bayesian.vam | R Documentation |
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.
bayesian.vam(formula, data)
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. |
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.
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.
R. Drouilhet
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.
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)
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