Application Example Automobile Windows

Up to now, the number of registered vehicle (including the intercity bus, truck, car and wagon) has tended to 18,215,069. Thus, with the growing number of vehicle, there is a need for automobile windows. For the safety, the automobile window always be the sandwich glass. The sandwich glass inserted with the special membrane (PVB film) between two pieces of tempered glass was dealt with by the high pressure of high temperature. The structure of the sandwich was displayed in Figure 7. After the glass is broken, chip can still be glued together, it is a kind of safe type glass. The sandwich glass can absorb the ultraviolet ray in the sunlight effectively; protect the personal safety in maximum.

Figure 7. The structure of the sandwich glass.

Tempered glass is commonly used with various applications in our real life.

Especially, it is used in automobile's side windows, front windows ( displayed in Figure 8, 9 ). There are some characteristic of the tempered glass: (1) the strength against still-mode impact resistance is three to five times over that of regular glass.

(2) Resilient to sudden temperature drop with its heat endurance much superior than common glass. (3) When broken, its fragments differ from usual pointy shards but rather in curd configuration, which greatly reduces the impact of cuts.

Based on these characteristics of the tempered glass, we have to temper the glass to avoid the dangers coming with the broken glass in some special occasions, like the automobile window, the microwave oven and so on. It is a high-impact glass with its broken fragments in curds featuring an optimal performance in safety.

Figure 8. Automobile’s front window Figure 9. Automobile's side window Tempered glass is derived by heating the raw glass sheeting to a temperature of near-melting point, with an evenly distributed cool air for rapid cooling to form a surface hardening process in order to overcome physical expandability found in glass. The outer surface is quickly cooled for a reinforced characteristic, which is known as tempered glass. In order to keep the high optical quality, we have to ask the thickness of the tempered glass at least 0.5mm. , no any distortion, wave and other defects on the surface due to it’s treatment temperature lower then the thermo tempered glass, so easy to laminating fabrication. Too thin tempered glass will result in danger when it broken (more break pattern) and increasing the difficult when it be processed and can’t suffer the outside force impact

To illustrate which has better capability between the two suppliers, we

PVB film Tempered glass

present a case study on the automobile window manufacturing process, which located on the Tafa industrial region in Taiwan. These factories manufacture various types of the tempered glass. For the particular model of the automobile window investigated, the lower specification limit, LSL of an automobile side window’s thickness is set to be 0.5mm. And we use thickness gauge to inspect the inspection for thickness. If the characteristic data does not fall over the tolerance

LSL, the safety of the automobile window will be discounted.

5.2.1 Data Analysis and Supplier Selection

Before doing the data analysis, we set two factors first, (1) the minimum of Cpl(2) the minimal difference of C _pl between these two suppliers,δ =C_pl2 −C_pl1, then we can know how many sample sizes we should sample with determined power by the selection method. In this example, we set the minimum of

Cpl =1.00 and the minimal difference of C_pl between these two suppliers,δ =0.25, the determined selection power = 0.95, then we can know we have to take 257 samples by checking Table 1. Then we present the data drew from these two suppliers in Table. In order to affirm these data as normal distributed, we show the distribution of these data in Figure 10-11. And we set these data to be a histogram in Figure 12-13

-3 -2 -1 0 1 2 3

Normal Distribution 0.50

0.52 0.54 0.56 0.58 0.60

data1

Figure 10. Normal probability plot for thickness data of Supplier I.

-3 -2 -1 0 1 2 3

Normal Distribution 0.50

0.52 0.54 0.56 0.58

data2

Figure 11. Normal probability plot for thickness data of Supplier II.

Figure 12. Histogram for supplier I. Figure 13. Histogram for supplier II.

5.2.2 Phase I－Supplier Selection

We will test H₀:C_pl1≥C_pl2 versus H₁:C_pl1<C_pl2 by comparing these test statistics ˆ ₁

Cpl , ˆ ₂

Cpl , and the selection value A &c based on the test statistic and the required sample sizes. If ˆ ₁ ˆ ₂

pl

pl C

C < and A<c then we conclude that the process capability of the new supplier better than that of the present supplier. The calculated sample statistics for two suppliers are summarized in Table 3.

Table 3. The calculated sample statistics for two suppliers.(Cpl) Population X S Cˆ_pl

I 0.5487296 0.01592503 1.019979 II 0.548967 0.01335757 1.221954

Based on the selection method, the values 019979ˆ 1.

1= Cpl

and ˆ 1.221954

2 =

Cpl . In this case one only need to compare the test statistic ˆ 1

Cpl and ˆ ₂

Cpl , by A=0.02891871 and c=0.2585227, the outcome presents

2

1 ˆ

ˆpl Cpl

C < and A<c, then we conclude that the process of this new supplier is capable.

5.2.3 Phase II－Magnitude Outperformed Detection

To realize the lower bound value of the magnitude, q , we will test

2 1

0 :C_pl q C_pl

H + ≥ versus H1:C_pl1 +q<C_pl2. By comparing these test statistics ˆ 1

Cpl , ˆ ₂

Cpl , and the selection value A &c based on the test statistic and the required sample sizes. From the estimation of Phase I, we list the obtained selection values A and c and the decision based on the selection procedure for

h = 0.01, 0.05, 0.07(0.001)0.074 in Table 4.

0.510.520.520.530.540.550.55 0.560.570.580.580.590.60 data1

0 5 10 15 20

0.51 0.52 0.52 0.53 0.54 0.55 0.55 0.56 0.570.580.580.590.60 data2

0 10 20 30

Therefore, from the analysis of magnitude outperformed detection based on sample statistics, the magnitude of the difference between the two suppliers is q

= 0.034. By the way, we can conclude that the new supplier is more capable than the present supplier at least a magnitude, q =0.074.

Table 4. Magnitude outperformed detection of selection procedure. (Cpl) ˆ 1

Cpl 1.029979 1.069979 1.089979 1.090979 1.091979 1.092979 1.093979

ˆ 2

Cpl 1.221954 1.221954 1.221954 1.221954 1.221954 1.221954 1.221954

q 0.01 0.05 0.07 0.071 0.072 0.073 0.074

A 0.04169824 0.1447203 0.2377967 0.2432623 0.2488044 0.2544226 0.2601165 c 0.2585227 0.2585227 0.2585227 0.2585227 0.2585227 0.2585227 0.2585227

Decision Reject Ho Reject Ho Reject Ho Reject Ho Reject Ho Reject Ho Don’t Reject Ho