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Sigma level complexity with Attribute data

Vishwadeep Khatri
Message added by Chitra Singh



Defective is a product or service that has one or more defects in it. Defective items are rejected by the customers




Defect is a feature or functionality in a product or service that fails to meet the customer requirements. Also known as errors, there can be multiple defects in a product or service




Defects Per Million Opportunities (DPMO) is a metric used to assess the performance levels of a process. It is the number of defects (or errors) made per total number of opportunities to make a defect (i.e. number of units times the number of opportunity per unit) normalized to one million




Yield is defined as the ratio of the total units delivered defect free to the customer over the total number of units that entered the system.


An application-oriented question on the topic along with responses can be seen below. The best answer was provided by     
Steve Cropp on 23rd May  2019.


Applause for all the respondents- Steve Cropp, Rohit Kumar Singh, Chander Mohan Dhingra, Rima, Ferdoz Yunis, Sreyash Sangam. 




Q. 161  Explain why some people prefer DPMO method and others prefer Defectives (Yield) method to calculate process performance. When would your prefer one over the other? 


Use calculator for DPMO at https://www.benchmarksixsigma.com/calculators/sigma-level-calculator-discrete-data-defects/ and calculator for Defectives at https://www.benchmarksixsigma.com/calculators/sigma-level-calculator-discrete-data-defectives/


Note for website visitors - Two questions are asked every week on this platform. One on Tuesday and the other on Friday.


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Interesting question.  My initial reaction is that when I was taught Six Sigma 20+ years ago by MBBs with a Motorola>Allied Signal or GE pedigree, they were very insistent that DPMO and RTY were the only acceptable ways to measure process performance with attribute data.  I did not completely agree, and still don't. 


I would use yield data for simple products of moderate to low value, since you don't want the burden of your defect tracking system to be a large percentage of the product cost.  You do capture data that can be turned into DPMO in your lower level cause categorization for defectives, i.e. a Pareto analysis.


I would use DPMO or DPU for more complex products, since yield would tend to summarize performance to a level that would be difficult to take action on.  For a service process, I would use DPMO, since a defect in this case is an unsatisfied (not returning) customer, so you would want to measure multiple points to satisfy or dissatisfy that same customer throughout the interaction to pinpoint areas that need attention.


Regardless of which method you use, identifying opportunities for improvement needs to be the primary focus, with comparing like processes important but not the most important

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Defective is binary. Yes or No hence it follow Binomial Distribution. 

Defect can be more in count or equal to defective count depend on the operation definition, Defect follows Poisson Distribution.

For example if i do a project on reducing number of defective invoice  , then one parameter like wrong currency is enough to reject the invoice.


However if i define invoice number, invoice amount, invoice currency , invoice approver, po number these 5 as criteria of defect count any one parameter go wrong then my invoice stands defective.


Based on this we use DPMO for defect and Defective yield concept.

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Defects Per Million Opportunities (DPMO) can be considered as the number of defects detected in a million opportunities or units. It is a measure of process performance on the whole.

Defects are the number of non-conformities or type of errors in one unit. For instance, in a service industry, Health Insurance claim form is being filled in by the outsourcing data entry processor and sent back to the quality analyst. One form can have different type of errors, like typo error, error of omission, comprehensive error and error of commission. The number of defects found in one claim form will make the form as defective.

Most of the service industry prefer to calculate DPMO rather than Defective (Yield) and Product-based industry prefers Defective (yield). The reason being that in a manufacturing company, sample units quality decides the whole performance level of the product. A defective product cannot yield benefits.

As per Sigma Level Calculator (Discrete Data – Defects) – DPMO

If 100 Sample units are audited and the number of known opportunities per unit is 4 and 10 defects are found in the audited sample. DPMO is 25000, Zst = 3.46, Zlt = 1.96.

If the same variables are considered and calculated on Sigma Level Calculator (Discrete Date – Defectives)

If 100 Sample units are audited and the number of defective units from the audited sample are 10. DPMO is 100000, Zst = 2.5, Zlt = 1

At the production stage, the six sigma level of the product is judged on the basis of Defectives (Yield) or Throughput (Yield), so that a better output is generated. And when the same product enters in the market for sale, the customer service decides the value of the product. Hence, the DPMO is considered over Defectives (yield) in order to generate better sales output.

It can be concluded that, both DPMO and Defectives (Yield) methods hold their own importance for the process performance and better Six Sigma level and improve industry standards.

SS 24th May.docx

SS 24th May.docx

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DPMO and DPU are both used to calculate and measure the results by analyzing from the available data sets.

DPMO - Defect per million opportunities are used in scenarios when the process contains uncountable errors or defects. Defects per unit (DPU) means the data is attribute data when the classification is in terms of binary i.e, yes/no, good/bad etc.

Former is used in cases of measurement data wherein the classification is binary like satisfied . not satisfied. These include the examples like conducting surveys of employee satisfaction, saying the quality attribute of an item in terms of good/bad, high/low etc. These can also be used in deciding the binary classification of an object like pass/fail etc.

However in the continuous attribute data which can not be counted like temperature, pressure, height, measurements, etc.In such scenarios we use DPO or Defects per unit is legitimate and most rationale in calculating the performance in such cases. These can be applicable in pharmaceutical, aeronautical, automobile and other industries wherein we are dealing with the continuous data.


In general, continuous data is preferred over the discrete data because they are most efficient as have to deal with fewer data points.


Therefore the usage and applicability of DPU or DPMO method depends on the pattern of data we are dealing with and the end point applicability. 

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Attribute Data means Data which is categoric (i.e., Colors, gender) or Count (I.e., No of Tickets, no of issues).


There are two term Defects and Defective use for Attribute Data.


Defects refer to error which fails to meet customer requirement and Defective refers to one or more defects on which customer can rejected that product.


People are using DPMO for Defects part and Yield for Defective parts.


DPMO refers to defect per million opportunities which is number of defects made for total number of opportunities available for defects


Yield is referred to the ratio of total number of units delivered defect free to the customer out of total number of units proceeds. 



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