Supplier selection problem is an important issue in the manufacturing industry. The decision maker usually faces the problem of selecting the better supplier between two candidates. For most manufacturing factories, process yield is the fundamental criterion for supplier selection. The index Spk provides an exact measure on the process yield. However, the supplier selection problem based on index Spk has not been done.
In this thesis, we compared the performance of Spk2
-
Spk1 and Spk2/
Spk1 with four different bootstrap methods including the standard bootstrap (SB), the percentile bootstrap (PB), the biased-corrected percentile bootstrap (BCPB), and the bootstrap-t (BT) methods. In error probability analysis, we found that SB and BCPB methods have stable error probabilities for both difference and ratio test.PB and BCPB methods are much powerful under the same sample size in selection power analysis. Thus, the performance of BCPB method is better than the other three methods. Forpractitioner’sconvenience,the useful information about the sample size required with designated selection power based on the BCPB method was tabulated. After that, we investigated a real world case on the color filter manufacturing process, and demonstrated the applicability of the proposed method step by step in the end.
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1 1 1 1
Spk11 1 1 1
Cp11 1 1 1
Ca11 1 1 1
Spk23 .7 0 9 5 6 6 8 2 1 .8 5 4 7 8 3 4 9 1 .2 3 6 6 1 6 6 2 1
Cp21 /4 1 /2 3 /4 1
Ca2B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B o o ts tr ap
USL= 2 0 ,
LSL= 1 0 ,
d= 5 ,
m= 1 5
0 .0 5 3 6 7 0 .0 5 4 6 7 0 .0 6 5 0 0 0 .0 6 0 6 7 0 .0 5 3 3 3 0 .0 5 6 6 7 0 .0 6 5 6 7 0 .0 6 1 3 3 0 .0 5 3 0 0 0 .0 5 2 0 0 0 .0 6 5 0 0 0 .0 5 9 6 7 0 .0 5 0 6 7 0 .0 5 4 6 7 0 .0 5 6 6 7 0 .0 5 3 3 3 P
-0 .1 5 9 5 1 -0 .1 6 3 8 1 -0 .1 5 6 4 9 -0 .1 5 6 5 9 -0 .1 5 9 5 6 -0 .1 6 3 8 5 -0 .1 5 6 5 6 -0 .1 5 6 6 5 -0 .1 5 9 6 7 -0 .1 6 3 8 7 -0 .1 5 6 8 1 -0 .1 5 6 8 6 -0 .1 6 4 6 6 -0 .1 6 4 9 5 -0 .1 6 4 9 0 -0 .1 6 5 0 5 L B o u n d
0 .1 0 0 6 8 0 .1 0 3 4 3 0 .1 0 4 1 6 0 .1 0 2 9 8 0 .1 0 0 6 5 0 .1 0 3 4 8 0 .1 0 4 2 6 0 .1 0 2 9 9 0 .1 0 0 7 6 0 .1 0 3 4 5 0 .1 0 4 2 9 0 .1 0 3 0 5 0 .1 0 1 1 8 0 .1 0 3 7 0 0 .1 0 4 1 5 0 .1 0 3 0 5 S td
n= 1 0 0 (D if fe re n ce T es t)
0 .0 3 5 3 3 0 .0 5 5 6 7 0 .0 6 5 0 0 0 .0 5 1 6 7 0 .0 3 4 6 7 0 .0 5 6 6 7 0 .0 6 5 6 7 0 .0 5 1 3 3 0 .0 3 4 6 7 0 .0 5 2 6 7 0 .0 6 5 0 0 0 .0 5 1 3 3 0 .0 3 8 6 7 0 .0 5 5 6 7 0 .0 5 6 6 7 0 .0 4 9 0 0 P
0 .8 3 7 8 0 0 .8 5 6 6 3 0 .8 6 2 6 5 0 .8 5 3 8 4 0 .8 3 7 7 3 0 .8 5 6 5 3 0 .8 6 2 5 6 0 .8 5 3 7 8 0 .8 3 7 6 2 0 .8 5 6 4 9 0 .8 6 2 3 5 0 .8 5 3 5 9 0 .8 3 3 1 7 0 .8 5 4 7 5 0 .8 5 4 8 6 0 .8 4 5 9 6 L B o u n d
0 .0 8 5 0 5 0 .0 8 6 2 8 0 .0 8 7 1 5 0 .0 8 6 4 7 0 .0 8 4 9 8 0 .0 8 6 3 4 0 .0 8 7 1 9 0 .0 8 6 4 4 0 .0 8 5 0 9 0 .0 8 6 3 0 0 .0 8 7 2 5 0 .0 8 6 5 0 0 .0 8 5 9 2 0 .0 8 6 5 8 0 .0 8 6 7 9 0 .0 8 6 1 7 S td
n= 1 0 0 (R at io T es t) T ab le 1 2 . T h e er ro r p ro b a b ili ty o f fo u r b o o ts tr ap m et h o d s fo r th e d if fe re n ce an d ra tio st at is tic w ith 1 6 co m b in at io n s o f (
Cp1,
Ca1) an d (
Cp2,
Ca2) u n d er
Spk1=
Spk2= 1 .0 0 .
