Processing times for new accounts at a bank are shown in the following table. Five samples of four observations each have been taken. Use the sample data in conjunction with the Table of Constants for Control Charts (provided) to construct upper and lower control limits for both a mean chart and a range chart. Do the results suggest that the process is in control? Total Sample 1 10.2 9.9 9.8 10.1 40.0 Sample 2 10.3 9.8 9.9 10.4 40.4 Sample 3 9.7 9.9 9.9 10.1 39.6 Sample 4 9.9 10.3 10.1 10.5 40.8 Sample 5 9.8 10.2 10.3 9.7 40.0

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Processing times for new accounts at a bank are shown in the following table. Five samples of
four observations each have been taken. Use the sample data in conjunction with the Table of
Constants for Control Charts (provided) to construct upper and lower control limits for both a
mean chart and a range chart. Do the results suggest that the process is in control?
Total
Sample 1
10.2
9.9
9.8
10.1
40.0
Sample 2
10.3
9.8
9.9
10.4
40.4
Sample 3
9.7
9.9
9.9
10.1
39.6
Sample 4
9.9
10.3
10.1
10.5
40.8
Sample 5
9.8
10.2
10.3
9.7
40.0
Transcribed Image Text:Processing times for new accounts at a bank are shown in the following table. Five samples of four observations each have been taken. Use the sample data in conjunction with the Table of Constants for Control Charts (provided) to construct upper and lower control limits for both a mean chart and a range chart. Do the results suggest that the process is in control? Total Sample 1 10.2 9.9 9.8 10.1 40.0 Sample 2 10.3 9.8 9.9 10.4 40.4 Sample 3 9.7 9.9 9.9 10.1 39.6 Sample 4 9.9 10.3 10.1 10.5 40.8 Sample 5 9.8 10.2 10.3 9.7 40.0
Institute of
Quality & Reliability
Subgroup size
(n)
2
3
4
5
6
7
8
9
10
15
25
Table 8A - Variable Data
X bar and R Charts
Chart for
Averages
Control
Limits
Factor
Tables of Constants for Control charts
ref: AIAG manual for SPC
X bar and s charts
X bar and R Charts
X bar and s Charts
Chart for Ranges (R)
A₂
d₂
1.880
1.128
1.023 1.693
0.729
2.059
0.577
2.326
0.483
2.534
0.419
2.704
0.076
0.373
2.847 0.136
0.337
2.970
0.184
0.308 3.078
0.223
3.472
0.153 3.931
Divisors
to
Estimate Factors for Control
Limits
Ox
= X
D3
CLX = X
CL S = S
-
-
-
Centerline
CLx =
CLR = R
0.223
0.347
0.459
Chart for
Averages Chart for Standard Deviation (s)
Divisors
to
Control
Limits
Factor
D4
A3
3.267
2.659
2.574
1.954
2.282
1.628
2.114 1.427
2.004 1.287
1.924
1.864
1.816
1.777
1.653
1.541
estimate Factors for Control
ox
Limits
C4
B4
0.7979
3.267
0.8862
2.568
0.9213
2.266
0.9400
2.089
0.9515
0.030
1.970
1.182 0.9594
0.118
1.882
1.099 0.9650
0.185 1.815
1.032 0.9693
0.239
1.761
0.975 0.9727
0.284
0.789 0.9823
0.428
0.606 0.9896 0.565
Control Limits
UCL =
UCLR=D&R
UCL = X + A₂S
UCL, = BAS
=X+A₂R
B3
LCL = X - A₂ R
X
LCLR = D₂R
LCLX = X - A₂S
LCL, = B35
1.716
1.572
1.435
6 x
R
d2
S
C4
Transcribed Image Text:Institute of Quality & Reliability Subgroup size (n) 2 3 4 5 6 7 8 9 10 15 25 Table 8A - Variable Data X bar and R Charts Chart for Averages Control Limits Factor Tables of Constants for Control charts ref: AIAG manual for SPC X bar and s charts X bar and R Charts X bar and s Charts Chart for Ranges (R) A₂ d₂ 1.880 1.128 1.023 1.693 0.729 2.059 0.577 2.326 0.483 2.534 0.419 2.704 0.076 0.373 2.847 0.136 0.337 2.970 0.184 0.308 3.078 0.223 3.472 0.153 3.931 Divisors to Estimate Factors for Control Limits Ox = X D3 CLX = X CL S = S - - - Centerline CLx = CLR = R 0.223 0.347 0.459 Chart for Averages Chart for Standard Deviation (s) Divisors to Control Limits Factor D4 A3 3.267 2.659 2.574 1.954 2.282 1.628 2.114 1.427 2.004 1.287 1.924 1.864 1.816 1.777 1.653 1.541 estimate Factors for Control ox Limits C4 B4 0.7979 3.267 0.8862 2.568 0.9213 2.266 0.9400 2.089 0.9515 0.030 1.970 1.182 0.9594 0.118 1.882 1.099 0.9650 0.185 1.815 1.032 0.9693 0.239 1.761 0.975 0.9727 0.284 0.789 0.9823 0.428 0.606 0.9896 0.565 Control Limits UCL = UCLR=D&R UCL = X + A₂S UCL, = BAS =X+A₂R B3 LCL = X - A₂ R X LCLR = D₂R LCLX = X - A₂S LCL, = B35 1.716 1.572 1.435 6 x R d2 S C4
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