Plot the data your control charts
Case Part A: Tesla’s Quality Challenge
1. Consumer Reports, the service that reports unbiased testing and ratings on cars (together with about everything else we buy), recommends avoiding new cars in their first year of production, especially those loaded with new technology. What can Tesla do to refute this recommendation?
Part B: Quality Control Analytics
𝒁_𝑳𝑺𝑳=[(𝑳𝑺𝑳−𝑿 ̿)/ 𝒁_𝑼𝑺𝑳=[(𝑼𝑺𝑳−𝑿 ̿)/𝝈]
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Probability(Zusl)=
Fraction defective (%)Explain what is means
Note the Lower Specification Limit is 1.4 LSL=
Use the sample Xbar Xbar=
Add probabilities
Explain the fraction defective (in %)Probabilility (Zusl) =
Probabilility (Zlsl) =
Total Prob= Prob (Zusl) + Prob (Zlsl) Fraction defective (in %)
Sigma=
4. What would be the Cpk for the process if it were centered (assume
the process standard deviation is the same)?
HINTS: Calculate Cpk for the lower spec limit component Cpk ...lsl… =
Calculate Cpk for the upperr spec limit component Cpk …usl… =
if the process were centered?
HINTS: Note that Upper Specification Limit is 2.4 USL=
Calculate Zlsl Zlsl=
Find probability using NORMSDIST(Zusl) Find probability using NORMSDIST(Zlsl).
2.40 1.9625
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Give | Given Sample data |
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1.40 1.900
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graph to help you with understanding the probability
| 0.5 | 2 | 1.8 | 0.8 Mean: | 0.65 | ||
|---|---|---|---|---|---|---|
| 2.2 | 2.2 | 1.9 |
| 2.2 | 2.1 | 2.1 | 2 | 1.8 | 1.7 | 1.9 | 1.9 | 2.02 | 0.7 |
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| 2.2 | 2.03 | 0.8 |
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𝑿 ̅−𝐂𝐡𝐚𝐫𝐭𝐂𝐨𝐧𝐭𝐫𝐨𝐥𝐋𝐢𝐦𝐢𝐭𝐬〖𝐔𝐂𝐋〗 _𝑿 ̅=𝑿 ̿+𝑨_𝟐𝑹 ̅
〖𝐋𝐂𝐋〗 _𝑿 ̅=𝑿 ̿−𝑨_𝟐𝑹 ̅𝑹−𝐂𝐡𝐚𝐫𝐭𝐂𝐨𝐧𝐭𝐫𝐨𝐥𝐋𝐢𝐦𝐢𝐭𝐬〖𝐔𝐂𝐋〗 _𝑹=𝑫_𝟒𝑹 ̅
〖𝐋𝐂𝐋〗 _𝑹=𝑫_𝟑𝑹 ̅Hint:
Arrange the sample data in 4 sample lots with 10 washers.m=
"for all samples" Rbar=
From Exhibit 10.13 find A2 (for Xbar Chart) A2=
〖𝐔𝐂𝐋〗 _𝑿 ̅
=𝑿 ̿+𝑨_𝟐𝑹 ̅
7. Plot the data on your control charts. Does the current
Try to create your own graph
For plotting Range Chart
Try to create your own graph
relative to fraction defective?
