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 4

Comparison of k₂ and k_2,existing.

k₂ determined by new integration method and k_2,existing being currently used in industry

Sample size n	1 − α = 0.75, p = 0.75		1 − α = 0.90, p = 0.90		1 − α = 0.99, p = 0.99
	k₂	k_2,existing	k₂	k_2,existing	k₂	k_2,existing
2 5 10 15 20 25 30 35 40 50 100	1.905 1.223 1.163 1.151 1.147 1.145 1.144 1.143 1.143 1.143 1.143	4.393^a 1.829^a 1.496^a 1.398^a 1.349^a 1.319^a 1.299^a 1.284^a 1.272^a 1.255^a N/A^c	8.629 2.597 2.112 1.981 1.916 1.877 1.851 1.831 1.816 1.794 1.744	15.512^a,b 3.499^a,b 2.546^a,b 2.285^a,b 2.158^a,b 2.081^a 2.029^a,b 1.991^a,b 1.961^a,b 1.918^a,b 1.823^b	160.441 8.291 4.907 4.170 3.835 3.638 3.507 3.412 3.339 3.235 3.005	234.878^a,b 10.220^a,b 5.610^a,b 4.621^b 4.175^b N/A^c 3.743^b 3.619^b 3.524^b 3.390^b 3.098^b

^a These factors are the ones that were provided by Wheeler [12].

^b These factors are the ones that were provided by ISO [24].

^c N/A means “not applicable”. Either Wheeler or ISO did not provide the two-sided tolerance limit factors for some sampling inspection parameters.

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