The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or period.

**1. Poisson Distribution**

**What is Poisson Distribution?**

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or period.

This Distribution name has been consider on the name of French Mathematician Simeon Denis Poisson.

**Attributes of a Poisson Experiment**

A Poisson experiment is a statistical experiment that has the following properties:

1. The experiment results in outcomes that can be classified as successes or failures.

2. The average number of successes (mu) that occurs in a specified region is known.

3. The probability that a success will occur is proportional to the size of the region.

4. The probability that a success will occur in an extremely small region is virtually zero.

Hence, that the specified region could take many forms. For instance, it could be a length, an area, a volume, a period of time, etc.

**Meaning of Poisson distribution**

A statistical distribution showing the frequency probability of specific events when the average probability of a single occurrence is known. The Poisson distribution is a discrete function.

**Use of Poisson distribution**

If a mean or average probability of an event happening per unit time/per page/per mile cycled etc., is given, and you are asked to calculate a probability of n events happening in a given time/number of pages/number of miles cycled, then the Poisson Distribution is used.

For more you can use:- *stattrek.com/probability-distributions/poisson.aspx*

In Six Sigma we have Two types of Sample Poisson Tests

1. 1 Sample poisson rate (Use for Base line Identification and for validation)

2. 2 Sample poisson rate (Use for comparison of rate of occurrence between two samples)

__How to use Minitab for these test__

__Sample poisson rate__

__Go to Stat>Basic stat>1-Sample Poisson Rate__

__Select Data from the box__

__We can see the Base line (95% CI)=(16.5405, 19.1828)__

__This base helps us to decide the next target for improvement__

__If we select the target here then it helps us for validation__

__P-Value>0.05, Ho (Null) is true, there is no significant impact on rate of occurrence__

__P- Value<0.05, Ha (Alternate) is true, there is a significant impact on rate of occurrence__

__Two Sample Poisson Rate__

__Go to Stat>Basic stat>2-Sample Poisson Rate__

__Select Data from the box__

__If we have 2 sample in two columns, then select the second option __

__P-Value>0.05, Ho (Null) is true, there is no significant impact on rate of occurrence__

__P- Value<0.05, Ha (Alternate) is true, there is a significant impact on rate of occurrence__

__Hence, there is a significant difference between the rate of occurrence of sample A and Sample B__