There are many process performance metrics that we can use to measure the current and future value of our processes.

Before we look at the metrics, though, let’s review some of the terms that we’ll be using. 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. For a physical product, these values might be strength and/or size measurements. For a service, these values might be KPIs like turnaround time. In a general sense, think of a defect as a failure to meet customer expectations of quality.**Opportunity:**A chance to add value for a customer. These apply 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 processes that were defect-free.`Yield = (Opportunities - Defects) / Opportunities`

## Opportunity vs Unit

It’s easy to get opportunities and units mixed up. The easiest way to differentiate them is to think about 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.

## Defects per Opportunity (DPO)

DPO stands for Defects per opportunity. This is a simple ratio. Just take that 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.**

For 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 value and counts as a defect. If the customer has to wait ten minutes (defect in speed of service), receives the wrong burger (defect in accuracy), and their burger is luke-warm (defect in freshness/heat), three defects have each detracted value from the end result.

**Potential gotcha: **Make sure that you’re using defects and opportunities for the same population. 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.

### Worked example of Defects Per Opportunity

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

- 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.

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 DPO = 200/4000 = 0.05 DPO = 5%

## 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.

### Worked example 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 were talking about
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%

## Defects per Million Opportunities (DPMO)

DPMO is based on DPO, but in 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 figure out how successful their current serving process is, and how it compares to other serving processes they might have tried.

Defects per Million Opportunities is typically extrapolated from a sample. In the worked 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:

- 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.

### 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)))

### 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

## Rolled Throughput Yield (RTY)

Rolled Throughput Yield is a great way of seeing how healthy a process is. Essentially, it’s the probability that a multi step process will produce a defect-free unit.

Before calculating RTY, you need to complete two important steps:

- Map the process so that you know how many steps it has.
- Take samples at each stage of the process and test for defects, so that you have data for the calculation.

### How to calculate Rolled Throughput Yield

Calculate RTY by multiplying the percentage of defect-free units at each step of the process.

RTY = DFU_{1}* DFU_{2}* DFU_{3}* DFU_{4}* ... DFU_{n}

Where:

`DFU`

is the percentage of defect-free units in a step.`n`

is the number of steps.

If you’re thinking that the more steps you have in the process, the lower RTY you’ll get… you’re absolutely right.

### Example

A sequence of 3 operations has first pass yield (right first time) rates as follows:

- 1st step: 93%
- 2nd step: 87%
- 3rd step: 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%

Each step by itself had a good chance of being acceptable. But when you take a look at the entire system, you see that the cumulative errors take a toll. In the above example, any item that the process produced only had a 74% chance of passing through without error or rework.

### 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)

I’ve assigned problems to steps somewhat arbitrarily – an issue with an incorrect order could actually be occurring at the assembly stage, for example. In a real-world example, you’d have data that applies more appropriately to each step.

Firstly, we calculate the defect-free percentage for each step of the process:

Step 1: (1000 - 50) / 1000 = 0.95 = 95% Step 2: (1000 - 50) / 1000 = 0.95 = 95% Step 3: (1000 - 25) / 1000 = 0.975 = 97.5% Step 4: (1000 - 75) / 1000 = 0.925 = 92.5%

Secondly, we multiply these percentages together to get our Rolled Throughput Yield:

RTY = 95% * 95% * 97.5% * 92.5% RTY = 0.8139 = 81.39%

### Calculating DPU from Rolled Throughput Yield

In addition to the Defects Per Unit calculations above, you can use a process’s RTY to calculate its Defects Per Unit. Use this equation:

DPU = -ln(RTY)

Reminder: ln is the natural log.

### Worked example of calculating DPU from RTY

We calculated above that the food delivery process used by Joe’s Burgers has an RTY of approximately 81.39%. To get the DPU, we plug that into the equation:

DPU = -ln(0.8139) DPU = 0.2059

Remember that we’ve been approximating to 4 decimal places, so it’s going to be a smidge out. So if we compare this to our previous worked example of calculating DPU from the sample period, we find that we got an answer of 20% – equivalent to our approximated answer here.

## First-Pass Yield (FPY)

First-pass yield is the number of defect-free units coming out of a process, compared to the number of units manufactured. It doesn’t include units that need to be reworked in the defect-free units.

Note: First-Pass Yield is also known as Throughput Yield (TPY).

### How to calculate FPY for a process

- Calculate the first-pass yield for each step in the process, based on the number of defect-free units going into each step (typically each step will have fewer units than the preceding step).
- Multiply the FPYs together to get the total first-pass-yield.

FPY_{t}= FPY_{1}* FPY_{2}* FPY_{3}* ... * FPY_{n}

Where:

`FPY`

_{t}is the total First Pass Yield for the process.`n`

is the number of steps in the process.

### Worked example of calculating FPY

Let’s go back to Joe’s Burgers. Here are the step defects that we decided to use earlier:

- 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)

Because we don’t have specific data for each step in the process, we’ll assume that each unit contains only one defect (so an order might have tasted bad, but not been wrong, cold, or taken too long).

So, we have:

1000 defect-free units going in and 950 (1000 – 50 defective) defect-free units coming out.`Step 1:`

950 defect-free units going in and 900 (950 – 50 defective) defect-free units coming out.`Step 2:`

900 defect-free units going in and 875 (900 – 25 defective) defect-free units coming out.`Step 3:`

875 defect-free units going in and 800 (875 – 75 defective) defect-free units coming out.`Step 4:`

To calculate total First Pass Yield:

FPY_{t}= FPY_{1}* FPY_{2}* FPY_{3}* FPY_{4}FPY_{t}= (950 / 1000) * (900 / 950) * (875 / 900) * (800 / 875) FPY_{t}= 0.8 FPY_{t}= 80%

## Final Yield (FY)

Final Yield is the number of non-defective units at the end of a process divided by the number of units that went into the process.

FY = defect-free units / total number of units

The FY metric includes reworked units as non-defective units. This is an important distinction, because in some situations you’ll need to use process performance metrics that highlight rework as an issue.

### Worked example of calculating Final Yield

Let’s go back to the Joe’s Burgers example that we used earlier. Here are the steps in the shop’s process:

- Take the order.
- Make the ordered items.
- Assemble the order.
- Take payment and deliver the order.

And here are the problems that arose, causing faulty units (remember, we’re treating each order as a unit):

- 50 customers had the wrong order
- 75 felt they waited too long
- 25 said their order was cold
- 50 said their burgers just tasted bad

This data doesn’t give us the number of defective units, though. So let’s assume – for this example only – that none of these defects overlapped. No customers received the wrong order *and* waited too long, for example.

That gives us 200 defective units (orders) out of 1000, or 800 defect-free units.

FY = defect-free units / total number of units FY = 800 / 1000 FY = 80%

But hang on. What if Joe’s Burgers institutes a check for appropriate temperature in the assembly step – Step 3? If an item in the order is cold, the order assembly staff replace it with a hot item – essentially ‘reworking’ the order. This doesn’t matter for RTY and FPY calculations, but it does contribute positively for FY calculations. Then they can eliminate the ‘order was cold’ defect from the calculation.

FY = defect-free units / total number of units FY = 825 / 1000 FY = 82.5%

## Using Process Performance Metrics

Once you understand the process performance metrics available, and how to use them, the next step is to decide which metrics to actually use.

### Primary vs Secondary Process Performance Metrics

Primary and secondary metrics aren’t static. Each organization will have its own priorities when it comes to process performance metrics, leading to different lists of primary and secondary metrics. These lists will even change from time to time, as an organization’s focus and business objectives change.

Generally speaking, then, primary process performance metrics are the ones that your organization decides to focus on most. The rest are secondary process performance metrics.

### Questions to Ask When Designing Your Process Performance Metrics Program

The following information was 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.

- 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?
- Do we agree on the definition for each metric, the reason for tracking it, and the target we are aiming for?
- Can we link each metric back to a business or corporate goal?
- 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?
- Have we incorporated both qualitative and quantitative metrics into our decision-making framework?
- Do we know which drill-down options are most useful for each metric?
- Do we know which styles of metrics presentation each stakeholder prefers?
- Have we run each metric during a trial period to establish a baseline?
- Have we agreed on refresh triggers or cycles for each metric to prevent them from becoming obsolete?
- Do we have a metric that can predict future problems?
- Do business partners feel comfortable alerting Finance when metrics need to change and adapt to the new environment?
- Do we eliminate old metrics when new ones become more representative?
- 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

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**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

## 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

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## Comments (11)

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.

Why have you added 1.5 in the formula?

Sorry, Divyansh. Which formula?

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

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.

Thanks, Charles. I’m glad it was helpful!!

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.

RTYFPYDoes that help?