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Topic C=0 Sampling Plans

C=0 Sampling Plans

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This topic contains 13 replies, has 7 voices, and was last updated by  Joe Perito 17 years ago.

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    I am looking for a website or publication that has C=0 Sampling Plans. Any recommendations?


    The American Society for Quality (ASQ) at 800-248-1946
    has an 8 1/2 x 11″ soft back book of approximately 30 pages called ” C=0, Zero Defects Sampling Plans” by Nickolas Sequeglia that is easy to read and understand. It explains the superiority of the C=0 sampling plan over the old Mil-Standard 105E. It explains how the plan is more sensitive to shifts in defect levels and will detect quality shifts faster than the Mil-Standard because its operational characteristic curves are steeper than the Mil-Standard’s. The C=0 sampling plan will also reduce your sampling and testing by “huge” amounts when you get into lot sizes of 500 pieces and higher. The C=0 table used for all lot sizes is a sigle table contained on one page of the book. You should note that the obsolete Mil-Standard 105E specifically said NOT to use C=0 samplings plans. However, the Military has done a complete about face and obsoleted the Mil-Standard and the Pentagon has mandated that the C=0 sampling plan be the only acceptance sampling to be used for Military procurement. The C=0 sampling plan is simpler, faster, reduces labor and testing, is statistically valid and more sensitive to quality shifts. Want a brain tickler? In doing “less” testing, it will “improve” the quality of your incoming supplies. Want an explaination?


    If you download an evaluation copy of STATGRAPHICS Plus from our site at, you can generate various types of sampling plans. On the main menu, choose Special…Quality Control…Acceptance Sampling…Attributes. On the initial dialog box, set Action to “Analyze Existing Plan”, specify your lot size, and select the AQL and LTPD for your process. Then set the acceptance number to c=0 and the sample size n to a size you would like to evaluate. The program will compute the producer’s and consumer’s risks and plot the AOQ curve. You can quickly evaluate the efficacy of various sample sizes and select one which gives you the risk levels or AOQL you require.


    While I believe in C=0 plans, anyone that believes that these give steeper OC curves doesn’t know how to derive one.



    I’ve reviewed some of the answers from Joe and Gary to your question. While C=0 sampling plans yield the lowest sample size possible for a family of sampling plans indexed on AQL there are some drawbacks you should be aware of.

    When selecting any sampling plan your should review the Operating Characteristic curve for it to insure it meets your quality intention. Two points on the curve that describe the protection provided by the sampling plan are the AQL and the LTPD. AQL stands for Acceptable Quality Level and is the average lot defective level the sampling plan will routinely “accept”. LTPD stands for Lot Tolerance Percent Defective and is the average lot defective level the sampling plan will routinely “reject”. They two values provide a good way of comparing various sampling plans to meet your quality objective of discriminating good and bad lots of product. The closer these two values are to each other the better the descrimination, but the larger the sample.

    C=0 sampling plans work very well after considerable process improvement has been done. Most of the time to routinely accept lots of product using a C=0 sampling plan the actual lot defective level will have to be 1/4 to 1/10 that of the desired AQL. For instance, referencing ANSI Z1.9 for an indexed plan with an AQL of 1% having an acceptance number of 0 gives a sampling plan of n=13 and a=0. The actual AQL of that sampling plan is 0.39% and the LTPD is 16.2%. This plan requires your process average defective rate to be less than 0.4% defective to have better than a 95% chance of acceptance. While this requirement is probably not such a problem consider your confidence statement upon acceptance of a given lot: “You are 90% confident that the lot defective rate is less or equal to 16.2%”. Using C=0 plans require that processes operate well below the planned AQL in order to accept lots most of the time. If this requirement is not met, then you will be spending much more time in dispositioning activities.

    If you want to lower your overall sampling, inspection, and dispositioning costs consider using a double sampling plan instead. For more information on sampling see “A Guide to Acceptance Sampling” by Dr. W. Taylor @ This reference comes with software to prepare statistically valid sampling plans. Wayne’s site also has a number of articales and references on inspection and validation sampling plans.

    Good Luck!



    Joe Perito wrote:

    Want a brain tickler? In doing “less” testing, it will “improve” the quality of your incoming supplies. Want an explaination?

    Gary writes – Yes absolutely I want an explanation. I don’t believe it.

    Want another brain tickler? Why in the world would a Quality professional or Six Sigma Black Belt believe that any after the fact sampling scheme would improve Quality? 2nd question – Why does a Six Sigma Black Belt believe that the OC curve for a C=0 plan is stepper than a MIL-STD-105 which were specifically designed for the shape of the curve?

