abcADM (version 1.0)

simu_failTime: Simulate samples of failure time using parameters \(\theta\)

Description

Simulate n observations of failure time from \(\theta = (\mu_a, \sigma_a, \mu_b, \sigma_b, \mu_c, \sigma_c, \mu_n, \sigma_n, \mu_{\sigma_0} , \sigma_{\sigma_0})\) for constant load test or ramp load test.

Usage

simu_failTime(paras, n, tau_c, t_c, verbose = FALSE)

Arguments

paras

either a vector or a matrix where each row is \(\theta\)

n

number of samples

tau_c

constant load level (can be set to infinity for ramp load test)

t_c

ending time of the constant load test in hours (can be set to infinity for ramp load test)

verbose

print information messages to console if TRUE

Value

Return a matrix of failure times. Each column contains samples from one \(\theta\). The name of the output matrix must be in the format "ID_\(\tau_c\)_t_c(in years)", e.g. simuConstLoad_4500_1Y.

Details

* The default \(\theta\) is provided and can be invoked via default_param.

* When sample pieces are subject to the load profile

\(\tau(t) = kt\) if \(t \le T_0\)

\(\tau(t) = \tau_c\) if \(t > T_0\)

where \(\tau_c\) is the selected constant-load level under the ramp-loading rate k, and \(T_0\) is the time required for the load to reach \(\tau_c\) under the ramp-loading rate k.

* The constant load level is assumed to be reached at the ramp-loading rate (k). The ramp-loading rate is 388,440 psi/hour.

Utilizes routines from the BRENT C++ root-finding library.

References

Brent, R. (2002). Algorithms for Minimization without Derivatives. Dover. ISBN: 0-486-41998-3.

Yang, C. H., Zidek, J. V., & Wong, S. W. (2019). Bayesian analysis of accumulated damage models in lumber reliability. Technometrics, 61(2), 233-245.

Examples

# NOT RUN {
# simulate data with constant load 4500 psi and test of duration 1Y (8760 hours)
simuConstLoad_4500_1Y = simu_failTime(default_param, 30, 4500, 8760, TRUE)

# simulate data for ramp load
simuRampLoad_Inf_1Y = simu_failTime(default_param, 30, Inf, 8760)


# }