Data Analysis and Supplier Selection - Application Example : PDP Producer with ITO Glass Suppli

6. Application Example : PDP Producer with ITO Glass Supplier

6.1. Data Analysis and Supplier Selection

LSL =

1100 1300

T =

Å.

6.1. Data Analysis and Supplier Selection

For the step1 of supplier selection, the practitioner should input the minimum requirement of and the minimum difference for two candidates. And in the step2, we decided the sample size based on the minimum requirement, the minimum difference and the selection power we need. In this application, the upper specification limit was 1500 Å, the lower specification limit was 1100 Å and the target value was 1300 Å. The minimum requirement for ITO product was 0.8 and the minimum difference of is 0.06 between two candidates with selection power 0.95.

By checking the preset table (Tables 7-8) with the data, we had to take 301 samples for the difference statistics and 282 samples for the ratio statistics. In the case, we took 310 samples for S1 and S2 respectively.

Y

Figure 9. Histogram of data S1. Figure 10. Histogram of data S2.

Figure 11. Normal probability plot for S1.

Figure 12. Normal probability plot for S2.

We display the histogram of 310 samples for S1 and S2 in Figures 9-10 and the normal probability in Figures 11-12 (the data of two suppliers were tabulated in Tables 15-16 in Appendix C). Kolmogorov-Smirnov test was also used to check whether the two suppliers’ data is normal in the step3. The statistic d for supplier 1 was 0.02916 and for supplier 2 is 0.02879. Because of the p-value with two suppliers are greater than 0.05, we didn’t reject the null hypothesis that the data was normally distributed. So we considered that the sample data for two suppliers could be regarded as taken form normal processes. Then the sample means, sample standard deviations and sample estimators for S1 and S2 were calculated and summarized in Table 9. Based on the selection procedure of step4, we executed the Matlab program to obtain the LCB for difference between two suppliers is

- and the LCB for ratio is /

Y

ˆ2

Y

q ˆ₁

Y = 0.021857

q ˆ₂

Y

q ˆ₁

Y

q =1.0262. Consequently, we could reject the null hypothesis and concluded that the new supplier S2 is more capable than the present supplier.

Table 9. The calculated sample statistics for two suppliers.

Supplier

X

Y

S1 1272.906 85.28163 0.81306

S2 1346.148 58.01418 0.86289

7. Conclusions

Supplier selection is more and more important in today’s modern quality improvement theory and customers consider many factors before they choose the supplier. Quality yield is a flexible index because it compares the quality of different characteristics of a product on a single percentage scale, and indicates how close a product comes to meeting 100% customer satisfaction in quality. Unlike the traditional process capability indices, the normality assumption isn’t needed in using quality yield. We use the quality yield to compare two suppliers and give customers a reference of supplier’s information for process capability in this study. ^q

Y

In this research, we first reviewed the process capability indices, process yield, process loss and quality yield. By comparing these indices, we indicated the advantages of and applied it in the supplier selection. Because the sample distributions of the difference and the ratio in are mathematically intractable, the nonparametric is computationally intensive but an effective estimation bootstrap method is applied to two Q-yield measures

Y

ˆ2

Y

q ˆ₁

Y

− and to compare the error probability and the selection power. In the error test, we compared the error mean, error standard deviation and occurrences out of the 25 cases. The selection power was compared in the designated sample size with on-target case we selected.

We finally chose the BCPB method after comparing the performance of simulation in four methods. For convenience of application, we used this method and tabulate the sample size required for various designated selection power with our selecting and showed the supplier selection steps. Then we presented a real example on the ITO glass manufacturing process to illustrate the sample size information and distinguish which supplier had a better process capability with these steps. In this paper, we did these works under the normal distribution. We may apply the bootstrap method to other distributions based on different product characteristics in the future research.

ˆ2

Y

q /

Y

ˆ_q₁

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Appendix A. Error probability analysis information

difference error

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

1 6 11 16 21

case number

error probability

SB PB BCPB BT 0.0603 0.05 0.0397

Figure 13. Error probability of four bootstrap methods under

Y

_q₂

− Y

_q₁

= 0

(

Y

_q₁

= Y

_q₂

= 0.83

ratio error

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09

1 6 11 16 21

case number

error prability

SB PB BCPB BT 0.0603 0.05 0.0397

Figure 14. Error probability of four bootstrap methods under

Y

_q₁

/ Y =

_q₂

1

(

Y

_q₁

= Y

_q₂

= 0.83

Table 10. Error statistics of the four bootstrap methods for the difference test (

Y

_q₁

= Y

_q₂

= 0.83

Difference Mean of these 25 cases error

Standard deviation of these 25 cases error

Number of out of limits

Out of limits case

SB 0.0554264 0.010892002 8 10,16,18,21~24

PB 0.0561468 0.008096025 5 18,21~24

BCPB 0.0567744 0.004927582 4 21~24

BT 0.0552672 0.013402981 10 5,10,15,16,18,20~24

Table 11. Error statistics of the four bootstrap methods for the ratio test (

Y

_q₁

= Y

_q₂

= 0.83

Ratio Mean of these 25 cases error

Standard deviation of these 25 cases error

Number of out of limits

Out of limits case

SB 0.0513732 0.012874211 8 5,10,15,20~24

PB 0.0561468 0.008096025 5 18,21~24

BCPB 0.0571200 0.005031908 5 2,21~24

BT 0.0456404 0.017325918 11 4,5,9,10,14,15,20~24

Table 12.The error probability of four bootstrap methods for the

methods _Error

prob.

