Statistical Process Control

Provide an Excel file containing your answers and calculations

Scenario: A manufacturer of automobile glass employs a constant quality control technique where the thickness of glass is checked periodically by taking a sample of 5 units and measuring the thickness. The results of one shifts quality control inspections are shown in the table below.

Sample	Thickness		Sample	Thickness
1	4, 3, 4, 2, 4		11	1, 6, 4, 4, 2
2	5, 3, 5, 4, 2		12	3, 3, 4, 5, 4
3	3, 3, 3, 3, 4		13	3, 8, 3, 8, 6
4	4, 5, 5, 4, 5		14	3, 2, 5, 4, 2
5	2, 8, 7, 2, 2		15	3, 3, 3, 2, 1
6	4, 5, 2, 5, 4		16	4, 4, 4, 5, 3
7	3, 5, 4, 4, 5		17	5, 3, 4, 4, 3
8	2, 4, 4, 4, 3		18	4, 4, 5, 3, 3
9	5, 4, 3, 2, 5		19	6, 4, 3, 3, 3
10	4, 4, 4, 4, 4		20	4, 4, 3, 5, 4

Question 21: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 22: Using the data contained in the scenario calculate the Lower Control Limit for an X-bar chart that reflect a 99.7% confidence level. (2.5 points)

Question 23: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 24: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.7% level of confidence. (2.5 points)

Question 25: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.7% level of confidence. (2.5 points)

Question 26: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)

Scenario: A canning company packages canned soup for a major soup manufacturer for distribution to regional wholesalers. The company processes 5,000 cans of soup each day using an automated packaging machine that is programmed to fill each can with 74.0 0.1 ounces net weight of soup. The company's quality assurance process consists of randomly selecting five cans from the production line each hour and carefully weighing them. Sample observations for a 24-hour production run are reflected in the table below.

Hour	Sample 1	Sample 2	Sample 3	Sample 4	Sample 5
1	74.030	74.002	74.019	73.992	74.008
2	73.995	73.992	74.001	74.011	74.004
3	73.988	74.024	74.021	74.005	74.002
4	74.002	73.996	73.993	74.015	74.009
5	73.992	74.007	74.015	73.989	74.014
6	74.009	73.994	73.997	73.985	73.993
7	73.995	74.006	73.994	74.000	74.005
8	73.985	74.003	73.993	74.015	73.988
9	74.008	73.995	74.009	74.005	74.004
10	73.998	74.000	73.990	74.007	73.995
11	73.994	73.998	73.994	73.995	73.990
12	74.004	74.000	74.007	74.000	73.996
13	73.983	74.002	73.998	73.997	74.012
14	74.006	73.967	73.994	74.000	73.984
15	74.012	74.014	73.998	73.999	72.866
16	74.000	73.984	74.005	72.652	73.996
17	73.994	74.012	73.071	74.005	74.007
18	74.006	72.356	74.018	74.003	74.000
19	74.785	74.002	74.003	74.005	73.997
20	74.000	74.010	74.013	74.020	74.003
21	73.982	74.001	74.015	74.005	73.996
22	74.004	73.999	73.990	74.006	74.009
23	74.010	73.989	73.990	74.009	74.014
24	74.015	74.008	73.993	74.000	74.010
25	73.982	73.984	73.995	74.017	74.013

Question 27: Using the data contained in the scenario calculate the Upper Control Limit for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 28: Using the data contained in the scenario calculate the Lower Control Limits for an X-bar chart that reflect a 99.7% confidence level. (5 points)

Question 29: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an X-bar chart, which samples are out of control? (5 points)

Question 30: Using the data contained in the scenario calculate the Upper Control Limit for an R chart that reflect 99.7% level of confidence. (5 points)

Question 31: Using the data contained in the scenario calculate the Lower Control Limit for an R chart that reflect 99.7% level of confidence. (5 points)

Question 32: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for an R chart, which samples are out of control? (5 points)

Scenario: The manager of the customer service hotline for an internet service provider has been approached by the President of the company regarding a perceived increase in the number of customer complaints regarding the lack of timely technical assistance being provided by hotline technicians. In order to evaluate the validity of the Presidents concerns he decided to survey customers regarding their satisfaction with the timeliness of the technical assistance they received. Surveys were conducted during a thirty-day period with two hundred (200) randomly selected customers participating in the survey each day. The number of customers surveyed who expressed dissatisfaction with the timeliness of the technical assistance they received is summarized in the following table.

Day	No. Complaints		Day	No. Complaints
1	22		16	15
2	29		17	17
3	25		18	17
4	17		19	19
5	20		20	22
6	16		21	23
7	31		22	27
8	16		23	29
9	31		24	41
10	29		25	21
11	15		26	24
12	12		27	22
13	22		28	24
14	23		29	23
15	27		30	31

Question 33: Using the data contained in the scenario calculate the Upper Control Limit for the number of complaints that reflect a 95.5% confidence level. (5 points)

Question 34: Using the data contained in the scenario calculate the Lower Control Limit for the number of complaints that reflect a 95.5%confidence level. (5 points)

Question 35: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the number of complaints, which samples are out of control? (5 points)

Question 36: Using the data contained in the scenario calculate the Upper Control Limit for the proportion of complaints that reflect 95.5% level of confidence. (5 points)

Question 37: Using the data contained in the scenario calculate the Lower Control Limit for the proportion of complaints that reflect 95.5% level of confidence. (5 points)

Question 38: Using the data contained in the scenario and the calculated the Upper and Lower Control Limits for the proportion of complaints, which samples are out of control? (5 points)