What is the interpretation I-MR-R chart in this question?

N

nicolasanelka39

The engineers in the Quality Control Department of the firm started to collect data for the
amount (g) of these hazardous contaminants in 400 g of chocolate hazelnut spread (weight
of a jar) on a daily basis for 20 days. At two different times (10 a.m. and 3 p.m.) of a day, one
jar is sampled from each of the two tanks. The collected data are shown in Table 1.
Table 1. Amount (in grams) of hazardous contaminant in inspected jars
10 a.m. 3 p.m.
AM - PM
Day Tank1 Tank2 Tank1 Tank 2
1 154,74 160,50 136,65 153,71
2 150,62 162,45 150,33 165,17
3 139,81 174,78 150,33 173,47
4 140,42 166,85 151,52 155,22
5 149,43 166,53 154,56 174,00
6 154,13 172,55 144,61 163,42
7 157,10 166,28 162,57 161,00
8 144,41 163,12 149,19 162,97
9 150,32 172,07 160,64 163,01
10 150,74 171,92 144,71 172,25
11 150,07 175,84 155,36 168,03
12 143,21 158,38 136,71 180,65
13 151,46 179,95 162,12 172,18
14 146,52 169,67 143,83 181,34
15 148,77 168,75 150,18 163,18
16 141,14 169,32 130,46 160,19
17 150,22 175,02 162,92 169,01
18 156,75 177,77 144,62 160,55
19 149,75 160,83 151,60 174,00
20 141,46 167,88 143,36 168,48
The engineers have decided to construct X̅-R chart to estimate the current mean and
standard deviation of the oil amount in jars, and to monitor the production process.
1. Comment on the appropriateness of use of ̅-R chart by analyzing the data.
2. Construct the chart and state what you observe on the chart in terms of being under
control for the process.
3. Identify the possible sources of variation in this production process and accordingly,
discuss the assumption(s) of the engineers in using the ̅-R chart.
After constructing and observing the control chart, these employees have observed that
the average hazardous contaminant amount is reasonable for their products. However, they
have realized that they failed to notice some source of variability in their process. The
engineers cannot agree on how the on-hand data should be used for monitoring their
production process.
March 22, 2017
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4. Help them to find the most appropriate way to monitor their data.
5. Construct the chart you proposed. If the chart is out-of-control, make necessary
adjustments in order to estimate the mean and standard deviation of the hazardous
contaminant amount.
6. Estimate the mean and calculate the standard deviation (between/within) of amount
of hazardous contaminant.
After selecting and constructing the most appropriate control charting approach, they
have concluded that the control chart limit estimates are reasonable, so they can start
monitoring the process, and data for the coming week in Table 2 are obtained from the
process.
7. As a consultant, suppose that you were asked to check whether there exists any outof-control
signal. If it exists, comment on the possible special causes in the process
according to the data in Table 2.
Table 2. Amount (g) of hazardous contaminant for the next week
10 a.m. 3 p.m.
Day Tank 1 Tank 2 Tank1 Tank 2
21 155,52 168,98 140,73 174,54
22 141,70 171,27 150,75 170,40
23 145,18 172,40 150,71 173,46
24 146,75 175,03 166,23 156,10
25 156,62 179,20 151,53 164,26