6.2 Given the table of coating weights shown here for samples of size n = 4: (a)

Question

6.2 Given the table of coating weights shown here for samples of size n = 4: (a) Calculate the X's and R's for samples 2 to 8 (b) Calculate the X and R values based on all eight samples. (c) Determine the appropriate constants that would be used with these data to construct X and R control charts, and calculate the control limits Sample x Range 18.90 18.5 21.2 19.4 17.919.0 20.3 21.2 19.6 22.2 21.5 20.8 20.3 19.1 22.8 19.0 20.721.020.5 19.1 16.5 4.7 2 19.820.4 20.5 4 20.6 20.8 21.6 22.223.2 23.0 20.5 20.3 19.2 8

Explanation / Answer

We have given that the table of coating weights shown here for samples of size n = 4.

Now we have to find following things :

a) Calculate Xbar's and R's for the sample 2 to 8.

b) Calculate Xbarbar, Rbar :

Xbarbar = sum of Xbar / n = 163.175 / 8 = 20.40

Rbar = sum of ranges / 8 = 2.21

c) The control limits for Xbar and R chart are :

For Xbar chart :

CL = Xbarbar = 20.40

UCL = Xbarbar + A2 * Rbar = 20.40 + 0.729*2.21 = 22.01

LCL = Xbarbat - A2 Rbar =  20.40 - 0.729*2.21 =18.78

For R-chart :

CL = Rbar = 2.21

UCL = D4*Rbar = 2.282*2.21 = 5.05

LCL = D3*Rbar = 0*2.21 = 0

D3, D4, and A2 were all obtained from the Control Chart Constants Table for a sample size of n = 4.

From the table of control chart :

D3 = 0

D4 = 2.282

A2 = 0.729

sample X1 X2 X3 X4 Xbar Range 1 18.5 21.2 19.4 16.5 18.9 4.7 2 17.9 19 20.3 21.2 19.6 3.3 3 19.6 19.8 20.4 20.5 20.075 0.9 4 22.2 21.5 20.8 20.3 21.2 1.9 5 19.1 20.6 20.8 21.6 20.525 2.5 6 22.8 22.2 23.2 23 22.8 1 7 19 20.5 20.3 19.2 19.75 1.5 8 20.7 21 20.5 19.1 20.325 1.9 163.175 17.7

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