Question

Quasar Exports Ltd, a fictional Turkish manufacturer of glass, wants to use a c-chart to monitor the number of defects in the sheets of glass it produces. The company wants to use the chart to address the production problems it is experiencing and use it on an ongoing basis as a monitoring tool. To construct the chart, the company collected data over 5 days by inspecting 30 sheets of glass and recording the number defects per sheet. The data are as follows:

Sample	Defects per Sheet	Sample	Defects per Sheet	Sample	Defects per Sheet
1	7	11	5	21	8
2	11	12	8	22	12
3	5	13	1	23	7
4	12	14	11	24	4
5	3	15	14	25	9
6	14	16	8	26	3
7	6	17	9	27	13
8	8	18	5	28	5
9	10	19	3	29	9
10	9	20	4	30	4

1. Using the data in the table, construct a c-chart using 3σ control limits. Why did the company choose a c-chart to monitor this process?
     

   		The defects are being counted over a consistent window of opportunity.
   		The defects are being counted over 5 days.
   		The defects per sample are being counted.
   		The defects are being counted over an inconsistent window of opportunity.
   		The defects are being counted for a set sample size.

2. After making quality improvements to the process and concluding that it is in control in the current week, the quality control manager of Quasar collected data on the number of defects per sheet for the following week using 20 glass sheets. The defects per sheet were as follows: 2, 7, 4, 5, 6, 4, 8, 1, 5, 3, 4, 4, 7, 2, 10, 3, 5, 6, 4, and 3. Plot the data on the c-chart, and determine whether the process is in control.
     

   		The process is in control.
   		The process is not in control.

Answer 1

c-bar = average(7,11,5,12,3,14,6,8,10,9,5,8,1,11,14,8,9,5,3,4,8,12,7,4,9,3,13,5,9,4) = 7.566666667

UCL = c-bar + z*sqrt(c-bar) = 7.566666667+3*sqrt(7.566666667) = 15.81893908
LCL = c-bar - z*sqrt(c-bar) = 7.566666667-3*sqrt(7.566666667) = -0.685605747 = 0 (Adjusted)

Correct answer is The defects are being counted over a consistent window of opportunity.

C-chart 1 2 10 18 19 20 3 4 - 5 6 7 8 Defects per sheet 9 — 11 LCL 12 — 13 14 C-bar 15 — 16 17 UCL

We can see the process is in control

Graph Data

Defects per sheet	LCL	C-bar	UCL
2	0	7.566667	15.81894
7	0	7.566667	15.81894
4	0	7.566667	15.81894
5	0	7.566667	15.81894
6	0	7.566667	15.81894
4	0	7.566667	15.81894
8	0	7.566667	15.81894
1	0	7.566667	15.81894
5	0	7.566667	15.81894
3	0	7.566667	15.81894
4	0	7.566667	15.81894
4	0	7.566667	15.81894
7	0	7.566667	15.81894
2	0	7.566667	15.81894
10	0	7.566667	15.81894
3	0	7.566667	15.81894
5	0	7.566667	15.81894
6	0	7.566667	15.81894
4	0	7.566667	15.81894
3	0	7.566667	15.81894