Relationship between AQL/RQL and Reliability/Confidence: 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.