Padgett and Spurrier (1990)8 obtained the following data set for the breaking strengths (in GPa) of carbon ?bers used in making composite materials.
|
1.4
|
3.7
|
3.0
|
1.4
|
1.0
|
2.8
|
4.9
|
3.7
|
1.8
|
1.6
|
|
3.2
|
1.6
|
0.8
|
5.6
|
1.7
|
1.6
|
2.0
|
1.2
|
1.1
|
1.7
|
|
2.2
|
1.2
|
5.1
|
2.5
|
1.2
|
3.5
|
2.2
|
1.7
|
1.3
|
4.4
|
|
1.8
|
0.4
|
3.7
|
2.5
|
0.9
|
1.6
|
2.8
|
4.7
|
2.0
|
1.8
|
|
1.6
|
1.1
|
2.0
|
1.6
|
2.1
|
1.9
|
2.9
|
2.8
|
2.1
|
3.7
|
(i) In their analysis, Padgett and Spurrier postulated a Weibull W (ζ, β) distribu- tion model with parameters ζ = 2.0 and β = 2.5 for the phenomenon in question. Validate this model assumption by carrying out an appropriate test.
(ii) Had the model parameters not been given, so that their values must be deter- mined from the data, repeat the test in (i) and compare the results. What does this imply about the importance of obtaining independent parameter estimates before carrying out probability model validation tests?