At Quickie Car Wash the wash process is advertised to take l

At Quickie Car Wash, the wash process is advertised to take less than 7 minutes. Consequently, management has set a target average of 390 seconds for the wash process. Suppose the average range for a sample of 9 cars is 10 seconds. Use Table A in the lecture note # 8 to establish control limits for sample means and ranges for the car wash process. (20 points)

TABLE A           |          FACTORS FOR CALCULATING THREE-SIGMA LIMITS FOR     

            |          THE x-CHART AND R-CHART

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

1.777

Solution

Here, target average is 390 seconds...and the average range for a sample of 9 cars is 10 seconds....
x-double bar =390..and R-bar = 10...

ucl for x-bar = 390 + 0.337*10 = 393.37.....and LCL for x-bar = 390 - 0.337*10 = 386.63....

ucl for R = 1.816*10 = 18.16..... and lcl for R = 0.184*10 = 1.84....