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 3

Simulation result.

One-sided

Sample size n	1 − α = 0.75, p = 0.75		1 − α = 0.90, p = 0.90		1 − α = 0.99, p = 0.99
Sample size n	k₁	Result (1-α)a	k₁	Result (1-α)a	k₁	Result (1-α)a
2 5 10 15 20	2.225 1.152 0.964 0.899 0.864	0.750145 0.749197 0.750319 0.749729 0.749845	10.252 2.742 2.066 1.867 1.765	0.899861 0.899606 0.900001 0.900345 0.899290	185.543 8.939 5.074 4.222 3.832	0.990003 0.990014 0.989846 0.989946 0.990018
Two-sided
Sample size n	1 − α = 0.75, p = 0.75		1 − α = 0.90, p = 0.90		1 − α = 0.99, p = 0.99
Sample size n	k₂	Result (1-α)a	k₂	Result (1-α)a	k₂	Result (1-α)a
2 5 10 15 20	1.905 1.223 1.163 1.151 1.147	0.750599 0.749557 0.749948 0.750224 0.750703	8.629 2.597 2.112 1.981 1.916	0.899754 0.899523 0.900041 0.900113 0.900088	160.441 8.291 4.907 4.170 3.835	0.990025 0.989940 0.990035 0.990117 0.989854

^a Each of the (1 − α) values was estimated from 1,000,000 observations.

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