Problem IV. Gauge Capability & Tolerance Stack-up (20 pts. total) Part 1. 20 parts are collected and measured by a single operator using a single measuring instrument as part of a complete and balanced gauge capability study. 80 measurements have been collected in random order and i = 19.98, R = 0.018. The sample variance of all 80 measurements - 0.009. a. (4 pts.) Estimate o gauge and parts b. (4 pts) Is the assumption of normally distributed measurements required? If so, what variance estimates are affected if normality is not true? Explain why? C. (3 pts.) If the product specifications are 20 +/-0.20 what is the P/T ratio, and what is your assessment of gauge capability? Part 2. An assembly of two parts of length X; and Xz is shown below, where the second part is inserted into the first part to a depth of X3. All X, are random variables. . (4 pts.) What is a linear model for the length of the assembly as a function of the X? b. (4 pts.) Assume X, X and X; are independent random variables with means and variances 42 = 10,0 = 0.2, H2 = 15, a = 0.4, Mz = 5,0} = 0.25. What is the mean and variance of the assembly length? c. (3 pts.) Is the assumption of normality of X1, X, and Xs required in part b? Explain. Problem IV. Gauge Capability & Tolerance Stack-up (20 pts. total) Part 1. 20 parts are collected and measured by a single operator using a single measuring instrument as part of a complete and balanced gauge capability study. 80 measurements have been collected in random order and i = 19.98, R = 0.018. The sample variance of all 80 measurements - 0.009. a. (4 pts.) Estimate o gauge and parts b. (4 pts) Is the assumption of normally distributed measurements required? If so, what variance estimates are affected if normality is not true? Explain why? C. (3 pts.) If the product specifications are 20 +/-0.20 what is the P/T ratio, and what is your assessment of gauge capability? Part 2. An assembly of two parts of length X; and Xz is shown below, where the second part is inserted into the first part to a depth of X3. All X, are random variables. . (4 pts.) What is a linear model for the length of the assembly as a function of the X? b. (4 pts.) Assume X, X and X; are independent random variables with means and variances 42 = 10,0 = 0.2, H2 = 15, a = 0.4, Mz = 5,0} = 0.25. What is the mean and variance of the assembly length? c. (3 pts.) Is the assumption of normality of X1, X, and Xs required in part b? Explain