At Quickie Car Wash, the wash process is advertised to take less than 8 minutes.

Question

At Quickie Car Wash, the wash process is advertised to take less than 8 minutes. Consequently, management has set a target average of 440 seconds for the wash process. Suppose the average range for a sample of 9 cars is 10 seconds. Use the accompanying table to establish control limits for sample means and ranges for the car wash process. Click the icon to view the table of factors for calculating three-sigma limits for the x-chart and R-chart. seconds and the LCLR equals seconds. (Enter your responses rounded to two The UCLR equals decimal places.)

Explanation / Answer

The given data is

Xdouble bar = 440 seconds

R bar = 10 seconds

For Sample size of 9, A2=0.337, D3=0.184 and D4=1.816

Now, we calculate the limits:

UCL = Xdouble bar + A2*Rbar = 440 + 0.337 * 10 = 443.37 seconds

LCL =  Xdouble bar - A2*Rbar = 440 - 0.337 * 10 = 436.63 seconds

Now, the limits for R Chart

UCLr = D4*Rbar = 1.816 * 10 = 18.16 seconds

LCLr = D3*Rbar = 0.184 *10 = 1.84 seconds

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