Applied Statistics and Probability for Engineers

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Data

Exponential probability plot

ML estimates

ML estimates

Mean 20.7362

Goodness of fit

AD* 0.692

Figure S6-2.

Exponential probabil-

ity plot (from Minitab)

of the data from Table

S6-1.

this reason, the Anderson-Darling test is sometimes called a “distance” test. The test is upper-

tailed; that is, if the computed value exceeds a critical value, the hypothesis of normality is

rejected. The 5% critical value of the Anderson-Darling statistic is 0.752 and the 1% value is

1.035. Because the Anderson-Darling statistic in Figure S6-1 is 1.904, and this exceeds the 1%

critical value, we conclude that the assumption of normality would be inappropriate.

Minitab can construct several other types of probability plots. An exponential probability

plot of the data in Table S6-1 is shown in Figure S6-2. Notice that the data lies very close to

the straight line in this plot, implying that the exponential is a good model for the data.

Minitab also provides an estimate of the mean of the exponential distribution. This estimate is

just the sample mean.

Figure S6-3 is a Weibull probability plot of the data from Table S6-1, constructed using

Minitab. The data lies approximately along a straight line, suggesting that the Weibull

distribution is also a reasonable model for the data. Notice that Minitab provides maximum

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1.0

Data

Weibull probability plot

ML estimates

ML estimates

Shape 1.01967

Scale 20.8955

Goodness of fit

AD* 0.679

Figure S6-3. Weibull

probability plot (from

Minitab) of the data

from Table S6-1.

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