At Quickie Car Wash, the wash process is advertised to take less than 7 minutes.
ID: 3389075 • 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 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
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
Explanation / Answer
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....
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