Question

Your company has started a drive to improve the quality of the products your manufacture. You and your co-workers want to help this effort, so you get together and discuss what you can do as a group.

You decide to analyze some inspection results to find out where to start. The products are processed and packed in groups of 100. The inspection results are recorded in such a way that if a part is found to have one or more scratches, it is recorded as one defective unit. Likewise, if a part is found to have one wrinkle or more or one crack or more, it is recorded as one defective unit. In the inspection data listed below, the first line shows 14 units with scratches and 10 units with wrinkles. These might or might not have occured on the same pieces. Each classification of defect is separate from the others. Only the sample size - 100 - is the same for all. What recommendations would you make for improving quality?

Solve the problem but only for the defect category of “Scratches”. You will have 20 samples total for the 100 items inspected for each sample.  

SCRATCHES
14

16

13

12

12

11

17

20

11

9

6

8

21

17

15

10

9

17

12

14

Answer 1

Solution

Let xi = Number of scratches in the ith sample, i = 1 to 20.

Average number of scratches per sample = ({?[i = 1, 20]xi}/20) = 13.2

Proportion of scratches, p = 13.2/100 = 0.132

So, Central Line, CL of p-chart = 0.132

Lower Control Limit, LCL = p – 3sqrt{p(1 – p)/100} = 0.0304

Upper Control Limit, UCL = p + 3sqrt{p(1 – p)/100} = 0.2335

All the given sample observations are within the control limits.

Hence, the recommendation is:

These limits can be employed for the future process control. ANSWER

Details of Excel Calculations

Sample #	# Scratches
1	14
2	16
3	13
4	12
5	12
6	11
7	17
8	20
9	11
10	9
11	6
12	8
13	21
14	17
15	15
16	10
17	9
18	17
19	12
20	14
Average	13.2
Prop Def p	0.132
p(1 - p)/100	0.0011458
Sqrt	0.0338491
LCL	0.0304528
UCL	0.2335472

DONE