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 2

Numerically determined factor k₂.

Sample size n	1 − α = 0.75 p = 0.75	1 − α = 0.90 p = 0.90	1 − α = 0.90 p = 0.95	1 − α = 0.95 p = 0.90	1 − α = 0.95 p = 0.95	1 − α = 0.99 p = 0.99
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20	1.905^a 1.385^a 1.270 1.223 1.199 1.184 1.175 1.168 1.163 1.159 1.157 1.154 1.153 1.151 1.150 1.149 1.148 1.148 1.147	8.629^a 3.779^a 2.937^a 2.597^a 2.413^a 2.297^a 2.217^a 2.157 2.112 2.075 2.045 2.020 1.999 1.981 1.965 1.950 1.938 1.927 1.916	11.109^a 4.722^a 3.629^a 3.191^a 2.953^a 2.804^a 2.700^a 2.623^a 2.564^a 2.517 2.479 2.446 2.419 2.395 2.375 2.356 2.340 2.326 2.312	17.304^a 5.433^a 3.801^a 3.192^a 2.875^a 2.680^a 2.547^a 2.449^a 2.375 2.316 2.268 2.228 2.194 2.165 2.140 2.118 2.098 2.080 2.064	22.272^a 6.782^a 4.691^a 3.917^a 3.514^a 3.266^a 3.098^a 2.975^a 2.881^a 2.806^a 2.746 2.695 2.653 2.616 2.584 2.556 2.531 2.509 2.488	160.441^a 21.377^a 11.317^a 8.291^a 6.884^a 6.075^a 5.551^a 5.182^a 4.907^a 4.695^a 4.525^a 4.386^a 4.269^a 4.170^a 4.085^a 4.011^a 3.945^a 3.887^a 3.835

^a Each of these two-sided tolerance limit factors is smaller than its corresponding one-sided tolerance limit factor. For example, if n = 5, (1 − α) = 0.99, and p = 0.99, then k₂ is 8.291 and k₁ is 8.939 (see Table 1).

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