Appliance cord. Use the Weibull distribution for the following analyses of the appliance cord data in Table 2. 1.
(a) Make separate Weibull plots of the data from the three tests and compare them visually for equality of the distributions. Are the distributions the same? Does the Weibull distribution fit adequately?
(b) Pool the data from the two tests on cord type B6 and make a Weibull plot. How does this plot compare with that for B7 cord?
(c) For each test, calculate the BLUES for the corresponding extreme value parameters and give the variance and covariance factors.
(d) Calculate two-sided approximate 95% confidence limits for the ratio of the Weibull shape parameters for tests 1 and 2. Are the data consistent with the assumption that the two true shape parameters are equal?
(e) Calculate a pooled estimate of the common extreme value scale parameter for cord type B6, and calculate its variance factor.
(f) Calculate two-sided approximate 95% confidence limits for the ratio of the shape parameters for cords B6 and B7. Are the data consistent with the assumption that the true shape parameters of the two types of cords are equal?
(g) Calculate two-sided approximate 95% confidence limits for the difference between the extreme value location parameters for tests 1 and 2, using the pooled estimate of the extreme value scale parameter from
(e). Give the interval for the corresponding Weibull scale parameters. Are the data consistent with the assumption that tests 1 and 2 have equal Weibull scale parameters?
(h) Repeat (8) for cords B6 and B7, using the pooled estimate of the common extreme value scale parameter for all three tests.
(i) Perform the test of homogeneity for the three extreme value scale parameters and state conclusions.
(j) Do (i) for the three extreme value location parameters.
(k) Calculate simultaneous (approximate) 90% confidence limits for all ratios of pairs of the three Weibull shape parameters, and state conclusions.
(l) Do (k) for all ratios of pairs of the three Weibull scale parameters.
(m) Explain why the analyses using the normal and Weibull distributions yield the same conclusions.