The following samples have been taken from an on-going process. Use these values

Question

The following samples have been taken from an on-going process. Use these values to create both an X bar and an R chart, and then answer the questions below.

Sample 1: 56 48 53 58 52

Sample 2: 50 59 57 54 54

Sample 3: 61 59 56 55 58

Sample 4: 57 51 47 57 50

Sample 5: 50 49 57 55 56

Sample 6: 56 55 60 58 54

1) What is the value of the centerline for an X bar chart?  (Round to two decimal places)

2) The upper control limit for the X bar chart is:

3) The lower control limit for the X bar chart is:

4) The upper control limit for the R chart is:

5) The lower control limit for the R chart is:

Explanation / Answer

1) from above centerline for an X bar chart =X =54.7333

2)for number of samples n=6; factor A2=0.483

therefore upper control limit for the X bar chart is =mean +A2*R =54.7333+0.483*9.4=59.2735

3)lower control limit for the X bar chart is =mean -A2*R =54.7333-0.483*9.4=50.1931

4))for number of samples n=6; factor D3=0 ; D4=2.004

therefore upper control limit for the R chart is =D4*R =9.4*2.004=18.8376

5) lower control limit for the R chart is =D3*R=0*9.4=0

Sample Number S. No 1st 2nd 3rd 4th 5th 6th X(Mean) R(Range) 1 56 50 61 57 50 56 55.0000 11 2 48 59 59 51 49 55 53.5000 11 3 53 57 56 47 57 60 55.0000 13 4 58 54 55 57 55 58 56.1667 4 5 52 54 58 50 56 54 54.0000 8 Total 273.6667 47 Mean 54.73333 9.4

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