K ormore calculates failure probability wrong

[reteprelief]

Use the test case issue1837 and change the failure probability of a node to 0.2.
For the case 2 ormore we should get .104:
1 - Rs with Rs = 2RR - 2 * RRR with R = 1 - 0.2

However, I get a negative number (-0.41)

[reteprelief]

I used info from the following links for the formula above.
http://reliawiki.org/index.php/Fault_Tree_Diagrams_and_System_Analysis voting or gate

http://reliawiki.org/index.php/RBDs_and_Analytical_System_Reliability k-out-of-n Parallel Configuration

[jjhugues]

Peter, agreed about the negative value, an oversight when reorganizing the additions in the final computation. Patch is ready

But the value you get is for 2 out of 3.
2 or more out of 3 should be ( (2 out of 3) or (3 out of 3), hence 0.112 = 0.104 + 0.2^3

[jjhugues]

Oh, I may have interpreted that to strictly. @reteprelief can you please confirm?

[reteprelief]

Jerome,
the voting OR gate section of http://reliawiki.org/index.php/Fault_Tree_Diagrams_and_System_Analysis states that "In a Voting OR gate, the output event occurs if or more of the input events occur. "

http://reliawiki.org/index.php/RBDs_and_Analytical_System_Reliability is a little confusing as it calls the logic k-out-of-n and presents it as success logic. The text states "This type of configuration requires that at least components succeed out of the total parallel components for the system to succeed."
The fail logic would be 1 - Psuccess. I interpreted this as n-k ormore failures.

[reteprelief]

The formula for 2 ormore of 3 failure would be P1P2(1-P3) + P1*(1-P2)P3 + (1-P1)P2P3 + P1P2P3 which leads to P1P2 + P2P3 + P1P3 - 2P1P2P3. For all components with the same P it would be 3PP - 2PPP where P is the failure rate.

[reteprelief]

Just noticed the multiply symbol is interpreted as Italic on/off :-) Only one actually shows.

[reteprelief]

Jerome,
when I assign different values to the three Modules in you test case I still do not get the right numbers.
When they are the same the numbers are ok.
Example:
in TMR_Archetype.impl EMV2 annex
properties
emv2::OccurrenceDistribution => [ProbabilityValue => 0.1; ] applies to ^Module_1@Failure;
emv2::OccurrenceDistribution => [ProbabilityValue => 0.2; ] applies to ^Module_2@Failure;
emv2::OccurrenceDistribution => [ProbabilityValue => 0.3; ] applies to ^Module_3@Failure;

The result should be .098 but is .064
From http://reliawiki.org/index.php/RBDs_and_Analytical_System_Reliability:
Hardware drive example:
The reliability of HD #1 is 0.9, HD #2 is 0.88 and HD #3 is 0.85, all at the same mission time. (Failure rates 0.1, 0.12, 0.15). The result should be 0.0414 but is 0.03376

[jjhugues]

Translating old BASIC stuff remembered me I had to double check indexes. This should now be settled. Thanks for your reviews @reteprelief