The DPMO formula is pretty straightforward: Show
DPMO = 1,000,000 * defects / (units * defect opportunities) where: defects - number of defects; units - number of units; and defect_opportunities - 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 defected in five different ways:
Moreover, when 10,000 pairs of jeans were sampled, we found 11 defects. So how to calculate DPMO? Use the DPMO formula defined above! defects is the number of defects found in a sample, so it's 11; units - for this example, it's 10,000 pairs of jeans; and defect opportunities - the number of defects opportunities per unit, so in our case, it's 5. DPMO = 1,000,000 * 11 / (10,000 * 5) = 220 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. Six Sigma is a framework to make an organization more competitive by focusing on being effective and efficient. It is a systematic problem solving approach that is centered around defect elimination and variation reduction which leads to process improvement.
Six sigma is a continuous improvement process, with focus on:
 Six sigma refers to the methodology and practice of focusing on developing and delivering products/services that perform at high standards. It is a Quality philosophy and a management technique. It is not a standard or certification or another metric like a percentage. Six Sigma’s Basic PremisesThe basic purpose of six sigma is to delight the customers; this can be achieved by delivering the quality product. Hence it is fundamentally focuses on variation reduction and waste elimination. This leads to increased efficiency. Variation is the range of difference between the statistical mean and all data points that are used to calculate the mean. In other words, the extent to which process performance varies around the mean. Waste or defects are measurable product characteristics that do not meet a customer’s requirements (i.e. defective products). In other words, any process performance outside of defined specification is considered waste or a defect. Six sigma methodologies are used to identify and eliminate the root cause of defects or minimizing the process variation (using statistical or process analysis methods) and also the costs that are associated with it. Using a manufacturing example, let’s say XYZ factory produces widgets. The widgets are all supposed to be a certain size, shape, and weight. Randomly sampled output discover that out of every 1,000 widgets fifty are flawed (e.g. wrong size, shape, or weight). To correct this, the factory uses Six Sigma to determine what’s causing the variation/defects and works to reduce them to a six-sigma level. Six Sigma’s Approach to Problem SolvingSix Sigma was originally coined by Bill Smith. He was an American engineer and also known as father of Six Sigma. It was first implemented at Motorola in the year 1986 as a general approach to measuring quality in business performance terms. Further, it became popular management approach at GE with Jack Welch in early 1990s’. General Electric reported tangible benefits of $2.5 billion per year due to Six Sigma initiatives and made it an organization-wide strategy. Now it became a project-driven approach for process improvements that follows the five-step process also called DMAIC cycle. (Also see: History of Continuous Improvement). Overview Video
What is a Six Sigma Level?Six Sigma derives from the normal or bell curve in statistics, where each interval indicates one sigma or one standard deviation. Moreover sigma is a statistical term that refers to the standard deviation of a process around its mean. In a normally distributed process, 99.73% of measurement will fall within ±3σ and 99.99932% will fall within ±4.5σ. For a process, the sigma capability is a metric that indicates how well that process is performing. Hence the higher the sigma value, the better the process. The 68-95-99.7 rule, also known as an empirical rule, is used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of one, two, and three standard deviations respectively. A six sigma capable process will have Cp >= 2.0, Cpk >= 2.0 and DPMO = 3.4 Where Does the 6 and Sigma come from?Let’s cover the Sigma first. Sigma denoted by symbol σ (a Greek letter) represents the standard deviation of a population. Primarily it characterizes the dispersion (or ‘spread’) of a set of data values with respect to mean. A standard deviation is a value you have to calculate and is dependent on the data your process generates. Now let’s cover the 6. The six refers to how many standard deviations away from the mean we set the specification limits in a 6 sigma process. Now let’s put them together for 6 Sigma: A Six Sigma process has a specification limit which is 6 times its sigma (standard deviation) away from its mean. The 6 refers to the ability to fit the good outputs of the process to fit within 6 standard deviations (or sigmas). Another way to say it is that only 3.4 defects per every million opportunities fall outside the specification limits that we’ve set at 6 sigmas away from center. You can also think of it as a level of excellence that can be quantified and easily compared against other processes. If you only get 3.4 defects per million out of your process, i.e. a 99.9999998% success rate, you have a 6 sigma process. Other Sigma LevelsFor each standard deviation you are away from the mean (0 in the graphic above) your process gets more and more defect-free. Let’s look at a 3 Sigma process for example. In a normally distributed process if mean ±3σ range of output is between USL and LSL then around 99.73% of the points of the output will be non-defective. The Primary Goals are to ImproveSix Sigma is a data-driven methodology that contains statistical tools and techniques to define the problem and evaluate each step of a process. In addition, it provides ways to improve efficiencies in a business structure, improve the quality of the organization processes and increase the bottom-line profit. Three Key Elements of Six Sigma
