Question

2. McDaniel Shipyards wants to develop control charts to assess the quality of its steel plate. They take ten sheets of 1" steel plate and compute the number of cosmetic flaws on each roll. Each sheet is 20' by 100'. Based on the following data, develop limits for the control chart, plot the control chart, and determine whether the process is in control. (Please keep two decimal points.) Number of flaws Sheet 1 1 2 3 4 5 6 2 0 1 5 7 8 9 10 0 2 0 2 a. What are the 2-sigma control limits for this process? b. Is the process in control? (use a control chart to support your answer).

Answer 1

c charts are used to observe variation in counting type attribute data such as number of flaws.

a.

$\overline{c}$ = $\sum c/k$

c is number of flaws & k is number of observations

$\overline{c}$ = (1+1+2+0+1+5+0+2+0+2)/10

$\overline{c}$ = 14/10

$\overline{c}$ = 1.4

UCL = $\overline{c}$ + z*$\sqrt{\overline{C}}$

UCL = 1.4 + 2*$\sqrt{1.4}$

UCL = 1.4 + 2* 1.183215

UCL = 3.766431

LCL = Min( $\overline{c}$ - z*$\sqrt{\overline{C}}$,0)

LCL = Min (1.4 - 2* 1.183215, 0)

LCL = Min(-0.96, 0)

LCL =0

b.

Plotting the c bar chart-

C bar chart 6 5 3 - Number of flaws 2 UCL LCL 1 N 0 Sheet 1 2 3 4 5 6 7 8 9

As 1 point (Sheet 6, Number of flaws 5) lies outside the control limits, the process is not in control.