    Want an explanation – email me, I will take whatever time is necessary to make sure you understand what is correct here. Also, Ken Myers answer from 3/18/01 is good and correct.


    Hi Ken,

    Thanks for the information on sampling plans. I would only add one thing; an operational definition for the term “confidence.” If you say that “You are 90% confident that the lot defective rate is less than or equal to 16.2%”, you can be confident of that statement 9 out of the 10 times you make it. You may be right all ten times but you cannot be confident. Also, you do not know which of the ten times the statement may be false.



    Sure Marc, but in this case the confidence you speak of
    is really the power of the test. In fact, the error you referenced is the beta error. Let’s make sure we all understand the O-C Curve is really the beta curve for the test.

    Remember, as Gary Cone mentioned recently acceptance
    sampling is NOT a prevention tool. In the interim it
    may be used to slow the COPQ bleeding. However, it
    can never stop it. Six Sigma is about removing the
    cause(s) producing defective products or services.
    But, acceptance sampling can never replace prevention!


    I am an importer of medical equipment and devices and receive mixed lots, all small, less than 5000 units each, and want to utilize an effective sampling plan to test the functionality and aesthetics of the reciept at my warehouse. This is a new start-up company.


    Gary, the OC curve “formula” doesn’t change. But you have to find a lot size in the C=0 sampling plan and compare it to the lot size in the Mil-standard. In “all” lot sizes the C=0 sampling plan acceptance number is “always” ZERO. Meanwhile, the Mil-standard (Column II) allows more and more defects as the lot size increases “AND” the sample size keeps geting bigger and bigger. Ploted side by side the C=0 samling plan has steeper curves because it does not allow the acceptance of defects nor does the sample size grow as fast as the Mil-Standard’s. Any novice comparing the two tables will see the difference by sight and realize there is a difference. What happens when you proceed to the right (Mil-Standard) on the proportion defective axis (allowing more defects)? The plotted curves get flatter. I suggest you plot the two tables and then come back and tell the readers what you found. I did years ago.


    Gary, here’s your answer… which will improve the quality of your supplies and your products? Accepting more and more defects in your raw materials like the Mil-Standard sampling plan allows? Or, accepting ZERO defects at receiving and requiring your suppliers to correct their problems? As Quality Manager of one of the Seimens Corporation companies I was hired to break the log jam at receiving inspection. We saved over 50% sampling by going to the C=0 sampling plan, stopped accepting defects, rejected lots , required corrective action, debited suppliers for non quality and expenses, used skip lot sampling, and used dock-to-stock for excellent suppliers. Total sampling reduction was 92% with an eventual reduction in quality problems of 78%. Fictitious and exaggerated numbers? Fact. Experience. The logic is simple. Even the beginners will understand this.


    Gary, I’ll make the brain teaser simple for you to understand. Which will improve your quality: accepting defects and over sampling like the mil_std allows, or accepting no defects (C=0 sampling plan) at receiving inspection and not allowing the defects into your processes? As Quality Manager at one Seimens Corporation, I was hired to break the log jam at receiving inspection. We dropped the Military Sampling plan 105E (which accepts defects), used C=0 to reduce sampling by more than 50%, added skip lot testing, used dock-to-stock for excellent suppliers, stopped accepting defects, rejected bad lots after the first defect was found, required corrective action from suppliers, and debited them for non quality and expenses. This reduced our sampling 92% and eventually reduced defects related to raw materials by 78%. As for the question about a Quality Professional… that’s job knowledge and experience. As for a why a six sigma novice would do such a thing, I doubt if a four week trainee has the training or experience to compare the sampling plans.



    I am flattered that you decided to spend so much time on me.

    I believe your statements about how much you reduced incoming inspection, I only wonder why you did not take it to 0 (it is non value added you know).

    I agree with everything you said with this respect except your claim that c=0 plans have a stepper OC Curve. They do not. Do I believe that c=0 plans drive a better mentality – absolutely. I also believe that the mentality of picking the right suppliers and defining critical characteristics and making sure gages agree and capabilities are good is even better.

    Thanks for thinking of me tonight.


    Gary, I have a problem with deceitfulness, bogus information, and cute quips that try to devert people’s attention who are trying to learn something. On the other hand, I have relayed industry best practices, valid quotes and resources that anyone and everyone can verify. Again, you misleed those needing help with sampling plans and receiving inspection with statements that are incorrect and deceitful since you project them to be factual information while impuning those who know bwtter. I have replied to your statement that ISO and QS-9000 has no references to receiving inspection. See the posting. Just for you, I am going to take a targeted interest in every one of your postings to let the public see exactly what you know. As soon as you start offering correct, helpful information, I will desist.

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