1 1 1 1
Spk11 .2 3 6 6 1 6 6 2 1 .2 3 6 6 1 6 6 2 1 .2 3 6 6 1 6 6 2 1 .2 3 6 6 1 6 6 2
Cp13 /4 3 /4 3 /4 3 /4
Ca11 1 1 1
Spk23 .7 0 9 5 6 6 8 2 1 .8 5 4 7 8 3 4 9 1 .2 3 6 6 1 6 6 2 1
Cp21 /4 1 /2 3 /4 1
Ca2B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B o o ts tr ap
USL= 2 0 ,
LSL= 1 0 ,
d= 5 ,
m= 1 5
0 .0 4 8 0 0 0 .0 5 4 0 0 0 .0 5 6 3 3 0 .0 5 3 3 3 0 .0 4 9 3 3 0 .0 5 3 0 0 0 .0 5 5 6 7 0 .0 5 3 3 3 0 .0 4 8 3 3 0 .0 5 3 0 0 0 .0 5 4 0 0 0 .0 5 2 6 7 0 .0 4 9 6 7 0 .0 5 6 3 3 0 .0 5 3 3 3 0 .0 5 0 3 3 P
-0 .1 6 1 4 5 -0 .1 6 1 8 2 -0 .1 6 1 5 7 -0 .1 6 1 7 3 -0 .1 6 1 4 6 -0 .1 6 1 7 2 -0 .1 6 1 6 9 -0 .1 6 1 8 3 -0 .1 6 1 5 5 -0 .1 6 1 9 1 -0 .1 6 1 7 9 -0 .1 6 1 9 4 -0 .1 6 6 5 6 -0 .1 6 2 8 1 -0 .1 7 0 0 4 -0 .1 7 0 2 7 L B o u n d
0 .0 9 8 6 5 0 .1 0 0 9 1 0 .1 0 2 2 7 0 .1 0 1 1 2 0 .0 9 8 6 7 0 .1 0 1 1 4 0 .1 0 2 4 0 0 .1 0 1 1 2 0 .0 9 8 6 9 0 .1 0 0 9 8 0 .1 0 2 4 0 0 .1 0 1 1 9 0 .0 9 9 5 5 0 .1 0 1 8 3 0 .1 0 3 0 2 0 .1 0 1 8 4 S td
n= 1 0 0 (D if fe re n ce T es t)
0 .0 3 3 0 0 0 .0 5 5 3 3 0 .0 5 6 3 3 0 .0 4 3 3 3 0 .0 3 5 3 3 0 .0 5 5 0 0 0 .0 5 5 6 7 0 .0 4 4 0 0 0 .0 3 5 3 3 0 .0 5 4 3 3 0 .0 5 4 0 0 0 .0 4 5 3 3 0 .0 3 3 6 7 0 .0 5 7 0 0 0 .0 5 3 3 3 0 .0 4 2 3 3 P
0 .8 3 7 2 2 0 .8 5 8 1 2 0 .8 5 8 3 5 0 .8 4 9 7 1 0 .8 3 7 1 8 0 .8 5 8 1 3 0 .8 5 8 2 3 0 .8 4 9 6 4 0 .8 3 7 1 0 0 .8 5 7 9 4 0 .8 5 8 1 3 0 .8 4 9 5 3 0 .8 3 2 7 3 0 .8 5 6 3 9 0 .8 5 0 5 8 0 .8 4 1 8 7 L B o u n d
0 .0 8 3 1 5 0 .0 8 4 5 1 0 .0 8 4 9 3 0 .0 8 4 2 6 0 .0 8 3 0 9 0 .0 8 4 7 6 0 .0 8 4 9 9 0 .0 8 4 2 2 0 .0 8 3 1 9 0 .0 8 4 7 0 0 .0 8 5 0 5 0 .0 8 4 3 4 0 .0 8 3 8 5 0 .0 8 5 5 6 0 .0 8 5 2 7 0 .0 8 4 6 2 S td
n= 1 0 0 (R at io T es t)
1 1 1 1
Spk11 .8 5 4 7 8 3 4 9 1 .8 5 4 7 8 3 4 9 1 .8 5 4 7 8 3 4 9 1 .8 5 4 7 8 3 4 9
Cp11 /2 1 /2 1 /2 1 /2
Ca11 1 1 1
Spk23 .7 0 9 5 6 6 8 2 1 .8 5 4 7 8 3 4 9 1 .2 3 6 6 1 6 6 2 1
Cp21 /4 1 /2 3 /4 1
Ca2B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B o o ts tr ap
USL= 2 0 ,
LSL= 1 0 ,
d= 5 ,
m= 1 5
0 .0 4 9 6 7 0 .0 5 4 0 0 0 .0 5 5 0 0 0 .0 5 4 0 0 0 .0 5 0 0 0 0 .0 5 5 0 0 0 .0 5 6 3 3 0 .0 5 4 3 3 0 .0 4 8 3 3 0 .0 5 3 3 3 0 .0 5 7 3 3 0 .0 5 2 3 3 0 .0 4 8 6 7 0 .0 5 7 3 3 0 .0 5 2 3 3 0 .0 4 9 0 0 P
-0 .1 6 1 4 8 -0 .1 6 1 7 9 -0 .1 6 1 6 8 -0 .1 6 1 8 2 -0 .1 6 1 3 9 -0 .1 6 1 6 1 -0 .1 6 1 6 6 -0 .1 6 1 8 5 -0 .1 6 1 5 9 -0 .1 6 1 7 2 -0 .1 6 1 9 0 -0 .1 6 2 0 4 -0 .1 6 6 5 3 -0 .1 6 2 8 4 -0 .1 7 0 1 0 -0 .1 7 0 3 3 L B o u n d
0 .0 9 8 4 6 0 .1 0 1 0 4 0 .1 0 2 4 3 0 .1 0 1 0 7 0 .0 9 8 6 1 0 .1 0 0 9 0 0 .1 0 2 3 8 0 .1 0 1 1 4 0 .0 9 8 6 7 0 .1 0 1 0 4 0 .1 0 2 4 7 0 .1 0 1 1 8 0 .0 9 9 4 4 0 .1 0 1 9 7 0 .1 0 3 0 5 0 .1 0 1 7 2 S td
