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# DPMO

DPMO

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.

An application-oriented question on the topic along with responses can be seen below. The best answer was provided on 16th July 2019 by Natwar Lal.

Applause for the respondents- Manjula Pujar, Vastupal Vashisth, Aparna MS, Amlan Dutt & Natwar Lal

Also review the answer provided by Mr Venugopal R, Benchmark Six Sigma's in-house expert.

## Question

Q﻿﻿. 176  What could be the possible pitfalls to using DPMO as a metric? You may refer to the DPMO calculator at https://www.benchmarksixsigma.com/calculators/sigma-level-calculator-discrete-data-defects/

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## Recommended Posts

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Defects Per Million Opportunities (DPMO) is a very powerful metric in understanding the performance of the process. However, following are the pitfalls while using DPMO

1. Calculation of DPMO makes sense only if we have Discrete (Attribute) data. It is difficult to imagine the number of opportunities for a Continuous (Variable) data. E.g. if we are monitoring temperature with an USL of 30. Then what is an opportunity? Defect is easy to tell (temp. going above 30) but determining the opportunity is difficult. Should be each second / minute etc. It is for this reason that for Continuous Data we first calculate the Sigma Level which is then converted to DPMO

2. Even for Discrete Data, DPMO is a metric that could portray a false picture about the process performance. Let's take an example.

Number of Units made = 1000

Opportunities for error (OFE) = 10

Total # of Defects = 124

Total # of Defectives = 36 (i.e. all these 124 defects were found in 36 units only).

Now, one could calculate the following metrics

Defects Per Unit (DPU) = 124/1000 = 0.124

Defective % = 36/1000*100= 3.6%

Defects Per Million Opportunities (DPMO) = 124 / (1000*10)*1000000 = 12400

Converting all these numbers to Sigma Level

DPU = 0.124; Z (long term) = 1.19

Defective % = 3.6%; Z (long term) = 1.80

DPMO = 12400; Z (long term) = 2.24

It is evident from the above example that for the same process and same numbers, the DPMO provides the best Sigma Level which might be misleading. This is the primary reason that vendor always wants to calculate quality in terms of DPMO while the client always insists on either DPU or Defective %.

3. For DPMO calculation, all defects have same importance. This sometimes becomes a challenge in service industries where some of the defects are considered more critical than others

4. DPMO does not give any indication on the number of units which have defects. It is quite likely that most of the defects could be found in only a handful of units while on the other hand it could also mean that same kind of defect could happen in multiple units. E.g. in my example 124 defects happened only in 36 units. However, these 124 could also happen in 124 units (1 defect in each of the 124 units).

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Benchmark Six Sigma Expert View by Venugopal R

Deciding and defining the “Opportunities” has been a highly debated topic while practicing DPMO. Let me share a couple of related points that I have come across.

Let’s take an example of insurance claim forms being processed. Assume that the form has 20 fields of information. Let’s say each field represents an opportunity for a defect. When 100 such forms are processed, the total number of defect opportunities are 2000. Now if we detect 50 defects after processing 100 forms, the defect per opportunity is the total number of defects divided by the total number of opportunities = 50 / 2000. The DPMO will be 50 / 2000 * 1000000 = 25000.

For the same example, if someone wants to consider the defect opportunities for each field as ‘wrong entry’ and ‘no entry’, this would mean that the number of opportunities in 100 forms will be 20 * 2 * 100 = 4000. The DPMO in this case will work out to 12500.

Without a clear and common understanding and agreement on the definition of ‘Opportunities’, the DPMO data could be misleading and also prone for manipulations of the sigma values. It is important to define and have a uniform agreement on the applicable ‘Opportunities’, so that the baseline of comparison remains relevant.

Another point of importance is that many a time, customers prefer ‘Defective’ based metrics. viz. % of parts that did not conform, Proportion of forms that are error free, etc. In such situations, for a same level of Quality, the Defective based metric will appear to be very stringent compared to the DPMO based metric, since the denominator of the latter could be very large.

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Let’s see an example for DPMO calculation for cinder blocks evaluated on length, breadth and height.