Philosophy & MethodologySix Sigma is a result-oriented, continuous improvement process that includes active involvement from senior management. Continuous improvement activities in an organization ensure to identify and solve the problems as and when they occur. Most of the modern quality improvement models such as sampling techniques, control charts, process capability and DOE have been influenced by the theory of continuous improvement. Why Use Six Sigma?Organizations face new challenges every day like rising costs, customer issues, an increase in defect rate etc. In fact, global competition had made it imperative to provide near-perfect quality at low cost to keep customers delighted and make organizations viable in the market place. Some of the key benefits from Six Sigma implementation are that it:
Six Sigma MethodologiesSix Sigma provides better value to customers, employees and all the stake holders in an organization. Additionally, it is a business initiative which improves quality, productivity and reduces cost. DMAICOne of the basic tools in Six Sigma is the use of the DMAIC methodology. (Also see DMAIC Overview). Particularly, DMAIC is a logical framework that helps you think through and plan improvements to a process in pursuit of achieving a Six Sigma level of excellence. In other words, it is a data-driven quality strategy for improving the process. There are five phases in DMAIC method. They are as follow:
Six Sigma teams define the problem, work with sponsors and stakeholders, and also deliver results that will be apprised at phase-gate meetings called DMAIC Tollgate Reviews. DMADVDMADV is one aspect of Design for Six Sigma (DFSS). In fact this was evolved from the continuous quality improvement and Six Sigma approach to reduce variation. However, the aim of DMADV is to create new processes and new products or services.
Six Sigma Frequently Asked QuestionsWhat is the concept of Six Sigma?Six sigma refers to the methodology and practice of focusing on developing and delivering products/services that perform at high standards. It is a Quality philosophy and a management technique. It is a systematic problem solving approach that is centered around defect elimination and variation reduction which leads to process improvement. What are the Five steps of six sigma?
Why is it called six sigma?Sigma denoted by symbol σ (a Greek letter) represents the standard deviation of a population. Primarily it characterizes the dispersion (or ‘spread’) of a set of data values with respect to mean. A Six Sigma process has a specification limit which is 6 times its sigma (standard deviation) away from its mean. In other words, the 6 refers to the ability to fit the good outputs of the process to fit within 6 standard deviations (or sigmas). Another way to say it is that only 3.4 defects per every million opportunities fall outside the specification limits that we’ve set at 6 sigmas away from center. What is an example of Six Sigma?Six Sigma means producing a defect free product 99.9996% of the time, allowing only 3.4 defects per million opportunities. Also, refer few examples of Six sigma implementation:
What are 6 Sigma tools?
Which companies are using Six Sigma?Six Sigma was originally coined by Bill Smith. He was an American engineer and also known as father of Six Sigma. While, this was first implemented at Motorola in the year 1986 as a general approach to measuring quality in business performance terms. Also see the companies that have embraced Six Sigma: Motorola, General Electric, Dupont, Sony, Kodak, Boeing, Johnson & Johnson, 3M, Amazon, Atos, Autoliv, BAE Systems, Bank of America, Becton Dickinson, Bechtel etc., Amusing: How this conversation usually goes:The Basics VideosAdditional ArticlesSix Sigma Tools Walkthrough Roles & Responsibilities Six Sigma Black Belt Certification Questions:Question: The primary reason that most companies implement six sigma is to: (Taken from ASQ sample Black Belt exam.) (A)
reduce defects Answer: How many defects per million opportunities does Six Sigma aim for?Six Sigma is often wrongly defined as "3.4 defects per million products," when in fact, Six Sigma is actually defined as 3.4 defects per million opportunities (DPMO). Six Sigma's goal is to improve all processes to that level or better.
How many defects per million opportunities are there?It's also possible to translate DPMO to a Six Sigma level. The goal is to reach 3.4 defects per 1 million opportunities.
What is meaning of the 3.4 defects per million in Six Sigma?Understanding Six Sigma
This means that a process is considered to be efficient if it produces less than 3.4 defects per one million chances. A defect is anything produced outside of consumer satisfaction. It is also a training and certification program, which teaches the core principles of Six Sigma.
What is the error rate DPMO for a process operating at the Six Sigma level?A six sigma level of performance has 3.4 defects per million opportunities (3.4 DPMO).
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