A car mechanic is thinking of guaranteeing customers that an oil change will take no more than 15 minutes with a 99.73% confidence level. He takes a few samples of size 5 and finds the process mean to be 13 minutes with a standard deviation of .2 minutes and average sample range of 1.2 minutes. Find the A 2 , D 2 , and D 3 values and use them to compute the upper and lower limits for an x-bar chart. Use the upper limit to determine if the mechanic can offer a 15 minute guarantee. Assume the mechanic plots the samples on the x-bar control chart and finds the process is in control, is there anything else the mechanic is missing to ensure the process is in control?

Question

A car mechanic is thinking of guaranteeing customers that an oil change will take no more than 15 minutes with a 99.73% confidence level. He takes a few samples of size 5 and finds the process mean to be 13 minutes with a standard deviation of .2 minutes and average sample range of 1.2 minutes. Find the A 2 , D 2 , and D 3  values and use them to compute the upper and lower limits for an x-bar chart. Use the upper limit to determine if the mechanic can offer a 15 minute guarantee. Assume the mechanic plots the samples on the x-bar control chart and finds the process is in control, is there anything else the mechanic is missing to ensure the process is in control?

Adrienne Michelle · Accepted Answer

Final Answer :

From Table S6.1 in the text,
A₂ = .577
D₄= 2.115
_D₃= 0
UCL = 13 + .577 (1.2) = 13.69 minutes
LCL = 13 - .577(1.2) = 12.308 minutes
The upper limit is less than 15, so the mechanic can offer the guarantee and be on time over 99.73% of the time. However, the mechanic forgot to calculate an R-chart to check his samples to ensure the process is in control.

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