n= 1 0 0 (D if fe re n ce T es t)
0 .0 3 4 6 7 0 .0 5 4 6 7 0 .0 5 5 0 0 0 .0 4 5 0 0 0 .0 3 4 3 3 0 .0 5 5 6 7 0 .0 5 6 3 3 0 .0 4 5 0 0 0 .0 3 5 3 3 0 .0 5 4 0 0 0 .0 5 7 3 3 0 .0 4 5 0 0 0 .0 3 4 6 7 0 .0 5 8 6 7 0 .0 5 2 3 3 0 .0 4 2 3 3 P
0 .8 3 7 2 0 0 .8 5 8 1 2 0 .8 5 8 2 9 0 .8 4 9 6 6 0 .8 3 7 3 4 0 .8 5 8 2 6 0 .8 5 8 2 8 0 .8 4 9 6 3 0 .8 3 7 0 9 0 .8 5 8 1 3 0 .8 5 8 0 9 0 .8 4 9 4 5 0 .8 3 2 7 3 0 .8 5 6 3 7 0 .8 5 0 5 3 0 .8 4 1 8 0 L B o u n d
0 .0 8 2 9 7 0 .0 8 4 6 7 0 .0 8 5 0 1 0 .0 8 4 2 3 0 .0 8 3 1 1 0 .0 8 4 6 6 0 .0 8 5 0 2 0 .0 8 4 2 8 0 .0 8 3 1 8 0 .0 8 4 6 2 0 .0 8 5 0 7 0 .0 8 4 3 1 0 .0 8 3 8 0 0 .0 8 5 6 7 0 .0 8 5 2 6 0 .0 8 4 4 8 S td
n= 1 0 0 (R at io T es t)
1 1 1 1
Spk13 .7 0 9 5 6 6 8 2 3 .7 0 9 5 6 6 8 2 3 .7 0 9 5 6 6 8 2 3 .7 0 9 5 6 6 8 2
Cp11 /4 1 /4 1 /4 1 /4
Ca11 1 1 1
Spk23 .7 0 9 5 6 6 8 2 1 .8 5 4 7 8 3 4 9 1 .2 3 6 6 1 6 6 2 1
Cp21 /4 1 /2 3 /4 1
Ca2B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B T B C P B P B S B B o o ts tr ap
USL= 2 0 ,
LSL= 1 0 ,
d= 5 ,
m= 1 5
0 .0 4 8 3 3 0 .0 5 1 6 7 0 .0 5 4 6 7 0 .0 5 2 3 3 0 .0 5 1 0 0 0 .0 5 1 3 3 0 .0 5 7 0 0 0 .0 5 3 0 0 0 .0 4 9 0 0 0 .0 5 2 3 3 0 .0 5 4 3 3 0 .0 5 3 6 7 0 .0 4 7 6 7 0 .0 5 7 3 3 0 .0 5 1 6 7 0 .0 4 9 0 0 P
-0 .1 6 1 5 0 -0 .1 6 1 6 7 -0 .1 6 1 6 7 -0 .1 6 1 8 8 -0 .1 6 1 4 7 -0 .1 6 1 7 4 -0 .1 6 1 6 7 -0 .1 6 1 8 8 -0 .1 6 1 6 2 -0 .1 6 1 5 8 -0 .1 6 1 7 0 -0 .1 6 1 9 6 -0 .1 6 6 5 6 -0 .1 6 2 7 9 -0 .1 7 0 0 2 -0 .1 7 0 2 3 L B o u n d
0 .0 9 8 6 3 0 .1 0 1 0 0 0 .1 0 2 4 4 0 .1 0 1 1 6 0 .0 9 8 4 9 0 .1 0 0 8 5 0 .1 0 2 4 2 0 .1 0 1 1 3 0 .0 9 8 6 2 0 .1 0 0 8 9 0 .1 0 2 4 1 0 .1 0 1 1 8 0 .0 9 9 4 7 0 .1 0 1 9 5 0 .1 0 2 9 3 0 .1 0 1 6 8 S td
n= 1 0 0 (D if fe re n ce T es t)
0 .0 3 4 6 7 0 .0 5 4 6 7 0 .0 5 4 6 7 0 .0 4 4 6 7 0 .0 3 4 3 3 0 .0 5 4 0 0 0 .0 5 7 0 0 0 .0 4 5 3 3 0 .0 3 5 3 3 0 .0 5 3 3 3 0 .0 5 4 3 3 0 .0 4 4 0 0 0 .0 3 4 6 7 0 .0 5 7 6 7 0 .0 5 1 6 7 0 .0 4 1 6 7 P
0 .8 3 7 2 1 0 .8 5 8 1 7 0 .8 5 8 2 3 0 .8 4 9 6 0 0 .8 3 7 2 3 0 .8 5 8 1 4 0 .8 5 8 2 6 0 .8 4 9 5 9 0 .8 3 7 1 4 0 .8 5 8 2 7 0 .8 5 8 2 4 0 .8 4 9 5 2 0 .8 3 2 7 6 0 .8 5 6 4 3 0 .8 5 0 6 2 0 .8 4 1 9 0 L B o u n d
0 .0 8 3 1 6 0 .0 8 4 6 6 . 0 .0 8 5 0 7 0 .0 8 4 3 1 0 .0 8 3 0 4 0 .0 8 4 5 3 0 .0 8 5 0 5 0 .0 8 4 3 1 0 .0 8 3 1 6 0 .0 8 4 5 8 0 .0 8 5 0 4 0 .0 8 4 3 2 0 .0 8 3 8 6 0 .0 8 5 7 0 0 .0 8 5 2 5 0 .0 8 4 4 9 S td
n= 1 0 0 (R at io T es t)
Table 13. Selection power of the four bootstrap methods for difference statistic with sample size n = 30(10)200.