Difference statistic Ratio statistic

Y

q case

Y

_q₂ case Bootstrap

methods _Error

prob.

Difference statistic Ratio statistic

Y

q case

Y

_q₂ case Bootstrap

methods _Error

prob.

Difference statistic Ratio statistic

Y

q case

Y

_q₂ case Bootstrap

methods _Error

prob.

Average LCB

Standard deviation Of LCB

Error prob.

Average LCB

Standard deviation of LCB

0.8 E 0.8 E SB

PB BCPB

BT

0.05267 0.05367 0.05467 0.05167

-0.03888 -0.03891 -0.03892 -0.03883

0.02429 0.02438 0.02449 0.02420

0.04900 0.05367 0.05500 0.04167

0.95201 0.95277 0.95277 0.95088

0.02905 0.02930 0.02947 0.02876

Appendix B. Power analysis information

Table 13. Selection power of the four bootstrap methods for difference statistic with sample size

n = 10(10)200

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

SB 0.07467 0.09000 0.10500 0.11800 0.14433 0.16900 0.19733 0.22933 0.26367 0.31200 PB 0.08600 0.09933 0.11933 0.13867 0.16067 0.19167 0.21967 0.25800 0.29800 0.35033 BCPB 0.09433 0.11300 0.13300 0.15133 0.17800 0.21067 0.23600 0.27800 0.32133 0.37867 10

BT 0.06667 0.08033 0.09267 0.10733 0.13033 0.15667 0.18100 0.20767 0.23767 0.28367 SB 0.07000 0.09267 0.12000 0.15233 0.18633 0.23500 0.29033 0.35100 0.40900 0.49733 PB 0.07700 0.10033 0.12967 0.15967 0.20167 0.25200 0.30633 0.36633 0.44000 0.52300 BCPB 0.08233 0.10667 0.13900 0.17167 0.21600 0.26467 0.31867 0.38200 0.46067 0.54600 20

BT 0.06800 0.08800 0.11200 0.14300 0.17567 0.21967 0.27233 0.33567 0.38967 0.46900 SB 0.07500 0.09600 0.12700 0.17033 0.22600 0.28500 0.36267 0.44267 0.53633 0.63633 PB 0.07767 0.10233 0.13033 0.17767 0.23467 0.29700 0.37567 0.45567 0.55467 0.65000 BCPB 0.07967 0.10633 0.14100 0.18800 0.24333 0.31067 0.39100 0.47367 0.57167 0.66833 30

BT 0.07167 0.09067 0.12300 0.16267 0.22067 0.27767 0.35133 0.42767 0.52167 0.61733 SB 0.08333 0.11333 0.16133 0.21267 0.27733 0.35467 0.44700 0.55200 0.65833 0.76300 PB 0.08600 0.11667 0.16600 0.21600 0.28167 0.36333 0.45833 0.56367 0.66900 0.77500 BCPB 0.09067 0.12333 0.17067 0.22767 0.29267 0.37167 0.46833 0.57500 0.68400 0.78800 40

BT 0.08200 0.10933 0.15433 0.20933 0.27133 0.34600 0.43767 0.54333 0.64533 0.75000 SB 0.07600 0.11200 0.15767 0.21367 0.29400 0.38467 0.49567 0.60533 0.71100 0.82000 PB 0.08000 0.11300 0.15933 0.21867 0.30067 0.39333 0.50567 0.61233 0.71933 0.82533 BCPB 0.08167 0.11567 0.16333 0.22400 0.30833 0.39933 0.51400 0.62100 0.72733 0.83100 50

BT 0.07467 0.10800 0.15267 0.20767 0.28967 0.37633 0.48700 0.59900 0.70233 0.81233 SB 0.08000 0.11500 0.17100 0.24067 0.32800 0.44000 0.55933 0.67733 0.78767 0.88433 PB 0.08167 0.11567 0.17467 0.24700 0.33600 0.44767 0.56700 0.68367 0.79333 0.88900 BCPB 0.08300 0.12000 0.17967 0.25600 0.34367 0.45667 0.57300 0.68900 0.79867 0.89400 60

