Poisson Distributions

     
Failure Rate (l)  per 106 Hours
Time (t)  Hours
No. of Failures (r)  
Probability (r=k) (P(r)):  
Probability (r<=k) (P(r)):  
Probability (r>k) (P(r)):  

This calculator calculates the Probability of k, k or less, and k or more failures occurring using the Poisson Distribution. The formula is as follows:
where:
l= failure rate per 106 operating hours
r= number of failures
t= time, expressed in hours
P(r)=probability of getting exactly r failures in time t
=probability of getting k or fewer failures in time t
=probability of getting more than k failures in time t
Example use of the Calculator:
The failure rate is estimated to be 0.04 failures per million hours. The product has accumulated 55,000,000 hours of operation time and 2 failures occurred. What is the probability of getting exactly 2 failures, 2 or fewer failures and more than 2 failures? Using the calculator as indicated, the probability of exactly 2 failures is 0.2681, the probability of 2 or fewer failures is 0.6227 and the probability of more than 2 failures is 0.3773
Enter: l = 0.04
  t = 55000000
  r = 2
Press Calculate
Solves for: P(2) = 0.2681
  = 0.6227
  = 0.3773