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.
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
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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