# How to calculate DPMO and Sigma

Six Sigma – iSixSigma Forums Old Forums General How to calculate DPMO and Sigma

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• #36256

J.J
Participant

If I have 50 units failed among 1,000 production units, what is the DPMO(defect per Miillion opportunity)? How to calculate it? and what is the sigma level?
Thank you.
J.J.

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#104091

Savage
Participant

J.J.,
How many opportunities for a defect per unit are there??

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#104092

J.J
Participant

Probably it has 3 failure modes. So, I will say 3.

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#104093

Savage
Participant

With 3 Opp, 50 defects (not defectives) and 1000 units, go here https://www.isixsigma.com/process-sigma-calculator/ and plug in the numbers.  Then you can look to the right pane and look at how the calculations are done.  Good luck

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#104097

Noname expert
Participant

First you have to define the opportunities  for defects,based on your experience ,without this figure it is not possible to calculate DPMO.Regards

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#104114

A.Singh
Participant

Dear JJ,
As everyone has said you need to know number of opportunity per unit before you calculate DPMO.
Still you can take down the formula to calculate it,
DPMO=(defects/opprtunities) * 1000000
defect = total defects in defective units
opportunities = total unit * number of opportunity per unit
For sigma calculation you can use following formula in MSExcel,
=Normsinv(1-defects/opportunities)+1.5
Cheers!
Ajit

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#104115

Charmed
Participant

Dear Ajit:
Very nicely explained. Just one last thing.
For sigma calculation you can use following formula in MSExcel,
=Normsinv(1-defects/opportunities)+1.5
Why calculate DPMO when it is not used at all in the sigma calculation? And, why add 1.5? Why not subtract it? Or, some other number other than 1.5 plus or minus? Cheers!

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#104116

Charmed
Participant

Dear JJ:
In the first post, you said 50 units failed out of 1000 units.  Then you mentioned three failure modes.  Let’s call the three modes A, B, and C.  Out of the 50 failed units, may be 20 are due to mode A, 15 due to mode B and 15 due to mode C.  The total failed units are 20+15+15 = 50.  Does this mean there are three opportunities? I am not so sure.  Or, a unit may have failed due to one or more modes prevalent at the same time.  Is this possible in your application?  For example, is there anything like AB failure mode, or BC failure, or AC failure, or ABC failure mode?   May be we need to think about this some more instead of just rushing to some kind of DPMO and Process Sigma calculation.  The math part is easy.  It is the rest that is difficult. That’s where we must invest some more time and effort.
Charmed I am by all this.

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#104117

Charmed
Participant

Dear JJ:
Just more clarification.  Matt had pointed out the need to distinguish between defective and defects. A defective part can have more than one defect. I am assuming that what you call failed “units” is the same as “defectives” that Matt is thinking about. The modes A, B, C (since you mentioned three failure modes) that I refer to are the ways in which a “unit” becomes “defective”, or has one or more “defects”.

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#104119

A.Singh
Participant

Dear Charmed,
1. DPMO is representative of capability as sigma is, the reason I mentioned it because it was part of JJ’s question.
2. 1.5 explains shift which difference in long term and short term capability, calculated over period of time and established emperically (Motorola was involved in the study). It is added to get the short term sigma. You can read about it in any six sigma book or site.
Also, just in case you are wondering why not subtract it, since you have just one sample for defect opportunity it can not give both ST and LT. The number you get out of normsinv gets treated as LT and 1.5 added to get LT.
(If you have more questions write to me on [email protected] )
Cheers!
Ajit

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#104123

Noname expert
Participant

Identical  with my question,you hit the point,thanks and regards.

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#104125

Charmed
Participant

Dear Ajit:
Let me refer again to the equation for Process Sigma calculation, kindly mentioned in your post.
For sigma calculation you can use following formula in MSExcel,
=Normsinv(1-defects/opportunities)+1.5
I asked, why calculate DPMO when it is not used at all in the sigma calculation? And, why add 1.5? Why not subtract it? Or, some other number other than 1.5 plus or minus?
Now, let me ask another question. (Thanks for the email ID.) Why use all this Normsinv and try to calculate Process Sigma and wonder about 1.5 sigma shift which has been beaten to death in our threads here. I have the value of DPMO, or DPO = defects/opportunities, or DPU = defects/units and then, I say, leave me alone and let my boss and I deal with this.  Forget all the rest. How about that for a new Smart Business Strategy (SBS), no SS, and no BS. Cheers.

