Instructions:

1. Construct the control charts in Excel, each problem takes ONE tab. Submit a SINGLE Excel file (with TWO tabs).
2. To minimize the possibility of typos during data transfer, please copy and paste the data table from this document to a new Excel worksheet.
3. Start interpreting a chart ONLY AFTER the chart has been found to be in statistical control (or stable). If the first iteration of the chart is not stable, remove those data points which are out of control and reconstruct the chart in the second iteration (to confirm it is now stable).
4. After constructing the charts, there are a few questions you need to provide brief answers to. These answers should be just a few sentences in length. You can type them in a blank spot right on the same Excel tab (by the charts).

Case 2: Bayfield Mud Company

In November 2015, John Wells, a customer service representative of Bayfield Mud Company, was summoned to the Houston warehouse of Wet-Land Drilling, Inc., to inspect three boxcars of mud-treating agents that Bayfield had shipped from its production plant in Orange, Texas, which is just west of the Louisiana -Texas border, to the Houston firm. Wet-Land had filed a complaint that the 50-pound bags of treating agents just received from Bayfield were over-weight by approximately 5%.

The over-weight bags were initially detected by one of Wet-Land's receiving clerks, who noticed that the railroad scale tickets indicated that net weights were significantly more on all three boxcars than those of identical shipments received on October 24, 2015. Bayfield's traffic department was called to determine if heavier packaging pallets were used on the shipments. (This might explain the heavier net weights). Bayfield indicated, however, that no changes had been made in loading or palletizing procedures. Thus, Wet-Land engineers randomly checked 50 bags and discovered that the average net weight per bag was 52.51 pounds. They noted from past shipments that the process yielded bag net weights averaging exactly 50.0 pounds, with an acceptable standard deviation of 1.2 pounds. Consequently, they concluded that the sample indicated a significant over-weight. Bayfield was then contacted, and John Wells was sent to investigate the problem.

Wet-Land management was not thrilled at receiving more products with the same amount of money. The charts followed by their mud engineers on the drilling platforms were based on 50-pound bags of treating agents. Over-weight bags might result in poor chemical control during the drilling operations and this adversely affect drilling efficiency. (Mud-treating agents are used to control the pH level and other chemical properties of the core during drilling cooperation.) This defect could cause severe economic consequences because of the extremely high cost of oil and natural gas well-drilling operations. Consequently, special-use instructions had to be created to accompany the delivery of these shipments to the drilling platforms. Moreover, the over-weight shipments had to be isolated in Wet-Land's warehouse, causing extra handling and poor floor space utilization. Thus Wells was informed that Wet-Land might seek a new supplier for mud-treating agents if, in the future, it receive bags that deviated significantly from 50 pounds. The quality control department at Bayfield suspected that the over-weight bags might have resulted from "growing pains" at the Orange plant. Because of the earlier energy crisis, oil and natural gas exploration activity had greatly increased. In turn, this increased activity has greatly increased demand for allied products made by related industries, including drilling muds. Consequently, Bayfield had to expand form a one-shift (2:00p.m to 10:00 p.m.) operation in mid-2013, and finally to three-shift operations (24 hours per day) in the fall of 2015 (Morning shift: 6:00-13:00; Late day shift: 14:00-21:00; Night shift: 22:00-5:00).

The additional night shift bagging crew was staffed entirely by new employees. The most experiences foremen were temporarily assigned to supervise the night-shift employees. Most emphasis was placed on increasing the output of bags to meet ever-increasing demand. It was suspected that these new employees are causing consistent over-weight shipments from the night shift. If that was actually the case, Bayfield would like to schedule more training and implement stricter weight tracking system to improve the bagging process performance during night. However, if the bags from night shifts are not noticeably different from the other two shifts, Bayfield would further explore other potential factors that may have contributed to this problem.

To verify the hypothesis, the Bayfield Mud quality control staff randomly selected Six bags in each hour of operations (6 bags per sample group). The statistics are presented in the data table below.

Please construct appropriate statistical control chart(s) and answer the following questions?

1. Were the bags from night shifts noticeably heavier than those from the other two shifts?
2. Was the bagging crew at the night shifts causing the weight fluctuation problem?

