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QuickE Lube has been monitoring its customer service times over the past 5 days. Each day...

QuickE Lube has been monitoring its customer service times over the past 5 days. Each day they took a sample of 10 customers and recorded the actual service times for those customers. The table below shows the sample mean and sample range for each of the 5 past samples.

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Sample

1

2

3

4

5

Mean

21

27

19.4

22.0

21.8

Range

0.5

3.1

3.2

2.9

1.0

What is the three-sigma upper control limits (UCL Only)the company should use to construct an X-bar chart for this service time data?

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Answer #1

Average range (R-bar) = Sum of the ranges for each sample/number of samples = (0.5+3.1+3.2+2.9+1.0)/5 = 10.7/5 = 2.14

Sample size = 5

For the sample size of 5 the factor for control limit for range(D4) = 2.114 (obtained from the table of constants for X-bar and R-chart)

UCL for R-chart = R-bar × D4 = 2.14 × 2.114 = 4.52

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