Sampling four pieces of precision-cut wire (to be used in computer assembly) eve

Question

Sampling four pieces of precision-cut wire (to be used in computer assembly) every hour fo rhte past 24 hours has produced the following results:

Develop appropriate control limits and determine whether there is any cause for concern in the cutting process.

HOUR x R 1 3.25" .71 2 3.1 1.18 3 3.22 1.43 4 3.39 1.26 5 3.07 1.17 6 2.86 .32 7 3.05 .53 8 2.65 1.13 9 3.02 .71 10 2.85 1.33 11 2.83 1.17 12 2.97 .4 13 3.11 .85 14 2.83 1.31 15 3.12 1.06 16 2.84 .50 17 2.86 1.43 18 2.74 1.29 19 3.41 1.61 20 2.89 1.09 21 2.65 1.08 22 3.28 .46 23 2.94 1.58 24 2.64 .97

Explanation / Answer

Let,

Xmean= central line of the chart and the average of past sample means, and A2= constant to provide three sigma limits for the process mean

Rmean= average of several past R values and is the central line of the control chart

D3, D2 = constants that provide three standard deviation (three-sigma) limits for a given sample size

From the provided table we get, Xmean = 2.982083, Rmean = 1.02375, n = 4 (as we are sampling 4 pieces of precision cut wire)

Using the table of control chart constraints,

D4 = 2.282, D3 = 0, A2 = 0.729

UCLR = D4*Rmean = 2.336198

LCLR = D3*Rmean= 0

UCLX= X mean +A2*Rmean = 3.728397

LCLX= Xmean-A2*Rmean = 2.23577

Thus, first we check the R chart if any observation is out of the limits UCLR and LCLR. We see that there is no observation which is out of limits.

Next, we check the x chart to see if any observation goes out of limits UCLX and LCLX. We see that all the observations are within limit. Thus, the whole process is in statistical control.

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