Suppose a manufacturing process produces small metal rods. The desired length of these rods is 50 cm. Quality control personnel take samples of 5 rods every hour and measure their lengths. After 8 hours, they have the following data for the average lengths (in cm) of the 8 samples: Hour (h): 1, 2, 3, 4, 5, 6, 7, 8 Average Length (X-bar): 49.8, 50.2, 50.1, 49.9, 50.3, 50.1, 49.7, 50.0 Additionally, the standard deviation (s) for each sample is provided: Hour (h): 1, 2, 3, 4, 5, 6, 7, 8 Standard Deviation (s): 0.1, 0.12, 0.11, 0.1, 0.12, 0.11, 0.09, 0.1 Based on the given data, is the process under control?
Suppose a manufacturing process produces small metal rods. The desired length of these rods is 50 cm. Quality control personnel take samples of 5 rods every hour and measure their lengths. After 8 hours, they have the following data for the average lengths (in cm) of the 8 samples:
Hour (h): 1, 2, 3, 4, 5, 6, 7, 8
Average Length (X-bar): 49.8, 50.2, 50.1, 49.9, 50.3, 50.1, 49.7, 50.0
Additionally, the standard deviation (s) for each sample is provided:
Hour (h): 1, 2, 3, 4, 5, 6, 7, 8
Standard Deviation (s): 0.1, 0.12, 0.11, 0.1, 0.12, 0.11, 0.09, 0.1
Based on the given data, is the process under control?
Here, there are a total of eight samples, and the sample size is 5, First, I will determine the X double bar, and S bar, Next, I will use formulas to determine the UCL and LCL for the X bar and S charts, The rest of the calculations are shown below,
Step by step
Solved in 4 steps with 4 images