Hint:

1. Combine all sample groups from the same shift (i.e. construct 3 sets of charts, one for each shift)

Index	Shift	Sample time	Sample Group Average Weight	Lightest in sample group	Heaviest in sample group
1	Morning	6:00	49.6	48.7	50.7
2	Morning	7:00	51	49.1	54.5
3	Morning	8:00	50.6	49.6	51.4
4	Morning	9:00	50.2	50.2	51.8
5	Morning	10:00	49.5	47.5	52.3
6	Morning	11:00	50.3	48.6	51.7
7	Morning	12:00	51.2	46.2	50.4
8	Morning	13:00	49.7	46.4	50
9	Late Aft	14:00	49.2	46.1	50.7
10	Late Aft	15:00	50.4	46.3	50.5
11	Late Aft	16:00	50.4	45.4	50.2
12	Late Aft	17:00	49.2	46.3	49.6
13	Late Aft	18:00	49.6	44.1	51
14	Late Aft	19:00	48.5	45.5	49
15	Late Aft	20:00	49.1	45.5	50.2
16	Late Aft	21:00	49.6	47.1	50.5
17	Night	22:00	50.6	47	51.6
18	Night	23:00	50.7	49.2	51.8
19	Night	0:00	52.5	50.2	52.7
20	Night	1:00	54.8	51	56.3
21	Night	2:00	51.3	49.9	55.7
22	Night	3:00	56.1	50.6	56.6
23	Night	4:00	53.6	49.6	54.2
24	Night	5:00	52.7	49.6	53.4
25	Morning	6:00	49.4	47.4	52
26	Morning	7:00	50.3	49.2	52.2
27	Morning	8:00	49.5	48	52.4
28	Morning	9:00	50.3	49.4	51.7
29	Morning	10:00	50.2	49.6	51.8
30	Morning	11:00	49.7	49	52.3
31	Morning	12:00	50.4	48.8	51.5
32	Morning	13:00	50.1	49.4	53.6
33	Late Aft	14:00	49.2	46.6	50.2
34	Late Aft	15:00	49.5	45	50
35	Late Aft	16:00	50	48.2	50.4
36	Late Aft	17:00	49.2	48.2	51.7
37	Late Aft	18:00	50.8	49	52.2
38	Late Aft	19:00	50	49.2	51
39	Late Aft	20:00	49.3	46.3	50.5
40	Late Aft	21:00	50.1	44.1	50.7
41	Night	22:00	52.8	49.6	53
42	Night	23:00	51.8	48.2	52.7
43	Night	0:00	50.5	46.3	51.9
44	Night	1:00	49.4	46.4	50
45	Night	2:00	51.6	42	52.2
46	Night	3:00	55.7	50.2	56.7
47	Night	4:00	49	46.3	49.7
48	Night	5:00	50.2	47.2	51.9
49	Morning	6:00	49.5	45.2	50
50	Morning	7:00	49.3	45.8	49.7
51	Morning	8:00	50.1	48	51.5
52	Morning	9:00	49.2	48.1	52.7
53	Morning	10:00	51	48.1	53.6
54	Morning	11:00	50.4	49.5	54.1
55	Morning	12:00	48.9	48.7	50.9
56	Morning	13:00	48.9	46.8	51.2
57	Late Aft	14:00	49.8	46.2	50.7
58	Late Aft	15:00	50.5	47	51.9
59	Late Aft	16:00	48.7	47.4	49.2
60	Late Aft	17:00	49.5	46.8	50
61	Late Aft	18:00	50.2	47.2	51.4
62	Late Aft	19:00	49.6	49	50.6
63	Late Aft	20:00	49.8	50.5	51.5
64	Late Aft	21:00	50.9	48.2	51.9
65	Night	22:00	50.7	49.4	52
66	Night	23:00	52	49.8	53.8
67	Night	0:00	50.8	50.1	51.6
68	Night	1:00	52	46.2	52.2
69	Night	2:00	53.6	50	55.7
70	Night	3:00	50.6	45.4	51
71	Night	4:00	53.4	47.6	54.9
72	Night	5:00	50.2	48.2	50.5