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A375221 Decimal expansion of 6^((3 + z_0.95)/6), where z_0.95 is the 95% quantile of the standard normal distribution (A329281).

%I A375221 #16 Aug 23 2024 08:40:59
%S A375221 4,0,0,3,1,3,0,7,5,9,6,0,0,8,5,2,2,4,7,2,0,0,9,6,2,3,7,3,9,3,3,5,6,5,
%T A375221 9,2,0,6,3,8,2,2,6,3,0,8,8,2,6,3,1,9,0,1,5,6,5,7,9,6,3,2,7,4,1,8,3,8,
%U A375221 0,9,5,5,6,7,6,3,7,6,8,4,6,1,2,1,3,1,0,3,6,0,7
%N A375221 Decimal expansion of 6^((3 + z_0.95)/6), where z_0.95 is the 95% quantile of the standard normal distribution (A329281).
%C A375221 This constant is often used in the service life requirements for critical parts in aviation, e.g., for the rotor disks of the turbines. The constant, rounded to y=4, serves as a safety factor when only one test result is available for the service life of a component with a log-normal service life distribution with an assumed known +-3 sigma scatter of 6. With a confidence level of 95%, it can then be assumed that the +-3 sigma range of the service life distribution does not fall below the demonstrated test life divided by y.
%D A375221 Sheldon M. Ross, Introduction to Probability and Statistics for Engineers and Scientists, Third Edition, Elsevier Academic Press, 2004. Chapter 7, Parameter Estimation, 7.3 Interval Estimates, page 242.
%H A375221 Junling Wang et al., <a href="https://iopscience.iop.org/article/10.1088/1742-6596/1213/2/022010">Fatigue Scatter Factor Analysis of Airplane Structures Based on Zero-failure Data</a>, Journal of Physics Conf. Series 1213 (2019) 022010.
%H A375221 Wikipedia, <a href="https://en.wikipedia.org/wiki/Log-normal_distribution">Log-normal distribution</a>.
%e A375221 4.0031307596008522472009623739335659206382263...
%t A375221 RealDigits[6^((3 + (x /. FindRoot[10*Erfc[x] == 1, {x, 1, 2}, WorkingPrecision -> 120])*Sqrt[2])/6)][[1]] (* _Amiram Eldar_, Aug 23 2024 *)
%o A375221 (PARI) 6^((3 + solve(x=1.0, 2.0, erfc(x)- 1/10)*sqrt(2))/6)
%Y A375221 Cf. A329281.
%K A375221 nonn,cons
%O A375221 1,1
%A A375221 _Hugo Pfoertner_, Aug 10 2024