How many parts per million defects will occur when the process is at a Six Sigma level of quality assuming a process shift of 1.5 sigma to one of the specification limits?

The DPMO formula is pretty straightforward:

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:

  • 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!

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.


Quality Glossary Definition: Six Sigma

Six Sigma is a method that provides organizations tools to improve the capability of their business processes. This increase in performance and decrease in process variation helps lead to defect reduction and improvement in profits, employee morale, and quality of products or services.

"Six Sigma quality" is a term generally used to indicate a process is well controlled (within process limits ±3s from the center line in a control chart, and requirements/tolerance limits ±6s from the center line).

  • Differing opinions on the definition of Six Sigma
  • What is lean Six Sigma?
  • Integrating lean and Six Sigma
  • Implementing Six Sigma
  • Six Sigma resources
  • Six Sigma certifications

Differing opinions on the definition of Six Sigma

The differing definitions below have been proposed for Six Sigma, but they all share some common threads:

  • The use of teams that are assigned well-defined projects that have a direct impact on the organization's bottom line.
  • Training in "statistical thinking" at all levels and providing key people with extensive training in advanced statistics and project management. These key people are designated "Black Belts." Review the different Six Sigma belts, levels, and roles.
  • Emphasis on the DMAIC approach to problem solving: define, measure, analyze, improve, and control.
  • A management environment that supports these initiatives as a business strategy.

Philosophy: The philosophical perspective of Six Sigma views all work as processes that can be defined, measured, analyzed, improved, and controlled. Processes require inputs (x) and produce outputs (y). If you control the inputs, you will control the outputs. This is generally expressed as y = f(x).

Set of tools: The Six Sigma expert uses qualitative and quantitative techniques or tools to drive process improvement. Such tools include statistical process control (SPC), control charts, failure mode and effects analysis (FMEA), and process mapping. Six Sigma professionals do not totally agree as to exactly which tools constitute the set.

Methodology: This view of Six Sigma recognizes the underlying and rigorous DMAIC approach. DMAIC defines the steps a Six Sigma practitioner is expected to follow, starting with identifying the problem and ending with the implementation of long-lasting solutions. While DMAIC is not the only Six Sigma methodology in use, it is certainly the most widely adopted and recognized.

Metrics: In simple terms, Six Sigma quality performance means 3.4 defects per million opportunities (accounting for a 1.5-sigma shift in the mean).


Six Sigma Quality Performance

What is lean Six Sigma?

Six Sigma focuses on reducing process variation and enhancing process control, whereas lean drives out waste (non-value added processes and procedures) and promotes work standardization and flow. The distinction between Six Sigma and lean has blurred, with the term "lean Six Sigma" being used more and more often because process improvement requires aspects of both approaches to attain positive results.

Lean Six Sigma is a fact-based, data-driven philosophy of improvement that values defect prevention over defect detection. It drives customer satisfaction and bottom-line results by reducing variation, waste, and cycle time, while promoting the use of work standardization and flow, thereby creating a competitive advantage. It applies anywhere variation and waste exist, and every employee should be involved.

Six Sigma on ASQTV™


Integrating lean and Six Sigma

Lean and Six Sigma both provide customers with the best possible quality, cost, delivery, and a newer attribute, nimbleness. There is a great deal of overlap between the two disciplines; however, they both approach their common purpose from slightly different angles:

• Lean focuses on waste reduction, whereas Six Sigma emphasizes variation reduction.

• Lean achieves its goals by using less technical tools such as kaizen, workplace organization, and visual controls, whereas Six Sigma tends to use statistical data analysis, design of experiments, and hypothesis testing.

Often successful implementations begin with the lean approach, making the workplace as efficient and effective as possible, reducing waste, and using value stream maps to improve understanding and throughput. If process problems remain, more technical Six Sigma statistical tools may then be applied.

