# DPMO Calculator

Created by Hanna Pamuła, PhD
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Feb 02, 2023

Welcome to the DPMO calculator (Defects per Million Opportunities) - a tool that will help you calculate this popular measure of process quality. Haven't you heard about this mysterious abbreviation before? No? Well, scroll down and you'll learn all about the DPMO meaning.

However, if you're wondering how to calculate DPMO and what's the formula behind it, you can also breathe a sigh of relief - you'll find all the explanations below.

## What is DPMO, and what does it stand for? DPMO meaning

DPMO stands for defects per million opportunities. It's a measure of process performance used to assess the quality of a process - e.g., the quality of a service or production. The lower the value of DPMO, the better, as it is tied with the probability of the presence of a defect.

The concept of DPMO may look similar to reporting defective parts per million (PPM). However, in DPMO it's possible to have in one unit:

• Multiple types of defects; or
• Multiple defects of the same type.

while PPM describes defective units per million units. Another related concept is DPU, which stands for defects per unit. DPU describes the average number of defects per unit of product/service.

## How to calculate DPMO? DPMO formula & example

The DPMO formula is pretty straightforward:

$\footnotesize \text{DPMO} = \frac{1,\hspace{-0.04cm}000,\hspace{-0.04cm}000\times \text{defects}}{\text{units}\times\text{defect opportunities}},$

where:

• $\small\text{defects}$ - number of defects;
• $\small\text{units}$ - number of units; and
• $\small\text{defect opportunites}$ - number of defect opportunities per unit.

Let's show how we can calculate DPMO with an example.

Assume that you're the owner of a cloth factory. You'd like to calculate the DPMO for the production of jeans 👖. You've gathered some information from your company managers, and you found out that every pair of jeans can be defective in five different ways:

• Missing button 🔘
• Dingy material;
• Faulty seams 🧵
• Inaccurate size; and
• Broken zip 🤐

Moreover, when 10,000 pairs of jeans were sampled, we found 11 defects. So how to calculate DPMO? Use the DPMO formula defined above!

$\small\text{defects}$ is the number of defects found in a sample, so it's 11;

$\small\text{units}$ - for this example, it's 10,000 pairs of jeans; and

$\small\text{defect opportunites}$ - the number of defects opportunities per unit, so in our case, it's 5.

\footnotesize \begin{align*} \text{DPMO} &= \frac{1,\hspace{-0.04cm}000,\hspace{-0.04cm}000\times \text{defects}}{\text{units}\times\text{defect opportunities}}\\[1.0em] &= \frac{1,\hspace{-0.04cm}000,\hspace{-0.04cm}000\times 11}{10,\hspace{-0.04cm}000\times 5}\\[1.0em] &= 220 \end{align*}

How good or bad is that result? The best possible DPMO is 0, while the DPMO will get a value of 1 million in the worst case. According to the six sigma methodology, highly capable processes experience less than 3.4 defects per million opportunities - an extremely unlikely event.

## DPMO & six sigma relationship

You may have heard about the three sigmas (more of that in our empirical rule calculator). How about the six sigmas? The six sigmas are a set of methods, metrics, and tools that help improve any kind of process by eliminating waste and defects, reducing variation, and ensuring quality control. DPMO is one metric that can be found in the six sigma methodology.

So what does six sigma mean, and what does it tell us?

The standard deviation - sigma σ - measures the dispersion of a set of values. (See our standard deviation calculator for an in-depth tour about standard deviation.)
The number of standard deviations between the mean of the process and the nearest specification limit describes the sigma level (does z-score ring a bell?🔔). If you want to express the amount of defect-free products created during your process, you can use the sigma levels instead of standard percentages:

1 Sigma = 30.85% defect-free;

2 Sigma = 69.146% defect-free;

3 Sigma = 93.319% defect-free;

4 Sigma = 99.379% defect-free;

5 Sigma = 99.977% defect-free; and

6 Sigma = 99.99966% defect-free.

The above values comply with the six sigma industry standard, where the empirically found value of the is used. Sigma shift is used to allow for the increase in process variation over time, which occurs in real-life situations.
The sigma level measure is useful when you want to compare different processes or find the ones that need improvement.

For the DPMO-sigma level conversion, this table may come in handy:

Sigma level (with 1.5σ shift)

DPMO

Yield, defect-free

691,462

30.850%

308,538

69.146%

66,807

93.319%

6,210

99.380%

233

99.977%

3.4

99.99966%

0.019

99.999998%

Alternatively, our DPMO calculator has a in-built feature that calculates both the DPMO and the sigma level using a 1.5σ shift. Check it out!

## An example on how to use the DPMO calculator

We've created this DPMO calculator to help you do the calculations in the blink of an eye!

1. Enter the number of defects that occurred in your sample. Let's say that you've found 17 errors in the spreadsheets.
2. Input the number of units in your sample. Let's assume that these 17 defects appeared in 20,000 spreadsheets that were checked (not by hand we hope!).
3. Fill in the defect opportunities field. Every spreadsheet has 75 fields, so there are 75 opportunities for error.
4. The calculator shows the result: DPMO = 11.333! You don't need to rack your brain anymore on how to calculate the DPMO, yay!

Additionally, the tool found out the sigma level of this process: 5.74. Experiment with the values and check out how many defects you could have to fulfill the six sigma rule.

Don't forget to look through our Advanced mode, where you'll find DPU and PPM calculated for you.

Hanna Pamuła, PhD
# of Defects
# of Units
# Defect opportunities
/ unit
Defects per Million Opportunities
DPMO
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