The Z1.4 AQL sampling plan tables do not translate to reliability/confidence level values. In fact, the Z1.4 tables do not translate to %quality values at 95% confidence level as well. This seems to be a general misconception regarding the Z1.4 tables. One cannot state that if the sampling plan criteria are met, the % non-conforming equates to the AQL value at 95% confidence level.
How can we define AQL in layman’s terms? Looking at the figure below, one can simply state that AQL is the % nonconforming value at which there is (1-α)% chance that the product will be accepted by the customer. Please note this does not mean that the product quality equals the AQL value.
Similar to the AQL value, we can also define the RQL value based on the picture above. RQL is the %nonconforming value at which there is β% chance that the product will be accepted by the customer.
The RQL value corresponding to the beta value is much more important than the AQL value. The RQL value has a direct relationship with the Reliability/Confidence values.
The relationship between β and RQL is shown below, based on the Binomial equation.
Where n = sample size, and x = number of rejects.
When x = 0, the above equation becomes;
Taking logarithms, the above equation can be converted as;
Interestingly, this equation is comparable to the Success Run Theorem equation;
Where C is the confidence level, and R is the reliability(%).
The Reliability value(%) is (1-RQL)% value at the desired β value.
The Reliability value(%) is (1-RQL)% value at the desired β value. The confidence level value translates to the β value, as shown in the equation above.
I have created a Shiny App through R-studio where the reader can play around with this. This web based app will create OC-curve, and provide values for AQL, RQL, and reliability values based on sample size and number of rejects.
… https://harishjose.shinyapps.io/OCR1 …
I encourage the reader to check out the above link.
I have a new post in this topic. Check out https://harishsnotebook.wordpress.com/2019/10/19/aql-rql-ltpd-oc-curve-reliability-and-confidence/
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Hello Harish,
Thank you for your thoughtful post. I wanted to suggest that Z1.4 tables does include operating characteristic curves that could be converted to a Confidence Reliability statement. These are found after the AQL switching rule tables. Take a look and let me know your thoughts.
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Hello Taylor,
Correct. But the confidence/reliability statement is not readily available. Not much can be said from an AQL standpoint.
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Thanks to the author of this online article for presenting this result.
However, the link between the RQL value and Reliability, as explained, is not straightforward.
Here, the author concluded that there is a link between the two values because he obtained a formula for the sample size for a given RQL and Beta that is comparable to the one that gives the sample size for a given reliability. But, from my perspective, this is not valid evidence linking RQL and reliability.
Also, the definition of a (1-RQL) at a given beta value does not have the same meaning as reliability.
Can someone give me references that allow me to write this article? I’m very curious, as I need to understand for a project I have.
Thanks a lot!
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Please check this post out. https://harishsnotebook.wordpress.com/2019/10/19/aql-rql-ltpd-oc-curve-reliability-and-confidence/
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Hello Mr. Harish,
Searching for mathematical relationship between AQL and RQL I found your article/post that I found interesting but I still do not see what that relationship is.
I do understand, or at least I’m aware of the multiple assumptions that some estimates must comply to sustain validity, but I hope an equation could be more informative than anything else. Could you, please share that mathematical expression for the relationship between AQL and RQL?
Thanks in advance for your kind and prompt answer.
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