Implementing Six Sigma

Six Sigma implementation strategies can vary significantly between organizations, depending on their distinct culture and strategic business goals. After deciding to implement Six Sigma, an organization has two basic options:

  1. Implement a Six Sigma program or initiative
  2. Create a Six Sigma infrastructure

Option 1: Implement a Six Sigma Program or Initiative

With this approach, certain employees (practitioners) are taught the statistical tools from time to time and asked to apply a tool on the job when needed. The practitioners might then consult a statistician if they need help. Successes within an organization might occur; however, these successes do not build upon each other to encourage additional and better use of the tools and overall methodology.

When organizations implement Six Sigma as a program or initiative, it often appears that they only have added, in an unstructured fashion, a few new tools to their toolbox through training classes. One extension of this approach is to apply the tools as needed to assigned projects. It’s important to note, however, that the selection, management, and execution of projects are not typically an integral part of the organization.

Implementing a Six Sigma program or initiative can present unique challenges. Because these projects are often created at a low level within the organization, they may not have buy-in from upper management, which may lead to resistance from other groups affected by the initiative. In addition, there typically is no one assigned to champion projects across organizational boundaries and facilitate change.

A Six Sigma program or initiative does not usually create an infrastructure that leads to bottom-line benefits through projects tied to the strategic goals of the organization. Therefore, it may not capture the buy-in necessary to reap a large return on the investment in training.

For true success, executive-level support and management buy-in is necessary. This can help lead to the application of statistical tools and other Six Sigma methodologies across organizational boundaries.

Option 2: Create a Six Sigma Infrastructure

Instead of focusing on the individual tools, it is best when Six Sigma training provides a process-oriented approach that teaches practitioners a methodology to select the right tool, at the right time, for a predefined project. Six Sigma training for practitioners (Black Belts) using this approach typically consists of four weeks of instruction over four months, where students work on their projects during the three weeks between sessions.

Deploying Six Sigma as a business strategy through projects instead of tools is the more effective way to benefit from the time and money invested in Six Sigma training.

Consider the following Six Sigma deployment benefits via projects that have executive management support:

  • Offers bigger impact through projects tied to bottom-line results
  • Utilizes the tools in a more focused and productive way
  • Provides a process/strategy for project management that can be studied and improved
  • Increases communications between management and practitioners via project presentations
  • Facilitates the detailed understanding of critical business processes
  • Gives employees and management views of how statistical tools can be of significant value to organizations
  • Allows Black Belts to receive feedback on their project approach during training
  • Deploys Six Sigma with a closed-loop approach, creating time for auditing and incorporating lessons learned into an overall business strategy

A project-based approach relies heavily on a sound project selection process. Projects should be selected that meet the goals of an organization’s business strategy. Six Sigma can then be utilized as a road map to effectively meet those goals.

Initially, companies might have projects that are too large or perhaps are not chosen because of their strategic impact to the bottom line. Frustration with the first set of projects can be vital experience that motivates improvement in the second phase.

Six Sigma is a long-term commitment. Treating deployment as a process allows objective analysis of all aspects of the process, including project selection and scoping. Utilizing lessons learned and incorporating them into subsequent waves of an implementation plan creates a closed feedback loop and real dramatic bottom-line benefits if the organization invests the time and executive energy necessary to implement Six Sigma as a business strategy!

Six Sigma Resources

You can also search articles, case studies, and publications for Six Sigma resources.

Books

The Certified Six Sigma Master Black Belt Handbook

The Certified Six Sigma Black Belt Handbook

The ASQ CSSBB Study Guide

The Certified Six Sigma Green Belt Handbook

The ASQ CSSGB Study Guide

The Certified Six Sigma Yellow Belt Handbook

The ASQ CSSYB Study Guide

Case Studies

Pitch Perfect (Lean & Six Sigma Review) Learning the ins and outs of capability analysis by examining a baseball pitcher’s performance.

The More The Merrier (Six Sigma Forum Magazine) It is well known in the world of quality that Lean and Six Sigma (LSS) initiatives are not likely to succeed or be implemented without the support of high-level management. In three case studies, this concept is demonstrated using real examples.

Save Your Steps (Six Sigma Forum Magazine) Linde Group, a gases and engineering organization, conducted process makeovers at several North American facilities to improve process efficiency using lean and Six Sigma principles.