BT 0.07967 0.11300 0.16567 0.23833 0.32500 0.43900 0.54933 0.67000 0.78000 0.88067 SB 0.08733 0.12733 0.18800 0.26500 0.35767 0.47967 0.61233 0.73167 0.83600 0.91800 PB 0.08767 0.12867 0.18967 0.26733 0.36300 0.48333 0.61633 0.73633 0.83967 0.91900 BCPB 0.08767 0.13400 0.19400 0.26933 0.37100 0.48833 0.62233 0.73867 0.84533 0.92200 70

BT 0.08633 0.12633 0.18600 0.26133 0.35767 0.47700 0.60900 0.72533 0.82933 0.91300 SB 0.07400 0.12133 0.19500 0.29033 0.40900 0.53567 0.67133 0.78933 0.89567 0.95533 PB 0.07567 0.12333 0.19900 0.29233 0.41367 0.54133 0.67667 0.79333 0.89800 0.95667 BCPB 0.07533 0.12633 0.20333 0.29867 0.41633 0.54733 0.68267 0.80133 0.89767 0.95800 80

BT 0.07267 0.12133 0.19033 0.28500 0.40600 0.53167 0.66933 0.78633 0.89300 0.95333

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 n

Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 SB 0.09400 0.14833 0.22000 0.31567 0.43633 0.57233 0.70633 0.83200 0.92200 0.97133 PB 0.09800 0.15300 0.22100 0.31500 0.44033 0.57367 0.71133 0.83367 0.92467 0.97200 BCPB 0.09767 0.15567 0.22533 0.31933 0.44400 0.58333 0.71500 0.84067 0.92500 0.97333 90

BT 0.09433 0.14833 0.21833 0.31300 0.43100 0.57000 0.70267 0.82967 0.91967 0.97167 SB 0.09900 0.16100 0.23733 0.34933 0.47733 0.61367 0.75100 0.86500 0.93700 0.97767 PB 0.09967 0.16133 0.24033 0.35467 0.48133 0.61867 0.75333 0.86700 0.93900 0.97800 BCPB 0.09933 0.16267 0.24300 0.35633 0.48233 0.62667 0.75533 0.87000 0.94000 0.97967 100

BT 0.09833 0.15767 0.23200 0.34467 0.47333 0.61467 0.74867 0.86300 0.93400 0.97800 SB 0.09233 0.15033 0.24900 0.36300 0.51767 0.65100 0.78767 0.88900 0.95167 0.98567 PB 0.09267 0.15400 0.25067 0.36467 0.52000 0.65667 0.79133 0.88933 0.95300 0.98767 BCPB 0.09533 0.15367 0.25267 0.37367 0.52500 0.66100 0.79233 0.89267 0.95500 0.98733 110

BT 0.09167 0.15067 0.24900 0.36367 0.51433 0.65000 0.78667 0.88667 0.95100 0.98467 SB 0.09600 0.15967 0.26667 0.38500 0.54167 0.68333 0.80833 0.90300 0.95600 0.98967 PB 0.09533 0.16200 0.26767 0.38500 0.54667 0.68700 0.81133 0.90167 0.95700 0.99033 BCPB 0.09700 0.16133 0.26900 0.39300 0.54967 0.68900 0.81267 0.90333 0.95933 0.99033 120

BT 0.09600 0.15933 0.26467 0.38200 0.54133 0.68267 0.80633 0.90400 0.95667 0.98967 SB 0.09133 0.16567 0.26800 0.40433 0.54533 0.69800 0.83233 0.92733 0.97367 0.99633 PB 0.09167 0.16567 0.26933 0.40567 0.55033 0.69900 0.83467 0.92700 0.97500 0.99633 BCPB 0.09433 0.16767 0.27333 0.40967 0.55467 0.70600 0.83833 0.93067 0.97600 0.99600 130

BT 0.09000 0.16433 0.26767 0.40233 0.54433 0.69733 0.82967 0.92667 0.97367 0.99600 SB 0.10100 0.17267 0.28967 0.43133 0.58533 0.73500 0.86100 0.94000 0.97667 0.99467 PB 0.10233 0.17433 0.29067 0.43533 0.58900 0.74000 0.86333 0.94033 0.97833 0.99467 BCPB 0.10567 0.17833 0.28933 0.43400 0.58933 0.74300 0.86500 0.94333 0.97867 0.99467 140

BT 0.10200 0.17333 0.28667 0.42867 0.58200 0.73367 0.85933 0.93900 0.97767 0.99500 SB 0.10033 0.18300 0.29800 0.44067 0.60367 0.76100 0.88067 0.95500 0.98700 0.99533 PB 0.10033 0.18233 0.30033 0.44033 0.60700 0.76400 0.88267 0.95667 0.98767 0.99533 BCPB 0.10267 0.18867 0.30100 0.44367 0.61067 0.76900 0.88200 0.95567 0.98700 0.99633 150

