# Calculating Sample Size for Pass/Fail Data

Six Sigma – iSixSigma Forums General Forums Tools & Templates Calculating Sample Size for Pass/Fail Data

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• #54325

Wendell
Guest

We test 2 containers per 180 on a pass/fail attribute basis. How do I determine a sample size with 95% confidence level?

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#194829

Don Strayer
Guest

The calculator and information at this site may be helpful. http://www.surveysystem.com/sscalc.htm

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#194830

MBBinWI
Participant

@wendelloh1 – I can’t vouch for the veracity of the calculator that Don pointed you to, but here’s the info that you need in order to set up a proper sampling plan.
First, you need to determine what is the Acceptable Quality Level. This is the highest defect rate that would still be acceptable (in your example, I assume that if you rejected the 2 containers then the entire lot of 180 would be rejected, thus your AQL would be 1/180 = 0.111%). To this you also need to identify the confidence level you want in evaluating that decision, here you identify 95%. (Here’s the description straight from Minitab – The poorest level of quality from a supplier’s process that would be considered acceptable as a process average. You want to design a sampling plan that accepts a particular lot of product at the AQL most of the time.
For example, you receive a shipment of microchips and your acceptable quality level (AQL) is 1.5%. Realizing that you won’t always make the correct decision (sampling risk) you set the producer’s risk (alpha) at 0.05. This means that approximately 95% of the time you will correctly accept a lot with a quality level of 1.5% or better and 5% of the time you will incorrectly reject the lot with a quality level of 1.5% or better.)

Second, you need to identify the Rejectable Quality Level, or how good can the lot be and still be rejected. In your case you reject at 2/180 = 1.111%. And again, you need to identify the risk level in making the wrong decision, usually you are willing to take a greater risk here (typically as low as 80%). (Here’s the description straight from Minitab – The poorest level of quality that the consumer is willing to tolerate in an independent lot. You want to design a sampling plan that rejects a particular lot of product at the RQL most of the time.
For example, you receive a shipment of microchips and your rejectable quality level (RQL) is 6.5%. Realizing that you won’t always make the correct decision (sampling risk) you set the consumer’s risk (beta) at 0.10. This means that at least 90% of the time you will reject a lot with a quality level of 6.5% or worse. At most 10% of the time you will accept the lot with a quality level of 6.5% or worse.
Also commonly known as lot tolerance percent defective (LTPD) and limiting quality (LQ).
While the RQL describes what the sampling plan will reject, the acceptable quality level (AQL) describes what the sampling plan will accept.)
The other thing you need to take into account is the variability of the items being sampled and the precision and accuracy of your measurement system. Attribute measurements are typically very susceptible to measurement errors and to compensate, a much higher sampling level is required. For example, if you are looking at color and you either get red or white, there is sufficient difference that you can decide on the sampling based solely on the proportions of each in the overall population. However, if you are looking at blue and green and you sometimes get some that are bluish-green and others that are greenish-blue, plus you have workers making the decision on these color differences that may have some degree of color blindness, now you will need to take a much larger sample to overcome not only the actual differences, but the measurement error differences due to the operator color blindness.
My recommendation is to look at converting to a continuous variable being measured instead of a pass/fail.

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#194832

Chris Seider
Participant

Nicely worded response @MBBinWI You spent tons of time…you learning patience? LOL

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#194836

MBBinWI
Participant

@cseider – naw, just cut/paste from Minitab help.

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#194837

MBBinWI
Participant

@cseider – and attributed, btw.

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#194839

uma
Participant

In the above case along with all sampling considerations it is also important to consider the resources available and the time for inspection and to see if it is within the practical levels.

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#200165

Why do you divide 180 by 1 instead of by 2 in your calculation? “I assume that if you rejected the 2 containers then the entire lot of 180 would be rejected, thus your AQL would be 1/180”

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#200166

The question is ambiguous. Are the “containers” the actual objects that are being tested or are the “containers” simply vessels that contain some number of the actual objects being tested? It seems you mean the former.

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