bayesian.vam: Virtual age model for Bayesian estimation

In rcqls/VAM: Virtual Age Models

Virtual age model for Bayesian estimation

Description

bayesian.vam is used to define a virtual age model for Corrective Maintenance (CM) and planned Preventive Maintenance (PM). The object define with bayesian.vam can be used to compute Bayesian estimators of the parameters thanks to the run.bayesian.vam method.

Usage

bayesian.vam(formula, data)

Arguments

formula	a symbolic description of the virtual age model and observations. The details of formula specifications are given under ‘Details’.
data	a data frame or possibly a list (when several system are considered together) containing the observations.

Details

The symbolic description of the model done in formula has the form response ~ model. response is a symbolic description of the data considered. The specifications are the same as those of model.vam function. model is a symbolic description of the virtual age model considered. The specifications are globally similar those of sim.vam function. The difference with model.vam is that each parameter value of model has to be replaced by a symbolic description of the prior distribution of the parameter. This symbolic description has the form ~ Prior. The available prior distribution for Prior are:

• Beta(a,b)or Be(a,b) or B(a,b) for a beta distribution with parameters a and b (see dbeta for supplementary informations about this distribution, a and b represent respectively shape and scale arguments of dbeta),

• Gamma(a,s)or G(a,s) for a gamma distribution with parameters a and s (see dgamma for supplementary informations about this distribution),

• Unif(a=0,b=1)or U(a=0,b=1) for a uniform distribution on the interval [a,b] (see dunif for supplementary informations about this distribution),

• Norm(m=0,s=1)or N(m=0,s=1) for a normal distribution with mean m and standard deviation s (see dnorm for supplementary informations about this distribution),

• LNorm(m=0,s=1)or LN(m=0,s=1) or LogNorm(m=0,s=1) for a log-normal distribution, that is to say Y=exp(X) follows a log-normal distribution if X follows a normal distribution with mean m and standard deviation s,

• NonInform(init=1,init_sigma=1)or NInf(init=1,init_sigma=1) or NI(init=1,init_sigma=1) for a a standard Jeffrey's non informative prior distribution for Weibull parameters (with a prior density in x proportional to 1/x). Init represents the initialization of the maximum likelihood method used to compute the initialization of the Gibbs sampling algorithm in the run.bayesian.vam method (in order to evaluate the posterior distribution). init_sigma represents the standard deviation of instrumental distribution of the Metropolis Hasting step of Gibbs sampling algorithm used in run.bayesian.vam to evaluate the posterior distribution. init_sigma is used only if this standard deviation is not specified in run.bayesian.vam. Those characteristics are defined since this non informative prior distribution is not a proper distribution, then it does not have a mean and standard deviation.

In addition, in this case the PM policy is useless, so it has not to be necessarily defined.

Value

The function produces an object of class bayesian.vam which contains the virtual age model considered, the prior distribution of the parameters and the corresponding observations.

Author(s)

R. Drouilhet

See Also

run.bayesian.vam to compute the Bayesian method. coef.bayesian.vam to extract the parameters estimation values of the Bayesian method. summary.bayesian.vam to produce a result summary of the Bayesian method. hist.bayesian.vam for plotting the histogram of the posterior distribution of the parameters. plot.bayesian.vam for plotting estimating characteristics of the model.

Examples

simARAInf<-sim.vam(  ~ (ARAInf(.4) | Weibull(.001,2.5)))
simData<-simulate(simARAInf,30)
bayesARAInf <- bayesian.vam(Time & Type ~ (ARAInf(~Unif(0,1)) | Weibull(~Unif(0,1),~Unif(2,4))),data=simData)
coef(bayesARAInf)

rcqls/VAM documentation built on Jan. 14, 2024, 9:07 p.m.