BT 0.10033 0.18233 0.29600 0.43967 0.60100 0.76167 0.87867 0.95600 0.98733 0.99500 SB 0.10633 0.19100 0.30900 0.46833 0.62700 0.77967 0.89467 0.96433 0.99000 0.99867 PB 0.10700 0.19500 0.31133 0.46700 0.62867 0.77867 0.89533 0.96533 0.99000 0.99900 BCPB 0.10867 0.19800 0.31600 0.47200 0.63200 0.78233 0.89833 0.96500 0.98967 0.99867 160

BT 0.10667 0.19233 0.30867 0.46833 0.62600 0.77567 0.89333 0.96333 0.99000 0.99867

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 n

Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 SB 0.10067 0.18677 0.30900 0.48233 0.65433 0.80133 0.90900 0.96633 0.99300 0.99867 PB 0.10067 0.18833 0.31100 0.48533 0.65700 0.80400 0.91033 0.96667 0.99367 0.99900 BCPB 0.10200 0.18967 0.31467 0.48900 0.65933 0.80100 0.90767 0.96833 0.99367 0.99867 170

BT 0.10000 0.18533 0.30767 0.48100 0.65400 0.79900 0.90677 0.96667 0.99267 0.99867 SB 0.10300 0.19800 0.33967 0.50233 0.68200 0.82233 0.92267 0.97633 0.99633 0.99933 PB 0.10367 0.20033 0.33767 0.50367 0.68033 0.82467 0.92267 0.97667 0.99633 0.99900 BCPB 0.10433 0.20100 0.34033 0.50533 0.68367 0.82300 0.92367 0.97700 0.99700 0.99900 180

BT 0.10067 0.19833 0.33933 0.50400 0.67900 0.82067 0.92133 0.97667 0.99633 0.99900 SB 0.11667 0.21667 0.34867 0.53000 0.69433 0.84400 0.93500 0.97967 0.99500 0.99933 PB 0.11533 0.21767 0.34767 0.52900 0.69433 0.84433 0.93467 0.97933 0.99500 0.99933 BCPB 0.11733 0.21700 0.34933 0.52967 0.69600 0.84633 0.93533 0.98133 0.99600 0.99933 190

BT 0.11533 0.21433 0.34600 0.53100 0.69333 0.84300 0.93333 0.98000 0.99500 0.99933 SB 0.10200 0.19500 0.33800 0.52033 0.71267 0.85800 0.94533 0.98567 0.99633 0.99933 PB 0.10167 0.19467 0.34167 0.52333 0.71333 0.86033 0.94533 0.98600 0.99633 0.99933 BCPB 0.10133 0.19400 0.34433 0.52167 0.71667 0.86367 0.94600 0.98467 0.99667 0.99933 200

BT 0.10267 0.19233 0.33667 0.52100 0.71433 0.85867 0.94367 0.98500 0.99633 0.99933

Table 14. Selection power of the four bootstrap methods for ratio statistic with sample size

n = 10(10)200

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8

n Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9

SB 0.02667 0.03167 0.03933 0.05100 0.05933 0.07400 0.09167 0.11067 0.13567 0.15600 PB 0.08600 0.09933 0.11933 0.13867 0.16067 0.19167 0.21967 0.25800 0.29800 0.35033 BCPB 0.09533 0.11433 0.13400 0.15500 0.18067 0.21133 0.23800 0.28067 0.32533 0.38000 10

BT 0.00933 0.01300 0.01433 0.01867 0.02200 0.02867 0.03767 0.05033 0.06400 0.07633 SB 0.04733 0.05767 0.07400 0.09667 0.12800 0.16667 0.21667 0.27100 0.33700 0.40867 PB 0.07700 0.10033 0.12967 0.15967 0.20167 0.25200 0.30633 0.36633 0.44000 0.52300 BCPB 0.08367 0.10867 0.14067 0.17333 0.21700 0.26733 0.32033 0.38533 0.46300 0.54867 20

BT 0.02400 0.03233 0.03900 0.05200 0.06733 0.08800 0.12300 0.15500 0.21267 0.28100 SB 0.05600 0.07600 0.09700 0.13133 0.17667 0.23800 0.30167 0.38533 0.48000 0.58067 PB 0.07767 0.10233 0.13033 0.17767 0.23467 0.29700 0.37567 0.45567 0.55467 0.65000 BCPB 0.08067 0.10667 0.14267 0.19067 0.24733 0.31500 0.39467 0.47633 0.57600 0.67100 30

BT 0.03900 0.05067 0.06500 0.08967 0.12233 0.16600 0.22967 0.29567 0.37833 0.48000 SB 0.06567 0.09400 0.12600 0.18467 0.23867 0.31400 0.40167 0.50633 0.61233 0.72467 PB 0.08600 0.11667 0.16600 0.21600 0.28167 0.36333 0.45833 0.56367 0.66900 0.77500 BCPB 0.09167 0.12533 0.17300 0.22900 0.29367 0.37400 0.47333 0.57933 0.68500 0.78967 40

