Contents - Index

Rate of Convergence at LTPD

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

As an example, the default probability of acceptance at the LTPD is 0.1.  Suppose this risk quadruples for the first bad lot following a series of good lots so that Max OC(LTPD) = 0.4.  The increased risk is then 0.4 - 0.1 = 0.3.  Suppose for the second bad lot the probability of acceptance decreases to 0.2.  Now the increased risk is 0.2 - 0.1 = 0.1.  The increased risk changes from 0.3 for the first bad lot to 0.1 for the second bad lot.  This is a 67% reduction which corresponds to a rate of convergence of 67%.