Question

(b) Does the process producing the cookies appear to be in control? What actions would you take based on the inspection results? 10 points) The quality of a cookie production job has been examined, and the results are shown below. The same definition of defec 4. ( t used in Problem 3 is also used here. Cookie No 4 10 Size (in) 9 18 27 9 18 9 27 9 Number of defects1 0 3 5 02 4 (a) Using an appropriate control chart to construct the control limits for Sample #4. Show calculations. You do not need to sketch the chart, but you need to show the control limits for Sample #4. What conclusion can you drawn by the result of this inspection? (b) Using an appropriate control chart, find one common set of control limits that can be used to monitor the quality characteristic for all samples. You do not need to sketch the chart, but you need to show the center line and the control limits of the chart. Does the process ap to be in control? What actions would you take? pear

Answer 1

a) Given number of defects and various sample sizes so we have to use U chart to detect under control of the process or not.

From the given data,

	Size (ni)	Number of defects (ui)
Cookie No.			ui = ci/ni	LCL	UCL
1	9	1	0.1111	-0.22855	0.478553
2	9	0	0	-0.22855	0.478553
3	18	3	0.1667	-0.125	0.375
4	27	5	0.1852	-0.07912	0.329124
5	9	0	0	-0.22855	0.478553
6	18	2	0.1111	-0.125	0.375
7	9	1	0.1111	-0.22855	0.478553
8	27	4	0.1481	-0.07912	0.329124
9	9	2	0.2222	-0.22855	0.478553
10	9	0	0	-0.22855	0.478553
Total :	144	18

The LCL and UCL values are calculated by using the above formulae.

b) U-Chart:

Here all points are lies between LCL and UCL so the process is under control