BT 0.04800 0.06667 0.09333 0.13367 0.18933 0.25167 0.33333 0.42600 0.54733 0.66133 SB 0.06133 0.09233 0.13267 0.18867 0.25933 0.35067 0.45733 0.57167 0.68433 0.79233 PB 0.08000 0.11300 0.15933 0.21867 0.30067 0.39333 0.50567 0.61233 0.71933 0.82533 BCPB 0.08300 0.11700 0.16533 0.22533 0.31200 0.40300 0.51800 0.62367 0.73000 0.83200 50

BT 0.04733 0.06900 0.10667 0.15100 0.21533 0.29400 0.39833 0.51167 0.63333 0.74333 SB 0.07033 0.09933 0.14767 0.21467 0.30100 0.40933 0.52333 0.64600 0.76333 0.86900 PB 0.08167 0.11567 0.17467 0.24700 0.33600 0.44767 0.56700 0.68367 0.79333 0.88900 BCPB 0.08400 0.12100 0.18033 0.25800 0.34567 0.45967 0.57667 0.69167 0.80033 0.89467 60

BT 0.05233 0.08200 0.12067 0.18100 0.26000 0.35533 0.47633 0.59800 0.72500 0.83367 SB 0.07567 0.11500 0.16700 0.24133 0.33200 0.44700 0.58333 0.70567 0.81533 0.90567 PB 0.08767 0.12867 0.18967 0.26733 0.36300 0.48333 0.61633 0.73633 0.83967 0.91900 BCPB 0.08900 0.13567 0.19633 0.27267 0.37233 0.49067 0.62367 0.74000 0.84700 0.92133 70

BT 0.06067 0.09500 0.14100 0.20633 0.29600 0.40633 0.53733 0.67100 0.78167 0.88567 SB 0.06567 0.10867 0.17100 0.26600 0.38500 0.50767 0.65167 0.77333 0.88067 0.94933 PB 0.07567 0.12333 0.19900 0.29233 0.41367 0.54133 0.67667 0.79333 0.89800 0.95667 BCPB 0.07600 0.12667 0.20633 0.30000 0.41667 0.54867 0.68467 0.80200 0.89867 0.95967 80

BT 0.05600 0.08933 0.14767 0.23367 0.34333 0.46567 0.61100 0.74067 0.85233 0.93100

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 n

Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 SB 0.08533 0.13600 0.20400 0.29400 0.41433 0.55100 0.68500 0.81367 0.91300 0.96800 PB 0.09800 0.15300 0.22100 0.31500 0.44033 0.57367 0.71133 0.83367 0.92467 0.97200 BCPB 0.09800 0.15667 0.22667 0.32033 0.44467 0.58467 0.71600 0.84100 0.92667 0.97267 90

BT 0.07133 0.11800 0.17900 0.26133 0.37467 0.51200 0.65333 0.78333 0.89667 0.96067 SB 0.08900 0.14600 0.21533 0.32567 0.45333 0.59833 0.73567 0.85233 0.93100 0.97433 PB 0.09967 0.16133 0.24033 0.35467 0.48133 0.61867 0.75333 0.86700 0.93900 0.97800 BCPB 0.10067 0.16267 0.24367 0.35700 0.48400 0.62767 0.75767 0.87133 0.94167 0.97967 100

BT 0.07333 0.12600 0.19267 0.29867 0.42333 0.56500 0.70767 0.82900 0.91933 0.96767 SB 0.08400 0.13867 0.23233 0.34033 0.49567 0.63200 0.77633 0.87533 0.94900 0.98400 PB 0.09267 0.15400 0.25067 0.36467 0.52000 0.65667 0.79133 0.88933 0.95300 0.98767 BCPB 0.09600 0.15533 0.25400 0.37533 0.52533 0.66067 0.79467 0.89300 0.95500 0.98733 110

BT 0.07533 0.11933 0.20600 0.31533 0.46433 0.60400 0.74867 0.85900 0.94267 0.98333 SB 0.08533 0.14800 0.24667 0.36700 0.52667 0.66567 0.79867 0.89533 0.95267 0.98867 PB 0.09533 0.16200 0.26767 0.38500 0.54667 0.68700 0.81133 0.90167 0.95700 0.99033 BCPB 0.09767 0.16267 0.26967 0.39333 0.55167 0.68900 0.81233 0.90467 0.96000 0.99067 120

BT 0.07567 0.13033 0.21933 0.33600 0.49500 0.64367 0.77467 0.88200 0.94733 0.98567 SB 0.08500 0.15367 0.25433 0.38567 0.52933 0.68367 0.81700 0.91967 0.97100 0.99567 PB 0.09167 0.16567 0.26933 0.40567 0.55033 0.69900 0.83467 0.92700 0.97500 0.99633 BCPB 0.09467 0.16867 0.27300 0.40933 0.55700 0.70700 0.83800 0.93200 0.97633 0.99600 130

