[原创]Binomial

Estimating a Defect Rate From a Sample

Voting Polls

Of 1000 voters sampled, 600 indicated that they were going to vote for Candidate A.

· How would you estimate the proportion of voters who will vote for Candidate A in the real election?

· How confident would you be that Candidate A will win the election?


To estimate a true process defect rate or a true process yield simply use the sample data:


or,



Exercises on Estimating
True Process Defect Rates
and True Process Yields

Defect Data Exercise:

If 27 defective units were found in a sample of size 13,000, provide an estimate of the true process defect rate:



Yield Data Exercise:

If 1163 good units were found in a sample of size 1165, provide an estimated of the true process yield:



How confident are you that these estimates are close to the true values? The next topic concerns placing confidence intervals around the estimates.

Two-Sided Confidence Intervals for Means

For most of the cases involving continuous data in DOE I, a two-sided confidence interval would be placed around the sample mean (the estimate of the true process mean).

The required information to construct the confidence interval included:

• sample mean
• sample standard deviation
• sample size

Continuous Data Example:

= 10
s = 2
n = 30

The 95% confidence interval is .

This is called a “two-sided” confidence interval, since the mean is bounded on two sides. The confidence interval contains both a lower bound (9.28 for this example) and an upper bound (10.72 for this example).

Interpretation: We are 95% confident that our confidence interval of has captured the true process mean.


One-sided Confidence Intervals for Proportions


For most of the cases involving proportional data, a one-sided confidence interval should be placed around the sample proportion.


Defect Data Example:

15 defective units were found in 300 units randomly collected from a process:

sample defect rate = (15/300) = 5%
95% confidence interval is

This is called a “one-sided” confidence interval.

Interpretation: We are 95% confident that the confidence interval has captured the true process defect rate.



For defect data, the lower bound is usually set to 0%, and only an upper bound is calculated and reported.


One-sided Confidence Intervals Continued


Yield Data Example:

1200 units were processed, and all 1200 units tested “good”.

sample yield = (1200/1200) = 100%
95% confidence interval =


Interpretation: We are 95% confident that the confidence interval has captured the true process yield.



For yield data, the upper bound is usually set to 100%, and only a lower bound is calculated and reported.



BKM for Using Binomial Methods versus Using Continuous Methods for 1-sample Defect Data or Yield Data

BKM for Using Binomial Methods versus Using Continuous Methods for 2-sample Defect Data or Yield Data GD