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

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, 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, 0, 9, 5, 5, 6, 7, 6, 3, 7, 6, 8, 4, 6, 1, 2, 1, 3, 1, 0, 3, 6, 0, 7

Offset: 1

Author

Hugo Pfoertner, Aug 10 2024

Keywords

• nonn
• cons

Comments

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.

Examples

			4.0031307596008522472009623739335659206382263...
		

References

• 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.

Links

• Junling Wang et al., Fatigue Scatter Factor Analysis of Airplane Structures Based on Zero-failure Data, Journal of Physics Conf. Series 1213 (2019) 022010.
• Wikipedia, Log-normal distribution.

Crossrefs

Cf. A329281.

Programs

Mathematica

RealDigits[6^((3 + (x /. FindRoot[10*Erfc[x] == 1, {x, 1, 2}, WorkingPrecision -> 120])*Sqrt[2])/6)][[1]] (* Amiram Eldar, Aug 23 2024 *)

PARI

6^((3 + solve(x=1.0, 2.0, erfc(x)- 1/10)*sqrt(2))/6)