Industrial Data Analytics for Diagnosis and Prognosis. Yong Chen

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      1 Evaluate the T2-statistic for testing H0 : μ = (9 13)T using the data.Specify the distribution of the T2-statistic from (a).Using (a) and (b), test H0 at the α = 0.05 level. What conclusion do you reach?

      1 Use the data in Exercise 10 to calculate the likelihood ratio test statistic LR using (3.23). Verify the correctness of (3.24) for this data.

      2 Consider the hot rolling process as described in Example 3.2. Check if the mean side temperatures for the defective billets at the following locations along Stand 5 deviate significantly from the nominal values:locations 10 and 15 with nominal mean temperatures equal to 1852.6 and 1872.4, respectively.locations 6, 7, and 8 with nominal mean temperatures equal to 1878.0, 1868.5, and 1860.6, respectively.locations 17, 18, 19, and 20 with nominal mean temperatures equal to 1876.7, 1875.7, 1872.7, and 1868.5, respectively.

      3 Perform Bayesian inference for the mean of side temperatures at locations 6, 7, and 8 based on the data set side_temp_defect. Please use the sample covariance of all the data at these three locations as the true covariance matrix and assume it is known. The mean and covariance matrix of the prior distribution is:

      1 Please find the posterior distribution of the mean temperatures at locations 6, 7, and 8 based on the first five (n = 5) observations, and the posterior distribution based on the first 100 (n = 100) observations, respectively. Comment on how the posterior distributions are different for different sample sizes. And compare the MAP estimate with the MLE.