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Basic Event Types |
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Basic Event Types |
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Basic Event Types
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Basic Event Types |
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Basic Event Types |
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RAM Commander allows several types of Basic Event reliability model. The description of each model and calculation formulas is given below.
# |
Basic Event Type |
Input Parameters |
Description |
Unavailability Q(t) |
Mean Unavailability Q mean |
Frequency (unconditional failure intensity) w(t) |
|---|---|---|---|---|---|---|
1. |
Probability |
Probability (q) |
Constant probability, not depends on mission time. Failure probability on demand. |
q |
q |
0 |
2. |
Frequency |
Frequency (f) |
Frequency. Events occur with a constant frequency (rate). |
0 |
0 |
f |
3. |
Constant mission time |
FR (λ) Probability (q) Mission time (Tm) |
Probability of event linked to element which works during some constant mission time, not depends on mission time |
1 – (1-q)*exp(-λTm) |
1 – (1-q)*exp(-λTm) |
0 |
4. |
Repairable |
FR (λ) Probability (q) MTTR (µ=1/ MTTR) |
Repairable element with known FR and MTTR. Failures are detected immediately. |
q*exp(-(λ+µ)t) + + (λ/(λ+µ))*[1–exp(-(λ+µ)t)] |
λ / (λ + µ) |
λ*(1-Q(t)) |
5. |
Unrepairable |
FR (λ) Probability (q) |
Unrepairable element with known FR |
1 – (1-q)*exp(-λt) (if λ<1e-15, simplified formula P=λt is used) |
1 |
λ*(1-Q(t)) |
6. |
Periodical tests |
FR (λ) Probability (q) MTTR (µ=1/MTTR) Test interval (Ti) Time to first test (Tf) |
Latent event linked to repairable element being inspected periodically, with known FR, MTTR and test interval. |
For Formula |
For Formula see Table 3 |
λ*(1-Q(t)) |
7 |
Latent |
FR (λ) Probability (q) Test interval (Ti) |
Latent event with known FR and inspection time. Element is not repairable during the mission. |
1 – (1-q)*exp(-λTi) |
1 – (1-q)*exp(-λTi) |
λ*(1-Q(t)) |
8 |
Average probability per mission hour |
Average probability/hour (q) |
Average probability of event during average mission (flight) hour. Linked element is unrepairable during the mission. |
1 – (1-q)t |
1 |
0 |
9 |
Periodical Tests #2 |
FR (λ) Probability (q) MTTR (µ=1/MTTR) Test interval (Ti) Time to first test (Tf) |
Extends the "Periodical tests" model, suits wider range of cases. Recommended instead of "Periodical tests". |
Algorithm with different formulas for different cases. |
Algorithm with different formulas for different cases. |
Algorithm with different formulas for different cases. |
Table 1: Basic Events Calculation
Formula # |
Condition |
Unavailability Q(t) |
|---|---|---|
1. |
t < Tf |
1 – (1-q)*exp(-λt) |
2. |
t = Tf + nTi |
1 – (1-q)*exp(-λTi) |
3. |
Tf + nTi < t <= Tf + nTi + MTTR |
1 – (1-q)*exp(-λTi)] + [(1-q)*exp(-λTi)] * [1 – (1-q)*exp(-λ(t1))] (t1-time since the last test) |
4. |
Tf + nTi + MTTR < t < Tf + nTi + Ti |
1 – (1-q)*exp(-λ(t1)) (t1-time since the last test) |
Table 2: Unavailability Calculation for Periodical Tests
Formula # |
Mean Unavailability Qmean |
|---|---|
1. |
q + (1 – q)*(1 – (1 / λTi)*(1 - exp(-λTi))) + (q + (1 – q)*( 1 - exp(-λTi)))*( MTTR / Ti) |
Table 3: Mean Unavailability Calculation for Periodical Tests