BMundela Company produces glass boards. Recently the ocompany received many complaints from its customers. The customers are not happy with the glass boards as they were inconsistent. The customers relationship manager discussed the issue with the quality control manager to figure out the cause of the inconsistency of the product. Prior to defining the cause, the quality control manger decided with his team to go through the process and make sure if they are under control. Out of 10 process, three processes have been selected for inspection. Process Three: Packaging In this process the quality controller selects randomly group of boxes and make sure if the box confima to the standards or not. The collected data is presented in the table below Number Number Number Number of Boxes confirms the of Boxes confirms the of Boxes confirms the of Boxes confirms Number Number Number Number of Boxes Selected Standards of Boxes Selected Standards Sample of Boxes Selected Standards Sample of Boxes Selected Standards the Sample Sample 1 190 180 11 215 190 21 215 190 31 180 170 190 180 12 205 195 22 205 195 32 180 180 200 185 13 205 190 23 205 190 33 175 165 4 200 190 14 195 180 24 195 180 34 170 160 190 170 15 195 190 25 195 190 35 175 165 195 180 16 210 185 26 210 185 36 190 180 7 195 185 17 205 190 27 205 190 37 180 180 200 190 18 210 195 28 210 195 38 170 160 200 180 19 210 200 29 210 200 39 185 180 10 180 170 20 210 200 30 210 200 40 190 170

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Question

Given the data collected, you are requested to help the quality management office to figure out which process/es is not under control and recommend what actions should be taken according to your findings.

BMundela Company produces glass boards. Recently the ocompany received many complaints from its customers. The customers are not happy with the glass boards as
they were inconsistent. The customers relationship manager discussed the issue with the quality control manager to figure out the cause of the inconsistency of the
product.
Prior to defining the cause, the quality control manger decided with his team to go through the process and make sure if they are under control. Out of 10 process,
three processes have been selected for inspection.
Process Three: Packaging
In this process the quality controller selects randomly group of boxes and make sure if the box confima to the standards or not. The collected data is presented in the
table below
Number
Number
Number
Number
of Boxes
confirms
the
of Boxes
confirms
the
of Boxes
confirms
the
of Boxes
confirms
Number
Number
Number
Number
of Boxes
Selected Standards
of Boxes
Selected Standards Sample
of Boxes
Selected Standards Sample
of Boxes
Selected Standards
the
Sample
Sample
1
190
180
11
215
190
21
215
190
31
180
170
190
180
12
205
195
22
205
195
32
180
180
200
185
13
205
190
23
205
190
33
175
165
4
200
190
14
195
180
24
195
180
34
170
160
190
170
15
195
190
25
195
190
35
175
165
195
180
16
210
185
26
210
185
36
190
180
7
195
185
17
205
190
27
205
190
37
180
180
200
190
18
210
195
28
210
195
38
170
160
200
180
19
210
200
29
210
200
39
185
180
10
180
170
20
210
200
30
210
200
40
190
170

Expert Solution

Step 1

The given data can be summarized as follows:

Sample	Number of Boxes Selected	Number of boxes confirms the standards	Number of defectives	Proportion of defectives
1	190	180	10	10/190 = 0.05263158
2	190	180	10	0.05263158
3	200	185	15	0.075
4	200	190	10	0.05
5	190	170	20	0.10526316
6	195	180	15	0.07692308
7	195	185	10	0.05128205
8	200	190	10	0.05
9	200	180	20	0.1
10	180	170	10	0.05555556
11	215	190	25	0.11627907
12	205	195	10	0.04878049
13	205	190	15	0.07317073
14	195	180	15	0.07692308
15	195	190	5	0.02564103
16	210	185	25	0.11904762
17	205	190	15	0.07317073
18	210	195	15	0.07142857
19	210	200	10	0.04761905
20	210	200	10	0.04761905
21	215	190	25	0.11627907
22	205	195	10	0.04878049
23	205	190	15	0.07317073
24	195	180	15	0.07692308
25	195	190	5	0.02564103
26	210	185	25	0.11904762
27	205	190	15	0.07317073
28	210	195	15	0.07142857
29	210	200	10	0.04761905
30	210	200	10	0.04761905
31	180	170	10	0.05555556
32	180	180	0	0
33	175	165	10	0.05714286
34	170	160	10	0.05882353
35	175	165	10	0.05714286
36	190	180	10	0.05263158
37	180	180	0	0
38	170	160	10	0.05882353
39	185	180	5	0.02702703
40	190	170	20	0.10526316
Total	7855		505	P bar = 0.06429

Step 2

Following formula can be used to determine the control limits for the p chart

Now, since the sample size varies for every sample. The control limits will be calculated for each sample.

Sample	Number of Boxes Selected	Number of boxes confirms the standards	Number of defectives	Proportion of defectives	LCL	UCL
1	190	180	10	0.05263158	0.004033	0.101231
2	190	180	10	0.05263158	0.004033	0.101231
3	200	185	15	0.075	0.019126	0.130874
4	200	190	10	0.05	0.003767	0.096233
5	190	170	20	0.10526316	0.03847	0.172056
6	195	180	15	0.07692308	0.019676	0.13417
7	195	185	10	0.05128205	0.003895	0.098669
8	200	190	10	0.05	0.003767	0.096233
9	200	180	20	0.1	0.03636	0.16364
10	180	170	10	0.05555556	0.004336	0.106775
11	215	190	25	0.11627907	0.050693	0.181865
12	205	195	10	0.04878049	0.003646	0.093915
13	205	190	15	0.07317073	0.018606	0.127736
14	195	180	15	0.07692308	0.019676	0.13417
15	195	190	5	0.02564103	0	0.059598
16	210	185	25	0.11904762	0.052005	0.18609
17	205	190	15	0.07317073	0.018606	0.127736
18	210	195	15	0.07142857	0.018113	0.124744
19	210	200	10	0.04761905	0.003532	0.091706
20	210	200	10	0.04761905	0.003532	0.091706
21	215	190	25	0.11627907	0.050693	0.181865
22	205	195	10	0.04878049	0.003646	0.093915
23	205	190	15	0.07317073	0.018606	0.127736
24	195	180	15	0.07692308	0.019676	0.13417
25	195	190	5	0.02564103	0	0.059598
26	210	185	25	0.11904762	0.052005	0.18609
27	205	190	15	0.07317073	0.018606	0.127736
28	210	195	15	0.07142857	0.018113	0.124744
29	210	200	10	0.04761905	0.003532	0.091706
30	210	200	10	0.04761905	0.003532	0.091706
31	180	170	10	0.05555556	0.004336	0.106775
32	180	180	0	0	0	0
33	175	165	10	0.05714286	0.004504	0.109782
34	170	160	10	0.05882353	0.004685	0.112962
35	175	165	10	0.05714286	0.004504	0.109782
36	190	180	10	0.05263158	0.004033	0.101231
37	180	180	0	0	0	0
38	170	160	10	0.05882353	0.004685	0.112962
39	185	180	5	0.02702703	0	0.062794
40	190	170	20	0.10526316	0.03847	0.172056
Total	7855		505	0.06429026

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