Management at websters, in Problem 16, is now concerned as to wether caulking tu

Question

Management at websters, in Problem 16, is now concerned as to wether caulking tube are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packages in large boxes of 144. Several boxes are inspected, and the following numbers of leaking tubes are found.

Sample      tubes      Sample      tubes      Sample      tubes     

     1              3              8                6             15             5

     2              5              9                4              16            0

    3               3              10             9               17            2

    4              4               11            2                18           6

   5               2               12             6               19           2

   6              4                 13           5                 20           1

   7             2                 14             1            total           72

Calculate p-chart three-sigma control limit to assess whether the capping process is in statistical control.

Explanation / Answer

N = 144, p = 72 /20(144) = 0.025

Sigma p = Square root p(1-p)/n = Square root (0.025(1-0.025)/144 = 0.013

UCL = p + z sigma p = 0.025+ 3(0.013) = 0.064

LCL = p – z sigma p = 0.025- 3(0.013) = -0.014 (adjusted to zero)

The highest proportion of defectives occurs in sample #10, but is still within control limits: p 10th sample = 9/144 =0.0625 . Therefore, the process is in statistical control.

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