 Item/Criteria Length Breadth Height Defective # of defects cinder block #1 correct incorrect correct yes 1 cinder block #2 correct incorrect incorrect yes 2 cinder block #3 incorrect correct correct yes 1 cinder block #4 correct correct correct no 0 cinder block #5 correct correct correct no 0 Opportunities/Unit 3 Total Units 5 Total Opportunities 15 Total Defects 4 DPO 0.266667 DPMO 266,667 Area to right 0.27 Area to left 0.73 Sigma level (with 1.5 sigma shift) 2.12

The flaws in using DPMO as metric are obvious, and listed below

1.       DPMO/Sigma Level are metrics which can theoretically be used to compare unlike products and processes

2.       Complexity of defects can’t be represented with DPMO; not all defects are equal sometimes

3.       Defect density is not captured by DPMO; i.e. a needle in haystack OR box of needles in haystack

4.       Back calculating DPMO from sigma level, if defects doesn’t follow a normal distribution then sigma level will be overestimated

5.       DPMO and PPM are not the same, except if # of opportunities for a defect/unit = 1. These are used interchangeable very often

6.       To make a jump from 2 to 3 sigma, DPMO has to be reduced by 241,731 while from 5 to 6 sigma is mere 230 (all with 1.5 sigma shifts). This shows that DPMO is sensitive to tails of distribution which is not always a nice thing. How? a Burr distribution with c=4.873717 and k=6.157568 perfectly resembles a standard normal distribution with mean = 0, sigma = 1, skewness = 0 and kurtosis = 3 but are very difference from DPMO standpoint. i.e. our realization of the ‘true’ distribution of a process will never coincide perfectly with the truth

7.       Chasing zero defects in accordance with DPMO, a good process can be made better but not perfect.

8.       Over relying on DPMO may give inappropriate approximations of Cpk

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DPMO

Part of six sigma is to calculate number of defects that process deliver.

These defects may calculated by

DPU -  Defects per Unit

DPO  -  Defects per opportunity

PPM  -  Parts per million opportunities

DPMO  - Defects per million opportunities

DPMO is ratio of number of defects in sample to total number of defects opportunities multiplied by 1 million

Calculation of DPMO

1.  First we should determine  size of sample  which should be small enough to manage and large enough to understand the problem

2. Determine number of defect or potential

defects or errors

3.Determine total number of defect opportunities

for sample size

4. Divide total defects by total opportunities

which gives and then multiply by 1 million to

get DPMO

Ex: If 2 defects found in sample of 100 units

where for each unit 5 areas are inspected

(NUMBER OF DEFECTS /NUMBER OF OPPORTUNITY FOR DEFECTS IN SAMPLE )*  1000000

2

DPMO= -------------- * 1000000

5*100

DPMO depends on opportunities in each unit. More number of opportunities may increase defects sometimes. If opportunities reduced to decrease the DPMO then there is failure in error free products or outputs.

If we fail to identify proper opportunity in unit may result into errors.which may effects to standards

Apart from production industry if I will take call centre example . Suppose there are 20+ non fatal parameters. If advisor's conversation goes well with customer and customer also satisfied by the answers and also customer got his query resolved. In call Advisor may have done mistakes like not using verbiage properly or not using name of customers as many times as quality parameters set. Here Defects may more in number though it is not effected to customer

Such impact will be case by case and also scenario based (can not consider for all

scenarios )

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Six Sigma:  A approach to process improvement which is defect oriented is very popular in many industries like: general Electric, Texas Instrument, Kodak and much more. The main objective to reduce output variability to increase customer satisfaction or we can say that this approach tries to keep specification limit more than six standard deviation in both direction. it means it wants lower defect level or below than 3.4 defects per million opportunities or 3.4 DPMO.

Now the question comes  when Six Sigma is not called Six Sigma and answer for this is that, when it is used as the Six Sigma Metric and there are various pitfalls of using as a Metric, which are given below;

1.  We use a term very often called opportunities to calculate DPMO, even DPMO full form is Defects per million opportunities and if the customer gives a weightage to the opportunities as per their importance , it will be very poor phenomenon for customer satisfaction because their are chances that metric can better and on the other hand customer satisfaction will be worse. for example we are improving one type of defect at the expense of any important one like someone is trying to eliminating 15 unimportant defect and while doing this he is leaving 5 important defects resulting overall improvement of 10 defects , leaving behind a poor customer satisfaction.

2. Every process has its own limitations and while calculating DPMO , it ignores process limitations and it consider only the gap between its existing performance and zero defects, so it fails to consider redesigning of the process.

3. You can play a game very easily with this unless until it is complemented by someone other. for example we are having two different group of experts and we have given them a job to identify the opportunities for the defect and we see that there will be  huge difference in their list.

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One of the possible pitfalls of using DPMO is its rigidity. The metric is not positively dynamic in nature when it would consider innovation or creativity.

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While Amlan, Vastupal and Natwarlal have given good answers, the winner this time is Natwarlal as he has picked the most important elements and explained them in the most lucid manner.

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