At Quickie Car Wash, the wash process is advertised to take less than 7 minutes.
ID: 422315 • Letter: A
Question
At Quickie Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 380 seconds for the wash process. Suppose the average range for a sample of 9 cars is 9 seconds. Use Table below to establish control limits for sample means and ranges for the car wash process.
TABLE: FACTORS FOR CALCULATING THREE-SIGMA LIMITS FOR THE X-CHART AND R-CHART
Factor for UCL and LCL for x-Chart (A2)
Factor for LCL for
R-Chart (D3)
Factor for UCL for R-Chart (D4)
size of sample (n)Factor for UCL and LCL for x-Chart (A2)
Factor for LCL for
R-Chart (D3)
Factor for UCL for R-Chart (D4)
2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777Explanation / Answer
Mean of the sampling distribution = x_double_bar = 380 seconds
Range of the sampling distribution = R_bar = 9 seconds
n=9
A2 = 0.337
D3 = 0.184
D4 = 1.816
UCLx = x_double_bar + A2 * R_bar = 380 + 0.337*9 = 383.033 or 383 seconds
LCLx = x_double_bar - A2 * R_bar = 380 - 0.337*9 = 376.967 or 377 seconds
UCLr = D4 * R_bar = 1.816*9 = 16.344 or 16 seconds
LCLr = D3 * R_bar = 0.184*9 = 1.656 or 2 seconds
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