S
pk1 1 1 1 1 1 1 1 1 1 1n
S
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.07467 0.11967 0.16467 0.21033 0.26133 0.30167 0.32867 0.35700 0.36100 0.36167 PB 0.10067 0.15900 0.22267 0.29000 0.36367 0.43733 0.51933 0.60000 0.66667 0.72967 BCPB 0.09433 0.14833 0.21000 0.27867 0.35200 0.42633 0.50700 0.58633 0.65900 0.71800 30
BT 0.06567 0.09767 0.14000 0.18433 0.23633 0.27500 0.30100 0.33000 0.33467 0.34300 SB 0.09067 0.14833 0.22067 0.30367 0.38867 0.46300 0.53133 0.58800 0.62167 0.63500 PB 0.10333 0.16367 0.24233 0.33033 0.42700 0.51800 0.61033 0.68600 0.76167 0.82267 BCPB 0.09800 0.15900 0.23700 0.32667 0.41367 0.51033 0.60333 0.67600 0.75300 0.81733 40
BT 0.08100 0.13300 0.19867 0.27700 0.35867 0.43700 0.50567 0.55833 0.59400 0.61533 SB 0.09200 0.16700 0.25133 0.34500 0.45600 0.55767 0.64500 0.72233 0.78400 0.80867
PB 0.10600 0.17833 0.26500 0.36733 0.47700 0.58233 0.67400 0.76033 0.83200 0.88000 BCPB 0.09833 0.17333 0.26033 0.35867 0.46500 0.57533 0.66767 0.75600 0.82667 0.87600 50
BT 0.08267 0.15200 0.23400 0.31933 0.42867 0.52867 0.61600 0.69267 0.76700 0.79367 SB 0.10333 0.19033 0.29300 0.39533 0.51700 0.62033 0.73133 0.80800 0.86400 0.90367
PB 0.11400 0.19933 0.30067 0.41367 0.52900 0.63567 0.74700 0.82500 0.88567 0.93167 BCPB 0.11100 0.20067 0.29767 0.40500 0.52267 0.63233 0.73867 0.82000 0.88000 0.92967 60
BT 0.09600 0.17667 0.27267 0.37767 0.49667 0.60200 0.70833 0.79067 0.85233 0.89400 SB 0.10833 0.19967 0.30167 0.43267 0.56367 0.70133 0.79933 0.87167 0.92200 0.95100 PB 0.11400 0.20800 0.31100 0.44367 0.57600 0.71233 0.81000 0.88233 0.93067 0.95667 BCPB 0.11133 0.20400 0.30867 0.43733 0.57100 0.70867 0.80367 0.87900 0.92933 0.95700 70
BT 0.10167 0.18567 0.29133 0.40767 0.54733 0.68933 0.78433 0.86267 0.91367 0.94900 SB 0.11000 0.21000 0.34500 0.49133 0.63300 0.75533 0.84067 0.90200 0.94300 0.97033
PB 0.11600 0.21900 0.35700 0.50233 0.64400 0.76167 0.84800 0.90700 0.94867 0.97567 BCPB 0.11367 0.21967 0.35200 0.49800 0.6420 0.76200 0.84767 0.90600 0.94833 0.97533 80
BT 0.10600 0.20100 0.32767 0.47833 0.61767 0.74267 0.83233 0.89500 0.93800 0.96800 SB 0.11700 0.23267 0.36000 0.51600 0.66567 0.78567 0.87267 0.92833 0.96367 0.98233
PB 0.12233 0.23867 0.37000 0.52433 0.67167 0.79367 0.88000 0.93233 0.96433 0.98367 BCPB 0.12067 0.23467 0.36967 0.52233 0.66967 0.78733 0.87633 0.92733 0.96333 0.98267 90
BT 0.11333 0.21933 0.34833 0.50400 0.65800 0.77600 0.86567 0.92500 0.96100 0.98100 SB 0.12567 0.24400 0.39567 0.57167 0.72767 0.84167 0.91400 0.95633 0.98067 0.99067 PB 0.13000 0.24967 0.40300 0.57967 0.73367 0.84433 0.91967 0.95800 0.98133 0.99167 BCPB 0.12800 0.24633 0.40167 0.57100 0.73167 0.84167 0.91933 0.95667 0.98000 0.99200 100
BT 0.11900 0.23500 0.38733 0.56300 0.71867 0.83300 0.91000 0.95233 0.97933 0.99000
S
pk1 1 1 1 1 1 1 1 1 1 1 nS
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.13000 0.27033 0.44200 0.62133 0.76167 0.87000 0.93567 0.97333 0.98933 0.99667 PB 0.13200 0.27700 0.44667 0.62833 0.76633 0.87433 0.93900 0.97333 0.99100 0.99667 BCPB 0.13200 0.27133 0.44700 0.62100 0.76633 0.87200 0.93867 0.97333 0.98933 0.99700 110
