
Select the links below to see commonly referenced tables. Within the links are explanations and examples of how to apply them.
ZDistribution: Areas of the standard normal distibution
The tables assumes the data set is normally distributed and the process is stable.
tDistribution: Critical values from the tDistribution
For the tdistribution, dF = n1, represents the degrees of freedom. If you have 29 samples, then dF = 28.
The tdistribution is used instead of the zdistribution (standard normal distribution) when the:
The tdistribution is a series of distributions, a unique distribution exist for each sample size. As the sample size increases it becomes taller and narrower and exhibits more characteristics of the normal curve. Generally applied with sample sizes <30.
Click here to learn more about the tdistribution and ttests with examples.
FDistribution: Percentage points of the FDistribution
NIST table with the most common levels of significance and degrees of freedom.
The Chisquare distribution is most often used in many cases for the critical regions for hypothesis tests and in determining confidence intervals.
1) Chisquare test for independence in an "Row x Column" contingency table
2) Chisquare test to determine if the standard deviation of a population is equal to a specified value.
BE CAREFUL when using tables, there are many varieties out there and all can be correct but only when used and interpreted correctly. Some tables are for onetailed test and others cover twotailed test.
The conversion table below is similar to the one above but lets discuss the differences.
It is very important to remember that DPMO and PPM may or may not be the same.
Lets use an exaggerated example to try an illustrate a point.
If ONE part has 1,000,000 opportunities for a defect, and one defect is found that makes the entire PART a defective PART.
So it is possible that you could have 1 PPM with a DPMO of 0.000001.
Also, Cpk is estimated from the sigma level and it isn't always an exact match since the Cpk calculation takes the better of the USL or LSL and doesn't consider the tail of the opposite tail.
It is most important to understand the basic relationships and memorize the most common levels of sigma, Cpk, and yield for normal distributions.
Also, if a process is CENTERED, then Cp = Cpk.
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