# What is the Poisson Distribution?

The Poisson distribution approximates the binomial distribution when the number of trials in) is large and the probability of each trial (p) is small. In this case the variable sometimes called the outcome parameter of the distribution is equal to np. The formula for the Poisson distribution is as follows:

where x is the outcome during a specific time or region and \ is the average number of outcomes in the time interval or region and

Use of the Poisson distribution is more appropriate when each event has an equal probability of failure, producing a “defect”. It is especially useful in complex production operations, where the possibilities or opportunities of defects increase very rapidly, and the probability of getting a single defect at a specific place or time is small. The Poisson-distribution-based charts (C or U charts) should be used when the area of opportunity or boundary of finding defects is kept constant. Examples are:

• Defects in a one-shift operation

• Solder defects in one electronic product

• Defect in one PCB

Defects in 20,000 units of production

Total number of defects in a computer system per month

The Poisson distribution implies occurrences of events or defects within a boundary of time, space, or region. It has no “memory”; that is, the outcome or defect during one interval is in proportion to its length, and independent of other intervals. In addition, the probability of two or more outcomes or failures in a single time interval is zero.