BT 0.12567 0.26000 0.42667 0.61633 0.75300 0.86500 0.93200 0.97167 0.98833 0.99700 SB 0.13033 0.26633 0.44900 0.63033 0.77800 0.87800 0.94700 0.97700 0.98900 0.99733 PB 0.13367 0.26967 0.45300 0.63500 0.78233 0.88433 0.94900 0.97767 0.98867 0.99700
BCPB 0.13200 0.26867 0.45000 0.63300 0.78033 0.88500 0.94767 0.97700 0.98867 0.99767 120
BT 0.12700 0.26133 0.43667 0.62267 0.76700 0.87633 0.94500 0.97467 0.98733 0.99733 SB 0.14067 0.29600 0.47900 0.65967 0.81467 0.90700 0.96033 0.98600 0.99400 0.99867 PB 0.14367 0.30300 0.48600 0.66667 0.81633 0.91133 0.96200 0.98667 0.99533 0.99867
BCPB 0.14300 0.30000 0.47733 0.66100 0.81633 0.90800 0.96067 0.98633 0.99533 0.99867 130
BT 0.13800 0.28767 0.47200 0.65300 0.80800 0.90133 0.95867 0.98533 0.99467 0.99867 SB 0.14233 0.31300 0.51133 0.70433 0.84600 0.92967 0.97000 0.98867 0.99700 0.99933 PB 0.14667 0.31633 0.51800 0.71100 0.85267 0.93167 0.97267 0.98933 0.99767 0.99933 BCPB 0.14833 0.31567 0.51600 0.70733 0.85167 0.92967 0.97233 0.98933 0.99767 0.99933 140
BT 0.13667 0.30700 0.50367 0.69567 0.83867 0.92500 0.96900 0.98800 0.99733 0.99933 SB 0.15133 0.31600 0.53033 0.72433 0.86900 0.94267 0.97700 0.99233 0.99833 0.99933 PB 0.15467 0.32033 0.53267 0.73067 0.87000 0.94533 0.97900 0.99300 0.99833 0.99933
BCPB 0.15400 0.31800 0.53200 0.72933 0.86833 0.94533 0.97800 0.99267 0.99833 0.99933 150
BT 0.15100 0.31000 0.52333 0.72067 0.86567 0.94167 0.97567 0.99233 0.99833 0.99933 SB 0.15167 0.32600 0.52800 0.73167 0.86867 0.94933 0.98100 0.99500 0.99900 1.00000 PB 0.15700 0.33167 0.53467 0.73633 0.87100 0.95267 0.98133 0.99467 0.99900 1.00000
BCPB 0.15600 0.33167 0.53200 0.73733 0.87100 0.95233 0.98233 0.99467 0.99900 1.00000 160
BT 0.14800 0.32233 0.52067 0.72733 0.86667 0.94833 0.98033 0.99467 0.99900 1.00000 SB 0.16500 0.34467 0.56933 0.77000 0.89200 0.96067 0.99000 0.99800 0.99967 1.00000 PB 0.16700 0.34733 0.57167 0.77267 0.89400 0.96233 0.99067 0.99800 0.99967 1.00000 BCPB 0.16567 0.34567 0.56967 0.77033 0.89467 0.96200 0.98900 0.99833 0.99967 1.00000 170
BT 0.16133 0.34000 0.55933 0.76200 0.89300 0.96167 0.98933 0.99767 0.99967 1.00000 SB 0.17500 0.37333 0.60000 0.78233 0.90867 0.96733 0.99067 0.99833 0.99933 0.99967 PB 0.17700 0.37700 0.60567 0.78867 0.91000 0.96833 0.99067 0.99833 0.99933 1.00000
BCPB 0.17467 0.37467 0.60467 0.78633 0.91067 0.97133 0.99167 0.99833 0.99933 1.00000 180
BT 0.17067 0.36900 0.59333 0.77567 0.90700 0.96667 0.99067 0.99800 0.99933 0.99967
S
pk1 1 1 1 1 1 1 1 1 1 1 nS
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.17300 0.36667 0.62100 0.80633 0.92400 0.97267 0.99367 0.99900 0.99967 0.99967 PB 0.17633 0.37100 0.62600 0.80933 0.92633 0.97400 0.99367 0.99900 0.99967 0.99967 BCPB 0.17367 0.36800 0.61967 0.80900 0.92600 0.97133 0.99433 0.99900 0.99967 0.99967 190
BT 0.16667 0.36100 0.61033 0.80667 0.92433 0.97133 0.99233 0.99867 0.99967 0.99967 SB 0.18500 0.39133 0.63233 0.82867 0.92967 0.98267 0.99467 0.99833 1.00000 1.00000
PB 0.18800 0.39667 0.63300 0.83167 0.93233 0.98233 0.99467 0.99833 1.00000 1.00000 BCPB 0.18900 0.39567 0.63267 0.83333 0.93267 0.98233 0.99467 0.99833 1.00000 1.00000 200
BT 0.18067 0.38400 0.62667 0.82400 0.93033 0.98233 0.99467 0.99833 1.00000 1.00000
Table 14. Selection power of the four bootstrap methods for ratio statistic with sample size n = 30(10)200.
