Description Usage Arguments Details Value References Examples
Give the estimated probability of failure after 30 years
(or can be set via set_returnPeriod
)
based on a large number of replications with given load profile.
The θ's, where
θ = (μ_a, σ_a, μ_b, σ_b, μ_c, σ_c, μ_n, σ_n, μ_σ0, σ_σ0),
will then be used to solve the Canadian ADM for time-to-failure T_f and probability of failure P_f with and without duration of load (DOL) effect.
1 | solveCanADM(inputTheta, inputPhi, verbose = FALSE)
|
inputTheta |
a matrix where each row is θ |
inputPhi |
performance factor φ of the load |
verbose |
displays the index, the number of failure of the current θ, and the number of failure of the current θ with no DOL effect to console if TRUE |
The equation of the Canadian model is:
d/dt α(t) = [(a * τ_s) * (τ(t) / τ_s - σ_0)_+]^b + [(c * τ_s) * (τ(t) / τ_s - σ_0)_+]^n * α(t),
where
* (a, b, c, n, η) are piece-specific random effects, and
- a|μ_a, σ_a ~ Log-Normal(μ_a, σ_a);
- b|μ_b, σ_b ~ Log-Normal(μ_b, σ_b);
- c|μ_c, σ_c ~ Log-Normal(μ_c, σ_c);
- n|μ_n, σ_n ~ Log-Normal(μ_n, σ_n);
- η|μ_σ0, σ_σ0 ~ Log-Normal(μ_σ0, σ_σ0) and set σ_0 = η / (1 + η).
* (x)_+ = max(x, 0).
* σ_0 serves as the stress ratio threshold in that damage starts to accumulate only when τ(t)/τ_s > σ_0.
* The performance factor φ comes from the load τ(t) = φ*R_o*(γ*D_d+D_s(t)+D_e(t)) / (γ*α_d+α_l).
* The default time step when solving the Canadian model numerically is 100 hours. It can be set via set_timeStep
.
* The probability is calculated as (number of failed samples / total number of simulation samples). Total number of simulation samples can be set via set_simuSampleSize
.
Returns a list of three elements. The first element of the list is the time-to-failure T_f.
The second element is the probability of failture P_f.
The third element is the probability of failure P_f without DOL effect.
The index of θ, the number of failure of the current θ, and the number of failure of the current θ with no DOL effect will be printed in this order along the way if verbose
is TRUE.
Yang, C. H., Zidek, J. V., & Wong, S. W. (2019). Bayesian analysis of accumulated damage models in lumber reliability. Technometrics, 61(2), 233-245.
Wong, S. W., & Zidek, J. V. (2018). Dimensional and statistical foundations for accumulated damage models. Wood science and technology, 52(1), 45-65.
1 2 3 4 5 6 7 8 9 10 | # This is a small demo with 50 simulated failure times
set_simuSampleSize(50)
# simulate the time-to-failures given theta under the residential loads
resList = solveCanADM(default_param, 1, TRUE)
# Below is a more realistic example, using 1000 simulated failure times
# for each posterior draw of theta
set_simuSampleSize(1000)
resTheta = abcMCMC(100, 100, 10, 0.4, c("constLoad_4500_1Y"))
resList = solveCanADM(resTheta, 1, TRUE)
|
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