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#104126

Charmed
Participant

Dear Ajit:
Just one more quick point. You said,
…..since you have just one sample for defect opportunity it can not give both ST and LT.
I didn’t interpret 50 failed units for 1000 units made in that fashion.  The number 50 here could be some kind of an “average” developed over a period of time. We don’t know.  It is not stated. Or, it could be just one data point, as you have interpreted.  But, I doubt that. Or, imagine this.  I break up 1000 units produced into smaller batches of 100 units or 50 units and then count the number of failed units.  The total is still 50.  Granted, I don’t have the details of what would happen.  What if JJ has such info and can post it for us. (JJ do you have it and can you post it if you do?). Now what?  We have to think about all these different possibilities before using the equation to find DPU, DPO, DPMO, or that Normsinv things with 1.5.
Sorry JJ.  I know you asked a simple question.  Hope all of this is still on topic for you.  Have a great weekend. Cheers.

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#104128

A. Singh
Participant

Dear Charmed,
The formulas were facts about how to calculate (straight answers to straight questions ). Now that since you are talking about should one calculate sigma after DPMO ?
My two penny – Ofcourse not! It does not make any sense to calculate sigma. Just DPMO and period.
As far as data is concerned I am not sure if 50 is defects or defectives. Worse situation will be if the opportunities are not even defined. So cant comment until I know what to use DPU, DPO or DPMO.
Hope this will suffice. Let me know.
Thnx
Ajit

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#104129

Charmed
Participant

Dear Ajit:
The formulas were facts about how to calculate (straight answers to straight questions ).  We are in agreement.  Some need help in this area, and that is what you have provided and I commend you for that.
Now that since you are talking about should one calculate sigma after DPMO ?  ……
My humble opinion is that beyond just blindly using mathematical formulae, we should think about what we are doing and why.  That is what I would do, if I was a teacher in a class and had students who were learning about Process Sigma and how to calculate it. JJ did not provide any details. Neither you or I know anything more.  But, we can certainly discuss the situation. I hope we soon hear from JJ. May be this helps clarify where I am coming from.

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#104130

A. Singh
Participant

Dear Charmed,
I am not surprised by your post, infact I was expecting it.
Your point is valid. I think it differently and I dont think so it is a problem as long as I make it clear what is being said.
If JJ has further clarifying question, would be happy to help.
Thnx
Ajit

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#104134

Charmed
Participant

Ajit, I agree fully. And on that happy note we have to end this, unless we learn some more. Regards.

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#104314

JJ
Participant

Thank you for all of your responses. In my case, we rejected the components if we found one defect, such like one demention out of specs, or leaking. either one could cause reject. Say, one kind of parts, 4 units rejected in April because of out of specs, and 5 units rejected in May because of leaking, and so on. How can I get DPMP for last 12 month? In our company, we calculate the DPMP for each month and use (4/total sample)*1000000. but I do not have the total number for a year to evaluate a certain supplier.

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#104323

JJ
Participant

Cont.
If 4 units rejected in April out of 3000 samples, DPMO is (4/3000)*1000000
If 23 units rejected in May out of 1200 samples, DPMO is (23/1200)*1000000
Those are current practice. I am not sure it is correct. most of time the parts are rejected just because of one defect, and they are not going to check more if found one defect in a part and the part will be returned.

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#104325

Charmed
Participant

Dear JJ:
Thanks for coming back.  Do provide more details, if it is not considered confidential and your bosees are not going to come after you. What does data for one year look like? May be you can make a small table which includes: Month, number made, number inspected, number rejected, reason for rejects (out of spec dimension, leaking, etc.) Please note I have suggested number made and number inspected, assuming less than 100% inspection. Since you mention “leaking” how is this determined?  What is the component?  What are the dimensions that are out of spec? If you can, tell us. Then later we can start talking about minimum loss to society. Wouldn’t that we wonderful if each one of us is focused on something so important! With my warmest regards.