S
pk1 1 1 1 1 1 1 1 1 1 1n
S
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.06033 0.08933 0.12967 0.17767 0.22200 0.25667 0.28700 0.31000 0.32333 0.32600
PB 0.10067 0.15900 0.22267 0.29000 0.36367 0.43733 0.51933 0.60000 0.66667 0.72967 BCPB 0.09600 0.15067 0.21367 0.28133 0.35533 0.43233 0.51067 0.59167 0.66233 0.72333 30
BT 0.03367 0.05400 0.07933 0.10900 0.14967 0.18267 0.20333 0.22767 0.24467 0.26100 SB 0.06967 0.12333 0.18700 0.26300 0.34300 0.41367 0.48700 0.54567 0.57967 0.60133 PB 0.10333 0.16367 0.24233 0.33033 0.42700 0.51800 0.61033 0.68600 0.76167 0.82267 BCPB 0.09967 0.16167 0.23933 0.33067 0.41833 0.51567 0.60700 0.68100 0.75900 0.81967 40
BT 0.04500 0.07733 0.12900 0.18733 0.25400 0.32600 0.38800 0.45600 0.49400 0.52167 SB 0.07467 0.13900 0.21900 0.30400 0.41100 0.51300 0.60567 0.67733 0.75000 0.78300
PB 0.10600 0.17833 0.26500 0.36733 0.47700 0.58233 0.67400 0.76033 0.83200 0.88000 BCPB 0.10033 0.17467 0.26267 0.36333 0.47033 0.57767 0.67067 0.75967 0.82900 0.87700 50
BT 0.05100 0.09400 0.16200 0.24000 0.31633 0.42300 0.51867 0.59300 0.66367 0.72367 SB 0.08700 0.16067 0.25500 0.36367 0.47600 0.58133 0.69167 0.77433 0.83733 0.88433
PB 0.11400 0.19933 0.30067 0.41367 0.52900 0.63567 0.74700 0.82500 0.88567 0.93167 BCPB 0.11200 0.20000 0.30000 0.40867 0.52500 0.63500 0.74033 0.82133 0.88333 0.93033 60
BT 0.05733 0.11633 0.20300 0.29800 0.39833 0.50933 0.61400 0.70900 0.78467 0.83633 SB 0.09300 0.17300 0.27667 0.39667 0.52767 0.66200 0.76800 0.85067 0.90467 0.94133 PB 0.11400 0.20800 0.31100 0.44367 0.57600 0.71233 0.81000 0.88233 0.93067 0.95667 BCPB 0.11267 0.20567 0.30967 0.43933 0.57567 0.71033 0.80467 0.87933 0.92933 0.95700 70
BT 0.06633 0.13000 0.22333 0.32900 0.44800 0.58367 0.70400 0.79933 0.86667 0.91467 SB 0.09800 0.18933 0.31100 0.45167 0.59733 0.72167 0.81933 0.88533 0.93367 0.96400
PB 0.11600 0.21900 0.35700 0.50233 0.64400 0.76167 0.84800 0.90700 0.94867 0.97567 BCPB 0.11467 0.21933 0.35267 0.50300 0.64500 0.76400 0.84967 0.90733 0.94967 0.97533 80
BT 0.07200 0.14433 0.25067 0.39000 0.53233 0.66000 0.77067 0.84900 0.90600 0.94467 SB 0.10233 0.20233 0.33300 0.48033 0.63200 0.75733 0.85433 0.91667 0.95400 0.97833
PB 0.12233 0.23867 0.37000 0.52433 0.67167 0.79367 0.88000 0.93233 0.96433 0.98367 BCPB 0.12000 0.23500 0.37133 0.52400 0.67300 0.78900 0.87733 0.92733 0.96433 0.98300 90
BT 0.07633 0.16033 0.28467 0.41667 0.56733 0.71067 0.81100 0.88833 0.93767 0.96767 SB 0.11167 0.22100 0.36333 0.53600 0.70100 0.81933 0.90000 0.94667 0.97633 0.98967 PB 0.13000 0.24967 0.40300 0.57967 0.73367 0.84433 0.91967 0.95800 0.98133 0.99167 BCPB 0.13067 0.24733 0.40233 0.57133 0.73433 0.84133 0.91933 0.95633 0.98067 0.99233 100
BT 0.08533 0.18133 0.31133 0.47067 0.64133 0.77067 0.87100 0.93000 0.96500 0.98567
S
pk1 1 1 1 1 1 1 1 1 1 1 nS
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.11500 0.24067 0.40933 0.58933 0.73600 0.85033 0.92233 0.96767 0.98667 0.99500 PB 0.13200 0.27700 0.44667 0.62833 0.76633 0.87433 0.93900 0.97333 0.99100 0.99667 BCPB 0.13300 0.27500 0.45000 0.62400 0.76733 0.87333 0.93867 0.97400 0.99000 0.99700 110
BT 0.09233 0.19833 0.35533 0.52867 0.68567 0.80800 0.90300 0.95567 0.98000 0.99267 SB 0.11500 0.24067 0.41833 0.59867 0.75367 0.86400 0.94000 0.97167 0.98567 0.99567 PB 0.13367 0.26967 0.45300 0.63500 0.78233 0.88433 0.94900 0.97767 0.98867 0.99700
BCPB 0.13300 0.26800 0.45167 0.63400 0.78000 0.88600 0.94833 0.97733 0.98833 0.99767 120
BT 0.09033 0.19967 0.36433 0.54367 0.71100 0.82467 0.91933 0.96133 0.98133 0.99167 SB 0.12733 0.27133 0.45167 0.63467 0.79167 0.89233 0.95333 0.98333 0.99367 0.99833 PB 0.14367 0.30300 0.48600 0.66667 0.81633 0.91133 0.96200 0.98667 0.99533 0.99867
BCPB 0.14333 0.30200 0.47767 0.66300 0.81667 0.91000 0.96100 0.98700 0.99567 0.99867 130
