Question

Management at Webster Chemical Company is concerned as to whether caulking tubes 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 packaged 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 8 8 3 15 4 2 5 9 6 16 7 3 3 10 6 17 8 4 8 11 5 18 3 5 2 12 7 19 0 6 1 13 3 20 4 7 6 14 3 Total 92 Calculate​ p-chart three ​-sigma control limits to assess whether the capping process is in statistical control.

The UCL Subscript p =

and the LCL Subscript p =

Answer 1

The formula for p chart is

UCL = p_bar + 3*sqrt(p_bar*(1-p_bar)/n_bar)

LCL = p_bar - 3*sqrt(p_bar*(1-p_bar)/n_bar)

CL = p_bar

p_bar = total number of defects / total number of samples

The calculated values are shown below along with the p chart. We can see that the process is in control