Contents - Index

Rate of Convergence at AQL

For sampling plans with varying protection, there are three OC curves: stationary OC Curve, maximum OC Curve and the minimum OC Curve.  The AQL is determined using the stationary OC curve.  The minimum probability of acceptance at the AQL is determined using the minimum OC Curve, and is denoted Min OC(AQL).  This worst case scenario frequently only occurs for the first good lot following a long sequence of bad lots.  For the second good lot, the probability of acceptance at the AQL is not as low.  For ANSI Z1.4 and Z1.9 this is a result of switching sampling plans.  The rate of convergence at the AQL describes how quickly the minimum OC curve converges back to the stationary OC curve at the AQL.  A rate near 100% is very rapid with most of the increase risk disappearing by the second good lot.  A rate near 0% is very slow meaning the increased risk persists for many good lots.

As an example, the default probability of acceptance at the LTPD is 0.95.  Suppose the risk of rejection quadruples for the first good lot following a series of bad lots so that Min OC(AQL) = 0.80.  The increased risk is then 0.95 - 0.80 = 0.15.  Suppose for the second good lot the probability of acceptance increases to 0.90.  Now the increased risk is 0.95 - 0.90 = 0.05.  The increased risk changes from 0.15 for the first good lot to 0.05 for the second good lot.  This is a 67% reduction which corresponds to a rate of convergence of 67%.