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#104327

JJ
Participant

Sorry, I cannot answer your questions. Those questions are not related to my original questions and I think latest post is clear enough. Why are you worry about what dimentions? Dimentions are out of specs is one kind of defects. no more information.
I just want to know, in my case, what correct practice would be.
Thank you!

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#104331

Charmed
Participant

Dear JJ: When you posted the second message, I was typing my message.  There is a time delay between events. May be you did not realize that. In my humble opinion, your calculation of DPMO is inconsistent. Let’s see what others feel. No more questions. Cheers!

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#105257

Charmed SIX
Participant

I appreciate greatly your input:guiding us to the  right location .kind regards.

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#105261

Well Wisher of Six Sigma
Member

My request to all . Use this forum to get value out of the discussions and not to challenge each other. It is surprising that you are talking about helping some one and end up not doing that in the end and in addition confuse all others as well.
Now to JJ :
Are you calculating this to compile your in process yield OR to calculate the Outgoing Quality of the product ( as received by your end customer).
The formulae that Ajit gave you in one of the mails is the Right one to calculate the in process DPMO. However you need to be clear on the opportunities for Defects. It depends on the number of parts that goes into the assembly of the final part say in a PC board your opportunities for defects are the number of components used, no of solder joints and no of process steps that go into the product. Any of these that can go wrong and end up as a defect is an OFD. This is the trickiest part of Six Sigma. Once you have come up with a number for OFD stick to it . Don’t change. This number might impact your absolute value of the DPMO. But if you looking at calculating the improvement in DPMO it does’t matter. This is what Motorola taught us.
Don’t get hassled by the Sixma calculations.
In case you are calculating the outgoing defect of the factory, it is a Binominal (Bad/Good) and just calculate the % defective (50/1000) and that is truly what the customer sees and cares about.
Hope this gives you some relief.
regards

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#105291

Participant

Defects Per million opportunities (DPMO):
Process standard deviation (*) can be estimated to be s or can be figured using the following formulas:
DPMO= d/u  X  1,000,000
Where d= number defectives units and u= number of units in total.
50/1000 X  1,000,000 = 50,000

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#105298

Participant

Defects Per million opportunities (DPMO):
Process standard deviation (*) can be estimated to be s or can be figured using the following formulas:
DPMO= d/u  X  1,000,000
Where d= number defectives units and u= number of units in total.
50/1000 X  1,000,000 = 50,000
Long-Run Process Sigma:
0.8406+ Square root of (29.37-2.221* (In (DPMO))
* This formula embeds the assumption that in the long run, there will be a shift in the process mean of up to 1.5 sigmas, due to speacial cause variation. This 1.5 sigma shift is not a statistiocally prescribed value,but is instead based on long-term experience from Motorola’s manufacturing operations, which in gave rise to its inclusion in the process sigma caliculations throught out six sigma quality practice.

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#105333

Jonathon L. Andell
Participant

I respectuflly disagree with that. Opportunities are based on what it takes to do the work, not on how it can fail. For instance, Motorola used to count each component on the bill of materials as one opportunity, and each electrical connection (solder joint, crimp, etc.) as one opportunity.
It didn’t matter that an electronic component could be placed in the wrong location, the wrong orientation, could be overlooked, could be damaged, etc. – installing the component was a single, countable assembly task. Likewise, a solder jonit can be defective for a variety opf reasons, but it still is just one joint. One opportunity per joint.
If you cannot establish an objective way to count the opportunities necessary to do a job, then each unit is a single opportunity.

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#105339

Antoniu
Member

DPMO=(50/1000)*1000000 = 50000
sigma level = 3.14 (according to conversion chart of sigma levels to DPMO)

regards, V

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#105357

JJ
Participant

Thank you for your information. I think my case would be Binominal. we are evaluating supplier quality level.

Thank you for everyone. I am clear of my questions now.

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#172579

Slimcane
Member

I couldn’t get access to call the Excel function properly. If you are using Office 2003, the function/dll file Excel calls is not even available! Try this for a complete VB solution:
http://www.source-code.biz/snippets/vbasic/9.htmThis worked flawlessly for me.

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