Tools › Statistics › Distributions › Distribution Fitting › Example
MIL-HDBK-17-1F Section 8.3.7 Problem 5: nonparametric B-basis by Hanson–Koopmans for 15 strengths
| Tool | Distribution Fitting |
| Source | U.S. Department of Defense (2002). Composite Materials Handbook, Volume 1: Polymer Matrix Composites Guidelines for Characterization of Structural Materials. MIL-HDBK-17-1F, 17 June 2002. Section 8.3.7.5, Problem 5; Tables 8.5.14 and 8.5.15. |
| Level | Professional |
Problem
Fifteen strengths (118.58, 121.77, 137.54, 140.39, 134.03, 133.44, 114.56, 123.28, 130.33, 138.00, 122.69, 137.10, 137.49, 122.87, 135.82) reject every parametric model at the 5 % level. Compute the B-basis value by the Hanson–Koopmans small-sample method.
Inputs to Enter
- Paste the 15 values of Problem 5
- Confidence 95 %, coverage 90 %
Answers
- Weibull OSL 0.047, normal 0.039, lognormal 0.035: all below 0.05, so the nonparametric method applies
- n = 15 → r = 8, k = 1.54 (Table 8.5.14); x(1) = 114.56, x(8) = 133.44
- B = x(r) (x(1)/x(r))^k = 105.50 by the handbook's formula with its printed r and k (the handbook prints 104.365, which would need k = 1.616)
- A-basis by Table 8.5.15: k_A(15) = 2.75672
Notes
Replace the default sample. The test script records the handbook's B value as inconsistent with its own table; the tool prints the formula value. Not the default case.