorrectto devide the defective parts by only the number of free-defects parts ?
I hope that you got my point.

Thank you in advance for your consideration.
Kind Regards.

Hello Anass Knidil,

You are saying defective (Scrap or rework), but scrap and rework are two different aspects, rework items may come back into the process, whereas scrap items will completely move away from the system.

Let’s see one more example here for better clarity

Example: A manufacturing process with 3 steps – Processes 1, 2, and 3. Let’s also say that on a particular day they note the following performance:

Process 1: 100 parts passed through this process and 84 “good” parts left this process (scrapped 16).

Process 2: With some WIP laying around 110 parts passed through this process with 82 “good” parts passing (28 scrapped)

Process 3: With even more WIP laying around this process they managed to produce 138 parts with 126 parts passing (12 scrapped).

Process 1 had a daily yield of 84% (84/100) while process 2 had a daily yield of 75% (82/110) and finally process 3 had a daily yield of 91% (126/138).

So, to calculate RTY we simply multiply these yields together giving us a composite yield for the day. Doing this gives us: 84% x 75% x 91% = 57%

For FPY, it is the probability of a defect-free output from a process.

When a process has a high total throughput yield and a low rolled throughput yield, it’s a sign that large amounts of rework are being performed. This rework is waste that adds cost and negatively affects delivery rates.

Thanks

Hi Ted excellent way of explaining, just have one confusion what is the difference between RTY (Rolled throughput yield) and FPYt (Total First-Pass-Yield) it seems both are same

Hi Ted,

I found the phrasing “first pass yield (right first time) ” is very misleading.

since when we are calculating FPY, we include the units passed with re-work, those units are not done correclty at “the first time”, otherwise it won’t need rework.

Best,
Xiang Liu

Hi Xiang,

Thank you for the note. The reason I state ‘right the 1st time’ is because first pass yield does not include units passed with rework. Only good units with no rework or repairs are counted as coming out of an individual process.

Best, Ted

I just wanted to inform you in case you weren’t aware, but the video right under the DPMO section has been removed by the original uploader, so we no longer have access to it.

Otherwise, this is very helpful.

BTW: The last example for RTY is wrong. 98-(5+10)/98 = 0.85 not 0.89.
“So, the Total Rolled Throughput Yield = 0.93*0.89*0.84= 0.695 ~ 70% yield” should be “So, the Total Rolled Throughput Yield = 0.93*0.85*0.84= 0.660 ~ 66%”

Hi Ted,

wish you could help. if I have 3 weekly DPU data (0.01, 0.02, and 0.03) . The weekly production volume is 5000 units. and the defect opportunities per process flow = 20
How can I get the DPMO ?
thank you in advance

This unit was EXTREMELY helpful! It really made everything I’ve been studying in the ASQ Handbooks and other reference material finally click! Thank you so much!

“Note: If you’re wondering where the numbers 0.8406, 29.37 and 2.221 come from, they are constants that help us calculate the DMPO or level simply.”

Will we be required to memorize these constants? I also wondered if we are authorized to use Microsoft Excel during the IASSC Green Belt exam? I have no clue how to calculate the natural logarithm of a number and know I can easily use the LN function in Excel. Therefore, that’s the reason I ask.

Very Respectfully,

Travis

Hi Travis,

For most exams you will not be required to memorize these constants. If you are taking an exam that allows reference materials, like the ASQ, I’d suggest having it bookmarked though.

I do NOT know of any exam that allows you to use excel however logarithm functionality is available on the standard calculators that the exams allow. Speaking of calculators, be sure to double check with your exam provider that the calculator you want to bring to the exam is on their acceptable list.

Best, Ted

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