a) Calculate the control limits by hand b) Construct the control chart in Minita

Question

a) Calculate the control limits by hand
b) Construct the control chart in Minitab
c) Make conclusions(e.g if the process is in control) and recommendations (e.g. if P bar is acceptable and actions to be taken)

The number of printing errors per page in a newspaper was recorded from a randomly selected page, each day, for 20 days. The data are to be used to prepare a control chart to monitor and control printing mistakes in the newspaper. Recommend a suitable control chart, and 4.7 compute the control limits. Days 1 2 3 4 5 6 7 89 10 11 12 13 14 15 16 17 18 19 20 No. of 7 6 1 2 4 1 8 14 2 9 10 2 49 21 3 5 4 25 errors

Explanation / Answer

Let Xi = number of errors in the page of ith day, i = 1 to 20.

X ~ Poisson (), where = average number of errors per page which also serves as the variance of the distribution.

Xbar = average number of errors per page

= (1/20)[1,20]xi

= 119/20

= 5.95.

Standard deviation, s = sqrt(5.95) = 2.439

Trial Control Limits for c-Chart

Central Line: CL = xbar = 5.95

Lower Control Limit = LCL = CL – 3s = 5.95 – (3 x 2.439) = 0 [LCL cannot be negative]

Upper Control Limit = UCL = CL + 3s = 5.95 + (3 x 2.439) = 13.267

By actual visual examination of the given data, we find that number of errors on page of 8th and 15th day are above the UCL.

Revised Control Limits

Eliminating the two data points which are out of control,

Xbar = (1/18)[1,18]xi

= (119 – 14 – 21)/18

= 84/18

= 4.667

Standard deviation, s = sqrt(4.667) = 2.160

Revised limits are as follows:

Central Line: CL = xbar = 4.667

Lower Control Limit = LCL = CL – 3s = 4.667 – (3 x 2.160) = 0 [LCL cannot be negative]

Upper Control Limit = UCL = CL + 3s = 4.667 + (3 x 2.160) = 11.147

By actual visual examination of the given data, we find that number of errors on page are all within limits.

Thus, [0, 4.67, 11.15] serves as the final limits for control purposes. ANSWER

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