Tools › Statistics › Distributions › Distribution Fitting › Example
MIL-HDBK-17-1F Section 8.3.7 Problem 1: Weibull fit and B-basis value of 30 compressive 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 8.3.7.1, Problem 1; Tables 8.3.7 and 8.5.8. |
| Level | Professional |
Problem
Thirty compressive strengths (ksi) from a composite material are to be reduced to a B-basis value. Fit the two-parameter Weibull distribution by maximum likelihood, test the fit with the Anderson–Darling statistic and its observed significance level, and compute the B-basis value with the handbook's V_B factor.
Inputs to Enter
- The 30 values of Problem 1 (loaded by default; the printed 1444.5 is the corrected 144.4 as in the handbook's Step 1)
- Confidence 95 %, coverage 90 %
Answers
- Weibull α̂ = 128.39, β̂ = 15.35 (tool 15.3714 to more digits)
- Anderson–Darling AD = 0.699, AD* = (1 + 0.2/√30) AD = 0.7245, OSL = 0.0576 (> 0.05, Weibull accepted)
- V_B(30) = 5.057 (Table 8.5.8); Q = α̂ (0.10536)^(1/β̂) = 110.88
- B-basis = Q exp(−V_B/(β̂ √n)) = 104.41 (tool 104.44)
- The handbook's selection rule picks the Weibull result
Notes
The tool's default sample is this problem; press Submit. The handbook's OSL formula evaluated at its own printed AD* gives 0.0603 rather than 0.0576; Problems 3 and 5 confirm the formula, so the test accepts the small difference.