Poisson Distributions

This calculator calculates the Poisson Distribution for Confidence level, Failure Rate, Time or Maximum Number of Failures allowed to satisfy a set of given conditions. The formula is as follows: 

where: 
l  =  failure rate per 10^{6} operating hours 
r  =  number of failures 
t  =  time, expressed in hours 
P(r)  =  probability of getting exactly r failures in time t 
CL  =  confidence level 


Example use of the Calculator: 
Assume that your product has been in the field for 43,800 hours and only 2 failures occurred. The product's failure rate was estimated to be 121.7 failures per million hours of operaton. How confident would you be that the failure rate of the population was 121.7? Using the calculator as indicated, you would be 90.1% confident that your product has a failure rate of 121.7 per million operating hours. 
Enter:  l  =  121.7 
 t  =  43800 
 r  =  2 
Press Calculate 
Solves for:  CL  =  90.1% 