BT 0.07400 0.13767 0.23133 0.35933 0.50500 0.65100 0.79900 0.90933 0.96567 0.99267 SB 0.09400 0.16333 0.27167 0.41267 0.56733 0.72500 0.84967 0.93667 0.97633 0.99400 PB 0.10233 0.17433 0.29067 0.43533 0.58900 0.74000 0.86333 0.94033 0.97833 0.99467 BCPB 0.10567 0.17867 0.29033 0.43500 0.59133 0.74367 0.86533 0.94300 0.97867 0.99467 140

BT 0.08100 0.14800 0.24667 0.38600 0.54533 0.70100 0.82900 0.92933 0.97233 0.99333 SB 0.09267 0.16767 0.28267 0.42100 0.59000 0.75000 0.87500 0.95167 0.98600 0.99533 PB 0.10033 0.18233 0.30033 0.44033 0.60700 0.76400 0.88267 0.95667 0.98767 0.99533 BCPB 0.10267 0.18933 0.30100 0.44600 0.61167 0.76967 0.88200 0.95567 0.98733 0.99633 150

BT 0.08267 0.15400 0.26067 0.39633 0.56933 0.72933 0.86000 0.94400 0.98400 0.99467 SB 0.09867 0.18167 0.29600 0.45467 0.61167 0.76967 0.88700 0.96133 0.98867 0.99833 PB 0.10700 0.19500 0.31133 0.46700 0.62867 0.77867 0.89533 0.96533 0.99000 0.99900 BCPB 0.11000 0.19900 0.31633 0.47133 0.63333 0.78433 0.89867 0.96500 0.98967 0.99867 160

BT 0.08467 0.16800 0.27967 0.43167 0.59100 0.75400 0.87267 0.95333 0.98867 0.99767

Yq1 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 n

Yq2 0.81 0.82 0.83 0.84 0.85 0.86 0.87 0.88 0.89 0.9 SB 0.09533 0.17833 0.29933 0.46700 0.63967 0.78800 0.90167 0.96467 0.99233 0.99867 PB 0.10067 0.18833 0.31100 0.48533 0.65700 0.80400 0.91033 0.96667 0.99367 0.99900 BCPB 0.10233 0.18967 0.31500 0.48867 0.66000 0.80233 0.90767 0.96767 0.99400 0.99867 170

BT 0.08500 0.16133 0.27733 0.44200 0.62167 0.77100 0.88967 0.96100 0.99133 0.99833 SB 0.09367 0.18867 0.32700 0.49167 0.66533 0.81467 0.91667 0.97533 0.99600 0.99900 PB 0.10367 0.20033 0.33767 0.50367 0.68033 0.82467 0.92267 0.97667 0.99633 0.99900 BCPB 0.10667 0.20100 0.34000 0.50533 0.68467 0.82467 0.92267 0.97733 0.99700 0.99900 180

BT 0.08400 0.17500 0.30500 0.46933 0.64233 0.80233 0.90767 0.97167 0.99500 0.99900 SB 0.10900 0.20500 0.33400 0.51767 0.68267 0.83767 0.92967 0.97767 0.99467 0.99933 PB 0.11533 0.21767 0.34767 0.52900 0.69433 0.84433 0.93467 0.97933 0.99500 0.99933 BCPB 0.11767 0.21767 0.34967 0.53100 0.69767 0.84767 0.93500 0.98100 0.99600 0.99933 190

BT 0.09767 0.18733 0.31700 0.49333 0.66367 0.82067 0.92200 0.97533 0.99400 0.99933 SB 0.09633 0.18333 0.32467 0.50600 0.70000 0.85233 0.94067 0.98433 0.99600 0.99933 PB 0.10167 0.19467 0.34167 0.52333 0.71333 0.86033 0.94533 0.98600 0.99633 0.99933 BCPB 0.10200 0.19433 0.34533 0.52233 0.71567 0.86367 0.94667 0.98533 0.99667 0.99933 200