BT 0.10167 0.22900 0.40033 0.57700 0.75467 0.86867 0.93767 0.97567 0.99067 0.99733 SB 0.12700 0.29100 0.47967 0.67967 0.82733 0.92100 0.96567 0.98600 0.99633 0.99900 PB 0.14667 0.31633 0.51800 0.71100 0.85267 0.93167 0.97267 0.98933 0.99767 0.99933 BCPB 0.14967 0.31867 0.51800 0.70933 0.85300 0.93000 0.97267 0.98900 0.99767 0.99933 140
BT 0.10267 0.24567 0.42800 0.63600 0.79367 0.90433 0.95533 0.98133 0.99300 0.99867 SB 0.13700 0.29500 0.50533 0.70533 0.84933 0.93633 0.97267 0.99200 0.99700 0.99933 PB 0.15467 0.32033 0.53267 0.73067 0.87000 0.94533 0.97900 0.99300 0.99833 0.99933
BCPB 0.15367 0.31933 0.53233 0.72833 0.86967 0.94467 0.97867 0.99233 0.99833 0.99933 150
BT 0.11333 0.25233 0.45467 0.66567 0.82200 0.91867 0.96467 0.98833 0.99433 0.99933 SB 0.14000 0.30400 0.50533 0.71100 0.85633 0.94333 0.97800 0.99367 0.99833 0.99967 PB 0.15700 0.33167 0.53467 0.73633 0.87100 0.95267 0.98133 0.99467 0.99900 1.00000
BCPB 0.15700 0.33200 0.53267 0.73633 0.87100 0.95200 0.98300 0.99500 0.99933 1.00000 160
BT 0.11600 0.26100 0.46367 0.66500 0.83000 0.92600 0.97400 0.99167 0.99800 0.99967 SB 0.15033 0.32300 0.54433 0.74500 0.88067 0.95333 0.98667 0.99733 0.99967 1.00000 PB 0.16700 0.34733 0.57167 0.77267 0.89400 0.96233 0.99067 0.99800 0.99967 1.00000 BCPB 0.16667 0.34600 0.56967 0.77200 0.89567 0.96233 0.98900 0.99833 0.99967 1.00000 170
BT 0.12667 0.28933 0.49500 0.71167 0.85500 0.94033 0.98067 0.99667 0.99933 1.00000 SB 0.15833 0.35167 0.57767 0.76367 0.89800 0.96133 0.98967 0.99767 0.99933 0.99967 PB 0.17700 0.37700 0.60567 0.78867 0.91000 0.96833 0.99067 0.99833 0.99933 1.00000
BCPB 0.17533 0.37533 0.60433 0.78800 0.91033 0.97133 0.99167 0.99833 0.99933 1.00000 180
BT 0.13367 0.31100 0.53800 0.73300 0.87667 0.95100 0.98567 0.99700 0.99900 0.99967
S
pk1 1 1 1 1 1 1 1 1 1 1 nS
pk2 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5SB 0.15900 0.34333 0.59067 0.79300 0.91600 0.96900 0.99167 0.99833 0.99967 0.99967 PB 0.17633 0.37100 0.62600 0.80933 0.92633 0.97400 0.99367 0.99900 0.99967 0.99967 BCPB 0.17200 0.36833 0.62100 0.81000 0.92667 0.97233 0.99433 0.99900 0.99967 0.99967 190
BT 0.13433 0.30900 0.55467 0.76400 0.89467 0.96267 0.99033 0.99767 0.99967 0.99967 SB 0.16733 0.37000 0.60800 0.81467 0.92267 0.97900 0.99367 0.99800 0.99967 1.00000
PB 0.18800 0.39667 0.63300 0.83167 0.93233 0.98233 0.99467 0.99833 1.00000 1.00000 BCPB 0.18867 0.39533 0.63367 0.83233 0.93333 0.98300 0.99467 0.99833 1.00000 1.00000 200
BT 0.14333 0.33433 0.57067 0.78433 0.90933 0.96967 0.99367 0.99733 0.99900 1.00000
Figure 13. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.05
. Figure 14. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.05
.Figure 15. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.10
. Figure 16. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.10
.Figure 17. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.15
. Figure 18. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.15
.Figure 19. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.20
. Figure 20. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.20
.Figure 21. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.25
. Figure 22. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.25
.Figure 23. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.30
. Figure 24. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.30
.Figure 25. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.35
. Figure 26. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.35
.Figure 27. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.40
. Figure 28. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.40
.Figure 29. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.45
. Figure 30. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.45
.Figure 31. The difference statistic with sample
size n = 30(10)200, Spk1
1.00
,Spk2 1.50
. Figure 32. The ratio statistic with sample size n = 30(10)200, Spk1 1.00
,Spk2 1.50
.Table 15. Sample data for supplier I.
