Select the links below to see commonly referenced tables. Within the links are explanations and examples. **BE CAREFUL** when using tables. There are many variations and all can be correct but only when interpreted correctly. Some tables are for one-tailed test and others cover two-tailed test.

There are several tables along with other Templates & Calculators available to download.

Z-Distribution: Areas of the standard normal distibution

The tables assumes the data set is normally distributed and the process is stable.

The z-score = x if the mean is 0 and the standard deviation = 1 which indicates a standard normal distribution.

t-Distribution: Critical values from the t-Distribution

For the t-distribution, dF = n-1, represents the degrees of freedom. If you have 29 samples, then dF = 28.

The t-distribution is used instead of the z-distribution (standard normal distribution) when the:

- Population standard deviation is unknown
- Population is normally distributed

The t-distribution 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 t-distribution and t-tests with examples.

F-Distribution: Percentage points of the F-Distribution

NIST table with the most common levels of significance and degrees of freedom.

The Chi-square distribution is most often used in many cases for the critical regions for hypothesis tests and in determining confidence intervals.

- Chi-square test for independence in an "Row x Column" contingency table
- Chi-square test to determine if the standard deviation of a population is equal to a specified value.

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 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, estimated Cpk, and yields for normal distributions.

Also, if a process is CENTERED, then Cp = Cpk.

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