BT 0.08867 0.16967 0.30667 0.48200 0.68467 0.83900 0.93500 0.98200 0.99467 0.99900

selection power in difference of Yq1=0.8 Yq2=0.81

selection power in ratio of Yq1=0.8 Yq2=0.81

Figure 15. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.81

Figure 16. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.81

selection power in difference of Yq1=0.8 Yq2=0.82

selection power in ratio of Yq1=0.8 Yq2=0.82

Figure 17. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.82

Figure 18. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.82

selection power in difference of Yq1=0.8 Yq2=0.83

selection power in ratio of Yq1=0.8 Yq2=0.83

Figure 19. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.83

Figure 20. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.83

selection power in difference of Yq1=0.8 Yq2=0.84

selection power in ratio of Yq1=0.8 Yq2=0.84

Figure 21. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.84

Figure 22. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.84

selection power in difference of Yq1=0.8 Yq2=0.85

selection power in ratio of Yq1=0.8 Yq2=0.84

Figure 23. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.85

Figure 24. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.85

selection power in difference of Yq1=0.8 Yq2=0.86

selection power in ratio of Yq1=0.8 Yq2=0.86

Figure 25. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.86

Figure 26. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.86

selection power in difference of Yq1=0.8 Yq2=0.87

selection power in ratio of Yq1=0.8 Yq2=0.87

Figure 27. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.87

Figure 28. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.87

selection power in difference of Yq1=0.8 Yq2=0.88

selection power in ratio of Yq1=0.8 Yq2=0.88

Figure 29. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.88

Figure 30. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.88

selection power in difference of Yq1=0.8 Yq2=0.89

selection power in ratio of Yq1=0.8 Yq2=0.89

Figure 31. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.89

Figure 32. The selection power for the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.89

selection power in difference of Yq1=0.8 Yq2=0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 50 100 150 200

sample size

selection power SB

PB BCPB BT

selection power in ratio of Yq1=0.8 Yq2=0.9

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

0 50 100 150 200

sample size

selection power SB

PB BCPB BT

Figure 33. The selection power for the difference statistic with sample size

10(10)200

n = Y =

_q₁

0.8 Y =

_q₂

0.9

Figure 34. The selection power the ratio statistic with sample size

10(10)200

n =

Y =

_q₁

0.8 Y =

_q₂

0.9 Appendix C. The sample data for application

Table 15. Sample data for supplier I (unit: Å).

1304.1 1346.7 1271.1 1315.4 1267.0 1305.4 1200.9 1233.7 1172.0 1129.8 1313.4 1345.3 1264.3 1357.7 1272.4 1241.9 1199.6 1311.4 1216.3 1286.8 1216.5 1323.3 1343.5 1125.2 1470.6 1140.6 1217.3 1327.2 1252.6 1237.8 1268.9 1216.6 1310.8 1410.5 1250.6 1142.7 1429.2 1228.3 1262.9 1180.3 1399.5 1362.5 1143.8 1206.9 1168.4 1305.0 1236.1 1230.2 1309.0 1255.1 1290.4 1198.7 1365.6 1199.5 1032.7 1399.7 1473.9 1122.4 1260.7 1167.7 1271.4 1180.7 1243.6 1219.6 1220.3 1206.6 1158.2 1326.8 1184.2 1217.8 1446.0 1279.0 1401.7 1244.2 1231.6 1230.5 1288.3 1217.6 1220.6 1058.0 1262.6 1311.3 1325.2 1284.4 1250.0 1320.5 1365.8 1343.4 1309.9 1223.4 1157.4 1380.4 1301.7 1360.3 1380.6 1178.2 1337.6 1389.6 1229.2 1256.0 1288.8 1412.7 1356.7 1190.7 1284.9 1253.7 1389.7 1236.2 1282.9 1303.9 1236.2 1341.1 1432.4 1262.5 1317.8 1347.9 1343.2 1288.9 1170.9 1333.5 1226.9 1404.2 1215.9 1422.3 1126.4 1231.1 1238.4 1218.4 1261.0 1244.3 1250.8 1330.6 1239.0 1269.9 1404.1 1115.4 1272.7 1329.2 1477.8 1268.3 1135.9 1341.4 1267.8 1387.7 1311.0 1323.3 1345.0 1053.5 1341.0 1245.8 1201.6 1372.8 1255.8 1207.0 1336.4 1305.6 1196.2 1258.7 1391.5 1276.5 1209.5 1312.4 1272.5 1252.8 1297.7 1381.3 1461.7 1191.5 1232.3 1280.6 1274.7 1333.7 1278.0 1058.8 1337.0 1148.1 1308.3 1283.2 1133.0 1312.8 1303.2 1204.6 1233.0 1341.6 1196.2 1309.7 1340.2 1387.7 1435.3 1345.3 1204.4 1163.1 1216.2 1262.4 1330.1 1281.7 1209.3 1311.0 1297.8 1267.2 1162.0 1369.2 1331.9 1291.8 1168.7 1239.3 1159.3 1372.0 1176.4 1375.7 1191.8 1356.9 1204.0 1388.7 1292.5 1389.1 1245.5 1328.4 1208.4 1331.1 1173.3 1273.3 1352.2 1176.4 1390.8 1229.2 1104.1 1219.8 1218.3 1240.6 1212.5 1299.5 1257.0 1445.9 1271.9 1222.6 1318.7 1326.3 1138.6 1323.7 1179.6 1284.4 1385.8 1271.7 1363.5 1350.8 1272.4 1115.3 1166.9 1390.3 1212.2 1120.4 1390.6 1330.8 1235.1 1356.2 1358.3 1392.9 1432.0 1389.8 1288.5 1267.4 1176.7 1331.8 1139.6 1029.1 1399.6 1331.0 1027.0 1253.8 1164.6 1293.3 1305.5 1200.1 1270.7 1304.8 1282.6 1268.0 1225.8 1289.0 1214.0 1196.5 1223.2 1379.6 1252.2 1384.6 1266.0 1176.7 1262.8 1284.6 1362.4 1229.0 1221.6 1265.7 1431.9 1341.1 1177.4 1239.0 1340.1 1353.1 1256.9 1145.4 1202.2 1267.8 1387.1 1183.6 1360.2 1241.4 1361.9 1139.2

