Question on LTPD

Curious · Guest

For a LTPD of 5%, does it make an difference whether we choose the sample size to be 45 (0,1) or sample size to be 77 (1,2). And if there is any difference, what is the difference?

Would appreciate your input.

Thank you and regards.

EE · Posted: Tue Jan 27, 2026 10:13 am Post subject:

Hi Curious

In theory they are equivalent - they will both make you reject 90% of the time lots with a defective rate of 95%. The advantages of the 45 (0,1) sampling scheme is that it consumes less resources (since the sample size is smaller), and it gives the operator the impression that defects are not allowed (since no rejects are tolerated).

Anyway, some use 77 (0,1) just to allow for the possibility of getting a reject. Just the same, it's probably better to stick with SS=45 and to just do re-inspection at a higher sampling rate if you see a reject in a lot that you can not afford to throw away outright.

Thanks and regards,
EE

Curious · Guest

Hello EE,

Thank you for your reply. My thinking is if the incoming lots defective level is around 5%, perhaps they are the same. Bu t what if the incoming lots defective level is higher, say 10%? Isn't it true that the discrimating power of the 2 sample sizes will then be different in this case? I am guessing that the operating curve for sample size of 77 will be steeper for defective level of more than 5%. Is this correct? Do you see where I am coming from?

Rgds.

EE · Posted: Wed Jan 28, 2026 11:15 pm Post subject:

Hi Curious,

You are correct! I looked at the OC curves of 2 sampling schemes for LTPD=5, and confirmed that the one with a higher sample size (and higher c) has a better chance of rejecting a lot with dpm >5%.

EE

Curious · Guest

Hello EE,

Thank you for checking this information out for me. On the other hand, would it be true to say that if the defective level of the incoming lots is less than 5% (say 3%, for example), the discriminating power for SS = 45 is going to better than SS=77. Again, I am guessing that the OC curve for SS=77 will be higher than SS=45 at 3%. Is this correct? If so, can we say in general that if the defective level is below 5%, smaller sample size is more discriminating but if defective level of incoming lots is above 5%, the higher sample size is better.

Would appreciate your input on this.

Thanks and regards.

EE · Posted: Thu Jan 29, 2026 4:35 pm Post subject:

Hi Curious,

You really know your OC curves very well! These are all very good info - thanks! So good in fact that I think I should add them to the article on LTPD/AQL. These forums are really useful not only for the readers, but for the website itself as well.

Thanks again and keep on contributing!

Best regards,
EE

Curious · Guest

Well EE,

I am flattered. I don't really know this stuff that much. I'm just using my intuition here. For example, I know what a curve for 100% inspection for 5% defect would look like in a graph (like a step-down function)--if you plot the probability of acceptance on the Y-axis vs. % defect on the X-axis. Then, I try to imagine what the curve for SS = 45 would look like in comparison to this "step-down" function; a curve rather than a step that also pass through the 10% probability of acceptance. Next, I try to figure out what an OC curve for SS = 77 would look like in comparison to SS - 45. As the sample is bigger, I guess the curve will be steeper--closer to a perfect 100% inspection. Then, I check the relative probability of acceptance for a situation less than 5% and greater than 5% for both these curves and come to the conclusion I mentioned in my previous mail. Of course, the probability of acceptance for 5% defect level is the same for all the 3 curves as they would all pass through the same point (10% probability of acceptance). It's all purely intuition. Wink

Rgds.

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