Question

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. Excel access Sample 1 2 3 4 5 Mean 22 19 19.4 22.0 21.8 Range 4.4 5.1 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?  

Answer 1

Based on the sample mean and sample range data shared, we will calculate X-dbar (X-double bar) which is the center line for X-bar chart. This is calculated by average out means.

X-dbar = Average of Sample means = (22+19+19.4+22.0+21.8)/ 5 = 20.84

Next, we will estimate Center lines for range (R-bar) by calculating average of the range i.e. R-bar.

R-bar = Average of Sample ranges = (4.4+5.1+3.2+2.9+1.0)/5 = 3.32

Now, for X-bar chart we will calculate three-sigma upper control limits (UCL)

UCL = X-dbar + A2 (R-bar)

where A2 is control chart factor for sample size n (n= 10 customer, each sample contains 10 customers)

Based on the control chart factor below, A2 = 0.308 for n=10

Hence, UCL = X-dbar + A2 (R-bar) = 20.84 + 0.308*(3.32) = 21.86

Three sigma upper control limit (UCL) is 21.86.

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