Articles

Lean Six Sigma Deployment And Maturity Models: A Critical Review (Quality Management Journal) The study signals an important need for scientific insight in the process of implementing approaches such as LSS, and for a more effective translation of established theory in organizational development to forms practitioners can use.

Human Side Of Six Sigma: Positive Feedback (Six Sigma Forum Magazine) This article explores the idea that for a lean Six Sigma project to be successful, team members and others involved in the process must be vigilant about giving positive feedback when commendable behavior is observed.

Webcasts

Lean Six Sigma in the Age of Artificial Intelligence Michael L. George, Sr., CEO of AI Technologies, using practical manufacturing examples and a case study, explains what AI is, why it’s important for analyzing Big Data and shedding light on Dark Data, and how it can be applied to your Lean Six Sigma and continuous improvement efforts to give you a substantial competitive advantage.

The Lean & Six Sigma Review Webcast Incoming editor, Dr. Jami Kovach, walks us through a brief overview of the new Lean & Six Sigma Review, highlighting new columns, features, FAQs, and hot topics.

Courses

Certified Six Sigma Black Belt Certification Preparation

Certified Six Sigma Green Belt Certification Preparation

Six Sigma Yellow Belt Certification Preparation

Certified Six Sigma Black Belt Question Bank

Certified Six Sigma Green Belt Question Bank

Certified Six Sigma Yellow Belt Question Bank

Lean Six Sigma Black Belt E-Learning

Lean Six Sigma Green Belt E-Learning

Lean Six Sigma Yellow Belt

Six Sigma Certifications

Six Sigma projects can bring benefits, including increased organizational efficiency, improved customer satisfaction, reduced costs, increased revenues, and more. The Certified Six Sigma Black Belt Handbook reports that many Six Sigma Black Belts "manage four projects per year for a total of $500,000-$5,000,000 in contributions to the company’s bottom line."

Certified Master Black Belt (CMBB)

The ASQ Master Black Belt certification is a mark of career excellence and aimed at individuals who possess exceptional expertise and knowledge of current industry practice. Master black belts have outstanding leadership ability, are innovative, and demonstrate a strong commitment to the practice and advancement of quality and improvement.

Certified Six Sigma Black Belt (CSSBB)

The Certified Six Sigma Black Belt is a professional who can explain Six Sigma philosophies and principles, including supporting systems and tools. A Black Belt should demonstrate team leadership, understand team dynamics and assign team member roles and responsibilities. Black belts have a thorough understanding of all aspects of the DMAIC model in accordance with Six Sigma principles. They have basic knowledge of lean enterprise concepts, are able to identify non-value-added elements and activities and are able to use specific tools.

Certified Six Sigma Green Belt (CSSGB)

The Certified Six Sigma Green Belt operates in support of or under the supervision of a Six Sigma Black Belt, analyzes and solves quality problems and is involved in quality improvement projects. A Green Belt is someone with at least three years of work experience who wants to demonstrate his or her knowledge of Six Sigma tools and processes.

Certified Six Sigma Yellow Belt (CSSYB)

The Certified Six Sigma Yellow Belt is aimed at those new to the world of Six Sigma who have a small role, interest, or need to develop foundational knowledge. Yellow belts can be entry level employees who seek to improve their world or executive champions who require an overview of Six Sigma and DMAIC.

How many defects per million opportunities occur at the Six Sigma level?

Six Sigma is a statistical term used to measure the number of defects that processes create. The term implies high-quality performance because a process performing at a Six Sigma level allows only 3.4 defects per one 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.

How many errors are there in a million in Six Sigma?

Hence the widely accepted definition of a six sigma process is a process that produces 3.4 defective parts per million opportunities (DPMO).

What is a 1.5 sigma shift?

If left to its own devices (ie. without controls in place) any system will tend to slowly revert to a lower level of performance. This is known as the 1.5 sigma shift. In other words, the centerline and process performance will be change by 1.5 sigma to the negative.