Table 16. Sample data for supplier II (unit: Å).

1327.6 1301.2 1354.6 1469.8 1399.0 1347.6 1432.2 1319.0 1406.6 1375.5 1273.0 1395.7 1322.6 1491.6 1425.0 1355.2 1419.8 1299.1 1407.9 1331.5 1393.6 1342.5 1455.5 1393.5 1372.6 1314.1 1275.9 1313.8 1332.0 1298.1 1345.1 1379.2 1325.9 1388.6 1291.3 1357.7 1307.5 1359.2 1414.3 1245.3 1351.5 1410.3 1392.7 1326.1 1370.5 1357.8 1338.7 1312.1 1345.3 1311.8 1266.5 1447.3 1344.4 1411.2 1452.6 1369.1 1374.9 1420.5 1373.3 1404.9 1303.2 1309.0 1273.1 1381.0 1350.9 1344.2 1405.0 1310.5 1255.2 1356.3 1288.8 1395.7 1235.4 1343.5 1278.4 1274.4 1453.6 1379.6 1401.0 1328.8 1328.8 1281.3 1310.3 1385.3 1230.7 1418.3 1353.9 1406.3 1344.2 1279.6 1298.4 1337.8 1325.1 1270.5 1420.4 1253.8 1436.4 1308.6 1328.8 1314.5 1339.7 1231.6 1365.4 1277.9 1345.5 1364.3 1310.9 1246.8 1373.1 1356.4 1312.6 1327.0 1372.6 1369.6 1411.1 1282.4 1378.6 1385.1 1339.6 1429.6 1338.1 1289.9 1470.7 1282.6 1383.5 1343.0 1432.1 1290.4 1330.0 1326.7 1363.7 1309.0 1335.8 1287.5 1324.2 1325.2 1413.9 1387.4 1368.2 1356.4 1394.2 1330.3 1364.9 1406.5 1343.2 1434.6 1260.2 1265.0 1289.4 1476.6 1280.3 1358.5 1325.2 1337.4 1439.2 1309.4 1366.2 1382.0 1317.6 1392.6 1368.4 1332.7 1296.2 1387.3 1385.2 1390.1 1298.8 1395.1 1326.6 1303.5 1302.1 1280.2 1257.6 1418.2 1279.5 1358.4 1322.1 1378.3 1345.7 1310.1 1355.0 1216.8 1371.4 1315.0 1438.3 1425.5 1282.5 1297.9 1419.6 1356.5 1435.0 1368.5 1335.9 1400.0 1402.6 1370.8 1378.7 1390.9 1342.7 1343.3 1342.0 1343.5 1318.3 1370.9 1397.5 1439.4 1307.4 1443.8 1345.5 1407.0 1382.5 1252.9 1313.5 1464.6 1248.4 1245.6 1314.7 1238.1 1380.4 1406.5 1416.2 1323.3 1416.1 1208.9 1360.7 1357.4 1378.0 1414.6 1365.1 1351.7 1436.7 1400.2 1356.7 1339.0 1358.4 1234.3 1459.8 1321.5 1423.3 1472.9 1277.6 1434.8 1305.1 1357.5 1388.4 1382.1 1407.2 1277.5 1359.9 1360.5 1261.4 1271.5 1360.6 1425.4 1371.0 1307.3 1248.8 1234.5 1343.0 1393.0 1266.6 1388.6 1243.3 1408.8 1348.6 1280.8 1359.7 1242.1 1325.1 1345.1 1317.9 1352.5 1412.4 1231.5 1264.5 1317.4 1228.4 1341.1 1368.7 1323.9 1359.5 1368.1 1314.0 1356.9 1387.7 1265.8 1330.4 1303.6 1489.6 1318.8 1326.4 1337.6 1260.3 1224.0 1344.5 1388.7 1369.8 1478.8 1360.7 1284.9 1275.2 1332.1 1338.4 1346.4 1373.5 1287.0 1214.1 1283.2 1315.3 1302.5

在文檔中依據品質良率指標Yq應用複式抽樣方法於供應商選擇 (頁 32-56)