Homework+4+Solution

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MECT 3367 Homework 4 1. A company manufacturing oil seals wants to establish x and R control charts on the process. There are 25 preliminary samples of size 5 on the internal diameter of the seal. The summary data (in mm) are as follows: ∑ 𝑋 𝑖 ̅ = 1,253.75, ∑ 𝑅 𝑖 = 14.08 25 𝑖−1 25 𝑖=1 (a) Find the control limits that should be used on the x and R control charts. (b) Assume that the 25 preliminary samples plot in control on both charts. Estimate the process mean and standard deviation. 2. A TiW layer is deposited on a substrate using a sputtering tool. Table contains layer thickness measurements (in angstroms) on 20 subgroups of four substrates. Date: 10/03/2023 10 10

(a) Setup x and R control charts on this process. Find the control limits. Is the process in control? Draw the control charts for both. UCLx = 460.82, CLx = 448.69, LCLx = 436.56, UCLr = 37.98, CLr = 16.65, LCLr = 0 X bar chart failed at point 18. Therefore, this process is not in control. (b) Estimate the mean and standard deviation of the process. Note: If students answered 𝑋 ̅ = 448.69, 𝜎 ̂ 𝑥 = 𝑅 ̅ 𝑑 2 = 16.65 2.059 = 8.086 (give them full point) 12 8

3. Suppose that following the construction of the x and R control charts in previous Exercise , the process engineers decided to change the subgroup size to n = 2. Table contains 10 new subgroups of thickness data. Is the process in statistical control? If not, then explain an assignable cause. Draw the control charts in excel. 10

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Homework+4+Solution

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