Hint:
Use the newly given Sigma Sigma=
Calculate Zusl Zusl=
Explain what is means
Xbar Chart
| Xbar | Xbarbar | UCL | LCL |
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2.20
| to plot Rchart | Sample Lot 1 | Sample Lot 4 | ||||
|---|---|---|---|---|---|---|
| Range Rbar | UCL | LCL | ||||
| Sample Lot 1 | 0.50 0.65 1.16 0.14 | |||||
| Sample Lot 2 | 0.60 0.65 1.16 0.14 | |||||
| Sample Lot 3 | 0.70 0.65 1.16 0.14 | |||||
| Sample Lot 4 | 0.80 0.65 1.16 0.14 | |||||
Range Chart
1.40
were no out of the control 0.20 limits since it is between the - |
Sample Lot 2 | Sample Lot 3 | Sample Lot 4 |
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| to use |
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| 0.650 |
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| Sample | Obs 2 | Obs 3 | Obs 4 | Obs 5 | X-bar | 2 | 4 | X-bar Chart | 16 | 18 | 20 | 22 | 24 |
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x-bar | range | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Number | |||||||||||||||||||||||||||
| 1 |
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10.40 | 10.30 | 9.90 | 10.20 | 10.28 | 10.28 | 0.70 | |||||||||||||||||||
| 2 | 9.98 | 10.25 | 10.05 | 10.23 | 10.33 | 10.17 | 0.35 | 10.8 | 10.168 | 0.35 | |||||||||||||||||
| 3 | 9.85 | 9.90 | 10.20 | 10.25 | 10.15 | 10.07 | 0.40 | 10.07 | 0.40 | ||||||||||||||||||
| 4 | 10.10 | 10.30 | 9.90 | 9.95 | 10.09 | 0.40 | 10.6 | 10.09 | 0.40 | ||||||||||||||||||
| 5 | 10.20 | 10.24 | 10.50 | 10.30 | 10.31 | 0.30 | 10.4 | 10.308 | 0.30 | ||||||||||||||||||
| 6 | 10.30 | 10.20 | 10.30 | 9.90 | 10.16 | 0.40 | 10.2 | 10.16 | 0.40 | ||||||||||||||||||
| 7 | 9.98 | 9.90 | 10.20 | 10.40 | 10.10 | 10.12 | 0.50 | 10 | 10.116 | 0.50 | |||||||||||||||||
| 8 |
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10.30 | 10.40 | 10.24 | 10.30 | 10.27 | 0.30 | 9.8 | 10.268 | 0.30 | |||||||||||||||||
| 9 |
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10.20 | 10.60 | 10.50 | 10.10 | 10.34 | 0.50 | 9.6 | 0 | 10.34 | 0.50 | ||||||||||||||||
| 10 | 10.40 | 10.50 | 10.10 | 10.20 | 10.30 | 0.40 | 9.4 | 6 | 8 | 10 | 12 | 14 | 10.3 | 0.40 | |||||||||||||
| 11 | 9.90 | 9.50 | 10.20 | 10.30 | 10.35 | 10.05 | 0.85 | 10.05 | 0.85 | ||||||||||||||||||
| 12 | 10.36 | 10.50 | 9.80 | 9.95 | 10.14 | 0.70 | 10.142 | 0.70 | |||||||||||||||||||
| 13 | 10.50 | 10.70 | 10.10 | 9.90 | 10.28 | 10.28 | 0.80 | ||||||||||||||||||||
| Range Chart | |||||||||||||||||||||||||||
| 14 |
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10.60 | 10.50 | 10.30 | 10.40 | 10.40 |
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10.4 | 0.40 | ||||||||||||||||||
| 15 | 10.30 | 10.40 | 10.55 | 10.00 | 10.36 | 0.55 | 1.4 | 10.358 | 0.55 | ||||||||||||||||||
| 16 | 10.60 | 10.15 | 10.00 | 10.50 | 10.29 | 0.60 | 10.29 | 0.60 | |||||||||||||||||||
| 17 | 10.40 | 10.60 | 10.80 | 10.10 | 10.42 | 0.70 | 1.2 | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 | 24 | 10.42 | 0.70 | ||||||
| 18 | 9.90 | 9.50 | 9.90 | 10.50 | 10.00 | 9.96 | 1.00 | 1 | 9.96 | 1.00 | |||||||||||||||||
| 19 |
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10.30 | 10.50 | 9.90 | 9.80 | 10.22 | 0.80 | 0.8 | 10.22 | 0.80 | |||||||||||||||||
| 20 |
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10.40 | 10.30 | 10.40 | 10.20 | 10.38 | 0.40 | 0.6 | 10.38 | 0.40 | |||||||||||||||||
| 21 | 9.90 | 9.60 | 10.50 | 10.10 | 10.60 | 10.14 | 1.00 | 0.4 | 10.14 | 1.00 | |||||||||||||||||
| 22 | 9.95 | 10.20 | 10.50 | 10.30 | 10.20 | 10.23 | 0.55 | 0.2 | 10.23 | 0.55 | |||||||||||||||||
| 23 | 9.50 | 9.60 | 9.80 | 10.30 | 9.88 | 0.80 | 9.88 | 0.80 | |||||||||||||||||||
| 0 | |||||||||||||||||||||||||||
| 24 | 10.60 | 10.30 | 9.90 | 9.80 | 10.18 | 0.80 | 10.18 | 0.80 | |||||||||||||||||||
| 25 | 9.90 | 10.30 | 10.60 | 9.90 | 10.10 | 10.16 | 0.70 | 10.16 | 0.70 | ||||||||||||||||||
| 10.21 |
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| Control limit graph coordinates | |||||||||||||||||||||||||||
| 10.56 = Upper Control Limit | X-bar Chart | UCL: |
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| UCL: | 10.56 | ||||||||||||||||||||||||||
| 10.56 |
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C-line: |
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| C-line: | 10.21 | ||||||||||||||||||||||||||
| 10.21 |
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Factors