0.61353 0.61552 0.61328 0.59529 0.62445 0.63116 0.65012 0.62375 0.65633 0.64408 0.59435 0.59097 0.62614 0.60378 0.67782 0.61163 0.64556 0.63773 0.62692 0.60146 0.63778 0.62606 0.60157 0.64230 0.60499 0.64875 0.62426 0.62012 0.58552 0.61908 0.65880 0.62996 0.64063 0.60310 0.65685 0.66685 0.66855 0.64960 0.59610 0.63888 0.63341 0.61983 0.66149 0.61941 0.61144 0.64516 0.61356 0.65074 0.66107 0.61672 0.62376 0.61054 0.62855 0.64133 0.64026 0.63572 0.65403 0.64628 0.64720 0.62483 0.63104 0.62912 0.60898 0.63509 0.64023 0.65852 0.65104 0.59553 0.66196 0.68931 0.60724 0.68533 0.62786 0.61883 0.63945 0.64187 0.61097 0.59440 0.62939 0.61212 0.62433 0.63652 0.62281 0.63842 0.64935 0.58631 0.63108 0.62256 0.63475 0.64225 0.63025 0.61676 0.62397 0.61954 0.64509 0.60708 0.64991 0.56073 0.62406 0.62531 0.64096 0.62553 0.65768 0.62151 0.65017 0.61804 0.62479 0.60577 0.63215 0.67966 0.63620 0.59486 0.61919 0.62155 0.69332 0.66096 0.62870 0.61128 0.64926 0.60463 0.65656 0.59263 0.58933 0.64777 0.59966 0.63912 0.61977 0.65170 0.62790 0.64034 0.62508 0.63078 0.59323 0.62059 0.60731 0.59209 0.63595 0.62983 0.65414 0.63975 0.59757 0.64739 0.63923 0.60957 0.64516 0.65291 0.64188 0.65894 0.65173 0.65041 0.65713 0.64089 0.61251 0.64204 0.60451
Table 16. Sample data for supplier II.
0.63319 0.59254 0.62833 0.62404 0.62587 0.63986 0.62282 0.63197 0.65559 0.62487 0.63279 0.62496 0.64915 0.66193 0.67187 0.61781 0.67295 0.62161 0.63615 0.62000 0.59515 0.66258 0.61672 0.61852 0.63554 0.63414 0.63669 0.65318 0.61482 0.60397 0.63083 0.62965 0.63395 0.63709 0.65171 0.64944 0.62016 0.62190 0.60291 0.61077 0.62443 0.63228 0.63950 0.61063 0.60707 0.63941 0.63165 0.63531 0.61413 0.64547 0.60578 0.60800 0.62913 0.64539 0.62872 0.64082 0.63443 0.67411 0.64527 0.65435 0.63899 0.62116 0.59434 0.63356 0.69966 0.62779 0.62603 0.65974 0.63938 0.60937 0.63111 0.64093 0.62817 0.63136 0.61867 0.65489 0.65627 0.63971 0.67058 0.63195 0.64312 0.64829 0.66236 0.62152 0.63707 0.62309 0.62204 0.61500 0.62732 0.64333 0.63400 0.61434 0.62025 0.62176 0.63370 0.63883 0.66446 0.61982 0.65033 0.62862 0.59215 0.63196 0.62114 0.63214 0.59213 0.64364 0.63453 0.64603 0.63416 0.62022 0.66804 0.61699 0.63538 0.65878 0.63233 0.64984 0.63401 0.64590 0.65861 0.63060 0.62151 0.64389 0.62741 0.62732 0.63666 0.64178 0.66165 0.64287 0.66001 0.61175 0.63604 0.63689 0.62332 0.63232 0.62386 0.65078 0.61185 0.64486 0.60997 0.62715 0.66274 0.64410 0.61564 0.62236 0.64297 0.62569 0.64367 0.63724 0.61243 0.62582 0.62871 0.64923 0.62483 0.63170 0.63772