A question concerning PFD avg.

Suppose to make a simple calculation, starting from a base event with the law "Test périodique simple" (Same considerations with other laws based on exponential probability), a gate OR, with this only base event. So you have E001 ad P001.
Suppose to have a mission time = 1 and time test =1 (proof test). Suppose lambda=0.12
The program gives the following results, with XFTA calculation:

Date   Pr/Pfd      Pfdavg
0       0.11308    0.11308
0.01   0.11308    0.11308
.....
1       0.11308    0.11308

These values are strange for the following reasons:

1)  According PFD definition (Qs(T) - ref p.7.2 XFTA manual) it is strange that Pr/Pfd = 0,11308.  Then it is also strange that pfdavg has the same value for the different times (spet times), for the reason  2) below.

2) Second, but most important, PFD avg is the 'average'. So, we could have roughly half of these values, if we appoximate the probability function as linear/ triangular .
  But, more exactly, If we have exponential law P(t) = 1 - e^(-labda*t) , the indefinite integral is: t + 1/lambda*e^(-labda*t) + c.  So, integrating P(t) from 0 to t , where t= proof test time, we have:   PFD average at time t is :   t + 1/lambda*e^(-labda*t) - 1/labda .

So, if we have for example lambda = 0,12,  proof test time = 1,
we should have  PFD avg=0,05767   
(for step 0,01 --> 0,00059976, for step 0,02 --> 0,001199  and so on..)

We could verifiy these values with a simple spreadsheet.

Or, alternatively,  using LOGAN program  (demo version full functioning up to 30 events..)  at link http://loganfta.com/download/download.html   (for example assuming Probability Type Unrevealed , lambda=0.12 (called in this case as 'frequency') and prrof test time =1)

Regards

Good evening,
first of all, Thank You for Your great software.
I've downloaded it this afternoon and now I'm trying to understand the use of the program with the standard example.

Generating the report with that example, I've notice also few rows concerning SIL in the report.
Concerning SIL, I saw  SIL 1  from 0.001 to 0.01,  SIL 2 from 0.0001 to 0.001, etc.
But, if we consider PFD, (probability of Failure on demand - ref.IEC 61508), these values should be 10 times greater: so, SIL 1 from 0.01 to 0.1 (RRF=risk reduction factor = 1/PFD --> from 10 to 100), SIL 2 from  0.001 to 0.01 (RRF from 100 to 1000) and so on.
Or didn't i understand well, and perhaps is there another meaning for the SIL for the quantities in the report? I searched something concernig Sil in the help, but i've found no information concerning that part of report.

Anyway, many thanks for Your fantastic software.

Roberto (from Italy)