Page 171 - Six Sigma for electronics design and manufacturing

Six Sigma for Electronics Design and Manufacturing
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the line is normally distributed with standard deviation of the noise
measurements equal to 10, what is the maximum error (in dB) of the
noise measurement population average given that the engineer wants
to express it with a probability of 99%?
Probability of 0.99% implies a significance ( ) = 0.01
z /2 = z corresponding to {f(z) = 0.005} = 2.575
E = 2.575 · 10/ 1 0 0 = 2.575 dB
The engineer can state with 99% probability that error between the
sample average and the population average is less then 2.575 dB.
Example 5.4
A factory makes PCBs and the gold plating thickness on the PCB fin-
gers is expected to meet a minimum value of 20 mils prior to shipping.
The gold thickness population is normal, with an average equal to 10
mils and standard deviation equal to 3.0. Process improvements
were made to reduce variability, and hence less gold can be plated on
average to ensure conformance to specifications. How many units
must be made with the new process to ensure with 95% probability (
= 0.025) that new population average is within ±1 mil?
n = (z /2 · /E) = (1.96 · 3/1) = 34.6 or 35 sample size
2
Example 5.5
A sample of nine measurements was taken for turn-on rise time of an
IC. The average of the sample was 51 units and the sample standard
deviation was 6. Given that this sample is derived from a population
with normal distribution, calculate the maximum error of the popula-
tion average with 95% confidence.
E = t /2, =n–1 · s/ n = t 0.025,8 · 6/3 = 2.306 · 2 = 4.612, or 4.612/51 = 9%
E is the maximum error between the sample average and the popula-
tion average, with 95% confidence.

5.1.4 Confidence interval estimation for the average
Engineers have found the use of the confidence percentage discussed
in the last section for estimating the average or average rather unfa-
miliar. They are more comfortable with the concept of the confidence
interval. This term shows the range of the average having the degree
of confidence (1 – )%. The endpoints are referred to as the confidence
limits. The formulas for the interval of the average estimation are for
high- and low-volume samples, respectively: