Relationship between AQL/RQL and Reliability/Confidence:

Untitled2

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.

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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.

rql

Where n = sample size, and x = number of rejects.

When x = 0, the above equation becomes;

eqn2

Taking logarithms, the above equation can be converted as;

eqn3

Interestingly, this equation is comparable to the Success Run Theorem equation;

eqn4

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.

Keep on learning…

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