Defining defect

Q: Is there a standard method for determining the number of opportunities that exist when computing defects per million opportunities (DPMO)?

A: To use the DPMO metric effectively, it is important to answer the following questions:

What is a defect? I have always lived by the principle that anything not done correctly the first time is a defect. Of course, this means understanding what it takes to do it right the first time and specifying those conditions in advance. It also means holding true to these definitions after they have been established.

For example, if a unit met any of the criteria for being declared defective but was later found to be usable by a material review board (MRB), the classification as a defect should remain intact. Some organizations are reluctant to embrace this position because it adversely affects their quality numbers or because they conclude that since the unit is usable, it must not be defective. A defect might not affect usability.

How can a defect occur? To address this question, many organizations have compiled a list of error families and error types within those families. Such a list should be complete in identifying all possible error types (collectively exhaustive). Also, each error type should be independent of all other error types (mutually exclusive). This allows you to recognize the occurrence of multiple defects on any given unit.

Avoid the temptation to exclude known error types because they happen infrequently. In other words, if an error family or error type is known to occur, include it on your list. In addition, it is useful to have an error family or error type deemed "other" because you might lack the foresight or wisdom to define everything in advance.

As you develop your list of defect types, it is useful to define them in pairs (too high or too low, too long or too short), particularly when physical, mechanical or electrical characteristics are under consideration. Use Table 1 as a starting point for such a list.

Table 1

Where can a defect occur? A defect can occur during a process when the outcome is not the outcome specified in advance.

Suppose an operator is soldering parts to a circuit card assembly precisely at the prescribed locations, according to the assembly instructions and drawing. The instructions specifically indicate that no parts should be soldered anywhere on the board other than where specified (you are specifying in advance the conditions under which a defect can occur). There are 100 such parts to be soldered, and the assembly operator has soldered each part correctly.

During the soldering process, the operator slipped and applied solder on the card in an area where no soldering was to be placed. Fortunately, the additional solder did not compromise the usability of the completed circuit card assembly.

Did a defect occur? Yes, because solder was applied to a location where it should not have been applied as specified in the assembly instructions and drawing. Perhaps the card can be reworked and the solder removed without destroying the circuit card assembly. A defect did occur, however, and it should remain in the company’s quality system.

So, to answer the question of whether there is a standard method for computing DPMO, the answer is yes and no. Yes, because the computational method of determining the number of DPMO is standard. No, because the method for defi ning and counting defects depends on each individual organization and that organization’s ability and willingness to create accurate and meaningful defect data.

T.M. Kubiak, author and consultant
Weddington, NC

Online Table 1

Online Table 2

Overcoming resistance to change

Q: My senior managers have assigned me to lead a cross-company team that will implement a major quality initiative at my company. I recognize that this initiative will involve significant change. How can I overcome resistance to change?

A: Overcoming resistance to change can be one of the most difficult assignments you can take on. There are several approaches that can be effective, depending on your situation and environment.

In selecting your implementation team, try to include people from across the organization. These people will be important in communicating what potential change issues exist in their areas and the progress of your team in those areas.

Early in the process, identify all potential barriers to change with your team and the actions you can take to address them. A force field diagram can be a useful tool.

Identify the influencers in your organization. These people’s opinions are respected by large groups of employees in the organization. These influencers are usually managers, but they don’t have to be. Meet with the influencers to understand how they view the change. Work toward gaining their support by showing how the change will benefit them and their group.

Remember that the most damaging people to your effort are not the ones who tell you they don’t support the change, but rather those who tell you they support the change while telling their circle of influence they don’t support the change.

Clearly communicate the change and how it will affect people in the company. Be sure that senior leaders are part of the communication process. Communicate early and often. By doing so, you’ll keep the rumor mill to a minimum and help reduce fear of the unknown. Leverage your team members and any existing communication vehicles (for example, meetings or the company newsletter) to disseminate your message.

Listen to concerns and show people you are addressing their concerns as best you can. Many times, change involves losing something, even if it’s just "the way we’ve always done things around here." Acknowledge the loss and show how the changes will benefit the people in your company.

Develop support mechanisms for the change and show people how to access those mechanisms. This will help people make adjustments and reduce anxiety.

Maintain flexibility. Be willing to make course adjustments based on your team’s observations and feedback.

Ken Cogan, senior manager of performance management, Intelstat
Columbia, MD

Sample equation

Q: Everyone knows the old standby sampling plan of "square root of (N + 1)" to determine a sample size for discrete numbers of materials. What is the exact source or rationale behind this equation?

Carolyn Tomlinson
Greenville, NC

A: The rule dates back to the 1920s as an easy-to-remember sampling scheme for agricultural regulatory inspectors. It was semiformalized in an unpublished report by the Assn. of Official Agricultural Chemists (now AOAC) in 1927.

As common as the use was, most quality personnel believed that the scheme was statistically questionable. It does meet the definition of a sampling plan in that it provides a sample size, an accept value (0) and a reject value (1). Even though the plan has been questioned, it was adopted by many international and federal regulatory agencies, including the United Nations, the World Health Organization and the Food and Drug Administration.

Hewa Sarandasa addressed this issue in an article published in Pharmaceutical Technology: "The accuracy of the 95% confidence probability statement for mean was compared for three distributions for sample size obtained from the square root of N plus one rule with the Edgeworth approximation derived sample size. Results showed that the sample size obtained from this rule is not even enough to declare less than 20% of defectives in a moderate size population with a high degree of confidence. Therefore, the author concludes this rule should not be used to select a sampling plan to infer a population defective rate."1


  1. Hewa Sarandasa, "The Square Root of N Plus One Sampling Rule: How Much Confidence Do We Have?" Pharmaceutical Technolgy, Vol. 27, No. 5, pp. 50-62.


  1. Keith Borland, "The Fallacy of the Square Root Sampling Rule," Journal of the American Pharmaceutical Association, Vol. 39, No. 7, pp. 373-377.
  2. Wayne A. Taylor, "Acceptance Sampling Questions," www.variation.com/FAQs.html (case sensitive).

I. Elaine Allen, associate professor of statistics
Babson College, Wellesley, MA

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