A double integration method for generating exact tolerance limit factors for normal populations | International Journal of Metrology and Quality Engineering (IJMQE)

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Table 7

AQLs corresponding to k₁ and k_2.

One-sided

Sample size n	1 − α = 0.90, p = 0.90		1 − α = 0.90, p = 0.95		1 − α = 0.99, p = 0.99
Sample size n	k₁	AQL	k₁	AQL	k₁	AQL
2 5 10 15 20	10.252 2.742 2.066 1.867 1.765	28.86% a 16.66% 13.81% 12.88% 12.40%	13.089 3.400 2.568 2.329 2.208	21.99% 10.05% 7.75% 7.04% 6.68%	185.543 8.939 5.074 4.222 3.832	nearly 0% 0.011% 0.131% 0.240% 0.318%
Two-sided
Sample size n	1 − α = 0.90, p = 0.90		1 − α = 0.90, p = 0.95		1 − α = 0.99, p = 0.99
Sample size n	k₂b	AQLb	k₂b	AQLb	k₂ b	AQLb
2 5 10 15 20	8.629 2.597 2.112 1.981 1.916	28.70% 16.68% 13.89% 12.97% 12.50%	11.109 3.191 2.564 2.395 2.312	21.56% 10.01% 7.79% 7.10% 6.74%	160.441 8.291 4.907 4.170 3.835	nearly 0% 0.013% 0.134% 0.239% 0.314%

^a The unit “%” was not omitted for clear discernment of the AQLs from the tolerance limit factors.

^b These two-sided tolerance limit factors and AQLs are the ones derived based on the assumption that the population mean coincides with the center of the specification range.

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