Calculating Defect Rate (PPM) from a Cpk value


Fully vaccinated are you?
Cpk Sigma and PPM

From: ABC123 (ASchlo3307)
Newsgroups: misc.industry.quality
Subject: Re: Cpk Sigma and PPM

Date: 03 Feb 2000 00:41:42 GMT

Brett and Tracey Kimmel wrote:

>I'm wondering if anyone can help. I am working on target goals for a
>production floor that has no experience with capability studies, and process
>capability. I'm trying to make a simple target in PPMs. I know that 1.33 Cpk
>at 6 sigma is approximately 64 PPM. what would that be if I used 4 sigma
>instead. I would appreciate the math formula too.

Step No. 1 - run a Capability Study on the process. I prefer using a standard Xbar & R chart as a format with five-sample subgroups for 20 subgroups. Reading will be taken on consecutive pieces (100% inspection). The Capability Study will tell you two important things. First, is the process variation random? Assuming it is, is the process capable of meeting the print tolerance (what is the Cp, CpK, CpU --- whatever capability index you choose to use)?

Step No. 2 - Assuming your process is varying randomly (read: predictable) and capable of meeting the spec, run a control chart over time. For example, sample five consecutive pieces with a frequency of 1 hour. You can use the control limits from your capability study and plot points as you go. Assuming the operator has adjustment control over the process, he/she can use this "real time" control chart to make adjustment decisions.

Personal note: All of the quality buzzwords are nothing more than a way to make consulatnts money. Every single statistically based quality program owes its roots to Deming. Save yourself many thousands of dollars and a lot of frustration (consulants have to make you feel "stupid" for the first few sessions to justify their full fee) by going to the library and reading some of Deming's books. His students wrote some, too and they are worth reading.

You'll learn that sigma is a measure of variation about it's mean and that it's value is not a constant; it changes with each process and can be calculated quite simply.

You'll learn that your own fear of the unknown is the biggest roadblock to quality improvement --- not lack of knowing a formula to calculate PPM based on some fictitious sigma value.

Finally, you'll learn that there is no rocket science involved here (no matter WHAT the thousands or "quality consulants," statistical guru's and black belts would have you believe).


Comments, folks?


"Every single Statistically based . . . . to Deming"
Try "Shewhart" Deming and Juran were students, as well as many others.

"Consultants make you feel stupid"
Only our own lack of self worth can do that.

Some consultants may be overbearing/overzealous in there actions, but I have not met one yet that is not committed to their job.


Fully vaccinated are you?
Brian: None of this is personal. The beginning post was from:
From: (ASchlo3307)
Newsgroups: misc.industry.quality

I re-posted this as an excerpt from a news group. I, being a consultant, are to some degree 'insulted' as well - which is in part why I posted it. Personally I have a fair amount of respect for someone who goes thru the Black Belt program - I would like to have the opportunity some time. But let's not get into that here. Rather have comments such as agree or not, with what and why.


Speaking of Six Sigma, found out today that my company is shipping me off to "Master Black Belt" Training.

Has anyone been there? What should I expect? There will be four week-long sessions, spaced a month apart.

As for consultants, the ones I have worked with, without exception, have been very earnest and bright men and women, who freely shared their knowledge and experience. The problem was the usual lack of upper management involvement.

Brian Dowsett

Well thanks a bunch to whoever wrote this. As a "blackbelt" I feel quite insulted by these comments. I don't think there is any need to make blanket assumptions about people based on what training course they attended.

[This message has been edited by Brian Dowsett (edited 08 February 2000).]

Brian Dowsett

To Mark,
Please accept my apologies for attributing the orignal text to your good self, I've edited out any references to "you"!

With regard to the next message from BRoyal, I'd say that your company is almost certainly sending you on blackbelt training, based on the course duration (exactly the same as my own). Master blackbelts are those who train blackbelts, I couldn't see you being sent to learn this without doing the blackbelt first.
The training will be to learn quality improvement tools, both "soft" and statistical, and will involve you applying these tools to a real project in between the sessions. (The first day back is spent presenting your work to date to the group).

Hope this helps and sorry for jumping to a wrong conclusion with Mark.



Jim Bongard

Calculating Defect Rate from a Cpk value

Is there a simple formula for determining a defect rate (Defective Parts Per Million) for a given Cpk value?

Thanks in advance.

[email protected]


Hi Jim,
In my search for info on a similar topic (which I posted a request on this site) I've came acrosss an article that may help you. I can't recall the exact title but I
have the referance for you.

Quality Engineering Journal, Vol 9, No2, Dec 1996, pages 305-316.

It discusses the affects of the various types of ditributions on Cpk and the affects on DPPM. It also notes that Skewness and Kurtosis has a significant impact on DPPM.

Hope this helps and hope the details are correct.

Best of Luck
Nick Viney

Marcel Boere

Its easy:

Cpk is commonly used as a process capability measure for normally distributed populations.
The Cpk value is directly related to both the Sigma and the 'distance'of the pop.average to the closest specification limit.
Thus Cpk=1 --> average 3 sigma from limit. Cpk=1.33 --> average 4 Sigma, andsoforth.
In every statistical study book you can find the normal distribution table. Look, in the one side table, for the z(?) value (z in this case equals the number of sigma's you found earlier above). In the table you will find the applicable percentage (or ppm) of the population outside the closest specification limit.

Please note you can only use the one sided table if Cpk<< Cp. Other wise repeat the procedure for each limit (upper and lower).
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