Page 168 - Six Sigma for electronics design and manufacturing

Table 5.1 Selected values of t , of student’s t distribution
= 0.10 = 0.05 = 0.025 = 0.01 = 0.005 = 0.001 = 0.0005

12.706
31.821
6.314
318.3
63.657
3.078
636.6
22.327
1.886
6.965
2.920
31.600
4.303
9.925
1.638
5.841
4.541
3.182
12.922
10.214
2.353
1.533
2.776
3.747
7.173
4.604
2.132
1.476
2.571
2.015
6.869
4.032
3.365
5.893
5.208
5.959
2.447
1.943
3.707
1.440
3.143
4.785
1.415
2.365
5.408
3.499
1.895
2.998
5.041
2.896
3.355
4.501
2.306
1.397
1.860
1.383
9 1 2 3 4 5 6 7 8 The Use of Six Sigma with High- and Low-Volume Products and Processes 8.610 137
3.250
4.297
2.821
2.262
4.781
1.833
10 1.372 1.812 2.228 2.764 3.169 4.144 4.587
20 1.325 1.725 2.086 2.528 2.845 3.552 3.849
30 1.310 1.697 2.042 2.457 2.750 3.386 3.646
1.282 1.645 1.960 2.326 2.576 3.090 3.290
Confidence 90% 95% 97.5% 99% 99.5% 99.9% 99.95%
or (1 – )
higher the confidence percentage, the larger the span of the confi-
dence interval and its endpoints, the confidence limits. For low-vol-
ume production data, the confidence limits for the population average
and standard deviation estimates are used to give an estimate of
the span of these two variables. The 95% confidence limits can be
used for calculating six sigma data (Cpk, defect rates, FTY), whereas
higher confidence numbers (99% and 99.9%) can be used as worst-
case conditions checks on the base calculations.
5.1.1 Examples of the use of the t-distribution for
sample and population averages
Example 5.1
A manufacturing line produces resistors in a normal process with an
average value of 500 ohms. A Sample of nine resistors were taken
from yesterday’s production, with sample average = 540 ohms and
sample standard deviation = 60. Does the sample indicate that the
production process was out of control yesterday?
Solution to Example 5.1
540 – 500
t = = 2.0 and = 8

60/ 9
In the t-distribution table (Table 5.1), the number 2 falls between
t ,8 values of 95% and 97.5% confidence (1.860 and 2.306, respective-
ly). Hence, the yesterday’s production process can be assumed to be in