Sample Size Question

[#1]

If I know my parts have a 30% failure rate, how many parts do I need to inspect to be 95% confident I will find at least one failure?  Assuming I made a process improvement and want to see if my failure rate decreased from 30% to 10% w/ 95% confidence, then how many parts do I need to inspect?  I think JMP can give me these answers through the DOE>Sample Size Explorer>Power wizard, but I'm not exactly sure how to use this script to get the answers to these pretty basic sample size questions.

[#2]

Have you seen the documentation for the Power for Two Independent Sample Proportions?

[#3]

Hi Mark, Thanks for the quick response as this does show me how to use the nice sample proportion wizard for this type of thing.  Taking a slight step back from my above question, let's say it takes 4hrs to inspect my part to see if it will fail.  I need to find a failure so that I can do some failure analysis work, but management wants me to give them a estimate of time for how long it will take to inspect parts before I actually find a failure.  Let's assume a historical failure rate of 30% rate and I want to be 95% confident I am giving management a good estimate of time.  How many parts should I anticipate inspecting before I find a failure?

[#4]

I like @dlehman1's approach. This explorer for reliability might also be helpful.

[#5]

Hi @chrsmth ,

How about using OC-curve for Hypergeometric / Binomial?

You did not mention the lot size, N.

If N is big, binomial is OK, but if N is small like <1000 maybe you want to use Hypergeometric distribution.

In this case, 95% confidence that it will detect at least 1 defective = Probability of acceptance, Pa=0.05 (in Y-axis of OC curve) because you will accept the sampling when c=0 @ 30% of defective rate (i.e X = 0.3).

During sampling of n sample size, you can detect 1 defective, 2 defective etc.

Usually, I just use Excel to develop OC curve because it's easier for me to understand the reasoning behind the choice of my sample size. But, JMP should be able to simulate that faster. Example as below;

Maybe this research can help: https://www.researchsquare.com/article/rs-3099107/v1 

[#6]

Mark,

                I found this tread and have been reviewing for a similar problem I am facing.

                We recently had a failure that we did not find in our normal sampling.

                After determining the root cause, we must items to verify that involve sample size.

                First item is we want to verify our containment by taking a sample from product produced before and after the event time frame we have defined.  We want to determine sample size we should use based on our lot size (250 pieces) and frequency we saw of failures during the event (8 to 30%).  Is there a profiler you would recommend helping us model this condition?  I am not a statistician.

                Second items is adjusting our sample size going forward.  Currently we are sampling 1 piece / Lot (destructive test), but only a small portion of products from this type of material.  We have already discided to increase the sample size to include all products, but want to understand the confidence of detecting a defect?  Can we factor in the samples taken increasing the products from about 20% of the population to 100%?  We hope to not have to sample many pieces from each lot, but I don’t know how to make or model this calculation.

Thanks in advance for your support and suggestions.

[#7]

I think the first question was answered by me at the start of this discussion.

I'm not sure how to address the second question. Have you surveyed the sample-size explorers to see if one suits your purpose?

[#8]

Hi @chris_dennis . I confess, and apologize, that neither of your questions are clear to me. What exactly are you assuming, and what exactly do you want to know?

[#9]

I have included a process diagram to help explain.

1 What sample size is needed to verify after corrective action that we have correctly contained the event.

2 What should our sample size be for future production to detect internally.

We will need to define confidence level for each sample size (1 &2).

[#10]

Hi @chris_dennis . I see in your diagram you say “What sample size needed to confirm no contamination
after corrective action (verification sample)”

The answer is 100% sampling (all 250 from each batch). If you want to “confirm” no contamination then the only option is 100% sampling; in other words, there is no sampling plan that can guarantee (with any level of confidence) 0. For any sampling plan ( that is less than 100% sampling) there must be some “acceptable” % defective.  And I don’t want to confuse “acceptable” with “desirable”. When I say “acceptable”, what I mean is what could you tolerate in the worst case.