For a sampling acceptance process with rectifying inspection

For a sampling acceptance process (with rectifying inspection) with N 2000, the following three different single sampling plans all provide equivalent protection and approximately same AOQL level of 2.0%. If the quality level (percentage of nonconforming products) is estimated to be ft 5% based on historical data, what will be the ATI for each of these 3 single plans? Which one should be selected based on the ATI?

Solution

Thus ATI plan C of n=20, c=0 is appropriate with lower risk.

	n=70	c =2				n=40	c=1			n=20	c=0
proportion defective	np	probability from poisson distribution			proportion defective	np	probability from poisson distribution			proportion defective	np	probability from poisson distribution
0.01	1.4	0.833			0.01	0.4	0.938	0.0096		0.01		0.951	= 0.049
0.02	2.8	0.469	=1-0.469 =0.531		0.02	0.8	0.809	0.0192	=0.191	0.02
0.03	4.2	0.21			0.03	1.2	0.663	0.0288		0.03
0.04	5.6	0.082			0.04	1.6	0.525	0.0384		0.04
0.05	7	0.03			0.05	2	0.406	0.048		0.05
0.06	8.4				0.06	2.4	0.308	0.0576		0.06