Calculating Sample Probabilities ( Poisson )

Ref : Design for Six Sigma Statistic (3.1.4.4)

When counting defects in a sample from a contineuous medium

The probability of observing exactly "X" defects in the sample is



Example

Let failure rate of a control systme : 30 failure per million hour

Assuming that if any one failure happen, it will be detected and repaired within 24hour.

If a second failure happpens before the 1st failure is repaired, the system will shut down unexpectedly causing great damage.

Assuming the spare part is replanished only once per year. How many spare should be keep if we want to have a 99% confidence we have enough spare to up the system in case failure