This Failure Rate Calculater uses either the Bayesian metodology with prior knowledge of failure rates or Chi-Squared where there is no known or limited prior industry failure data.  See the Instructions tab for further instructions  
First: Enter your industy data, one of the data point should be 90% - 95% confidance or has a high failure rate (Maximum)  
Dangerious Undetected
failure data 		Industry Data #1 Industry Data #2 Industry Data #3 Industry Data #4 Industry Data #5 Industry Data #6 Industry Data #7 Industry Data #8 Industry Data #9 Industry Data #10  
MTTF (Yrs)  
Second: Select your industry Prior failure Gama distribution parameters for the data above  
Failure Distribution Parameter <---Adjust to obtain 90%-95% probabliity failure rate for determining the new LambdaDU (/hr) once data is collected  
Prior Data Probability Confidence <--(90% or Greater)              
Avg Prior Failure Rate (/Hr) <---Select this as your initial failure rate based on prior industry data        
Prior Use: Once the device(s) have been in use, document the failures and obtain your new failure rate  
First: Enter the testing interval, hours of operation, and number of Dangerous Undetected failures.  
  Avg Partial Proof Test Interval (Yrs);Default = 1 <--Make equal to 100% proof test interval if no partial test    
Avg 100% Proof Test Interval (Yrs); Default = 1            
Your Data #1 #2 #3 #4 #5 #6        
Total Hours        
# of Failures        
Second: Your New Failure rate based on selected probability confidance and your failure data  
  Probability Confidence Current Failure Rate            
λDU /hr λDU /FITs MTTF (Yrs.)            
  ProSIS-FSE        
     
IEC61511 Requirement                                      
11.9.4 The reliability data uncertainties shall be assessed and taken into account when calculating the failure measure.  
  NOTE 1 The reliability data uncertainties can be evaluated according to the amount of field feedback (less field feedback results in more uncertainty) or/and exercise of expert judgement.
     
  Published standards (IEC 60605-4), Bayesian approaches, engineering judgement techniques, etc. can be used to estimate the reliability data uncertainties.            
  -use of an upper bound confidence of 70 % for each input reliability parameter instead of its mean in order to obtain conservative point estimations of the failure measures  
  -use the probabilistic distributions functions of input reliability parameters, perform Monte Carlo simulations to obtain an histogram representing the   
  distribution of the failure measure and assess a conservative value from this distribution (e.g., that there is a 90 % confidence that the true failure measure is better than the value calculated).  
16.2.2 Operation and maintenance procedures shall be developed in accordance with the relevant safety planning and shall provide the following:          
  f)  procedures for collecting data related to the demand rate and SIS reliability parameters;
                        
  NOTE 1 Collection and analysis of failure data has many benefits including the potential to reduce maintenance costs   
  if failures rates in operation are significantly lower than what were predicted during design.   
  Implementation costs of new installations can also be reduced because new designs can be based on less conservative failure rates.  
 
How to Use the Reliability Calculator  
There are two possible approaches to determine the Prio Use failure rate  
  a) Bayesian: You have prior knowledge failure rate of similar devices  
  b) Chi-Sq:  You have a device with no industry published failure rate data  
 
BAYESIAN METHODOLOGY (Used if you have no historical data on your devices)  
1) Based in the two options above, enter the reliability data Bayesian Method  
2) Select the target confidance of the data point that you have defined as the high confidance data.   
 This data will have the worst failure rate and thus the highest confidance  
  - Typical confidance is 90 to 95%   
  - The software will select the distribution that bests represents your data and target confidance  
  - The actual confidance will be shown and the failure rate to use in your SIL Calculations  
3) Enter the total number of hours of operation and the number of failures  
  -  If available enter the data for your devices currently installed.  
  - If no past failure data is available,  collect data and enter this data in the future   
  - Select your upper bound confidance limit (70% is the minimum)  
     
NOTE: Before you have collected your field data, select your initial device failure rate.  We recommend at least 5 device failure rates to use Bayesian Prior Use methodology.  
We recommend that the data set be a collection of different failure rates with values that represent the range of industry data.    
One of the values needs to be of 90%-95% probability confidence orthe highes failure rate.  
   
CHI-SQUARED METHODOLOGY (Used if you have a volume of user historical data)  
1) Based in the two options above delete /clear the data set  
2) Enter the total number of hours of operation and the number of failures  
  - Enter the data for your devices currently installed.  
  - Select your upper bound confidance limit (70% is the minimum)