Description Usage Arguments Value References Examples
This method estimates the parameters and calculates normal approximation confidence
intervals for a two- or three-parametric lifetime distribution in the frequently used
(log-) location-scale parameterization. ml_estimation
uses the
Lifedata.MLE
function which is defined in the
SPREDA package.
For the Weibull the estimates are transformed such that they are in line with
the parameterization provided by the stats package like
pweibull
. The method is applicable for complete and (multiple)
right censored data.
1 2 3 4 | ml_estimation(x, event, distribution = c("weibull", "lognormal",
"loglogistic", "normal", "logistic", "sev", "weibull3", "lognormal3",
"loglogistic3"), wts = rep(1, length(x)), conf_level = 0.95,
details = TRUE)
|
x |
a numeric vector which consists of lifetime data. Lifetime data could be every characteristic influencing the reliability of a product, e.g. operating time (days/months in service), mileage (km, miles), load cycles. |
event |
a vector of binary data (0 or 1) indicating whether unit i is a right censored observation (= 0) or a failure (= 1). |
distribution |
supposed distribution of the random variable. The
value can be |
wts |
optional vector of case weights. The length of |
conf_level |
confidence level of the interval. The default value is
|
details |
a logical variable, where the default value is |
Returns a list with the following components (depending on
details
argument):
coefficients
: Provided, if distribution
is "weibull"
.
η is the estimated scale and β the estimated shape parameter.
confint
: Provided, if distribution
is "weibull"
.
Confidence interval for η and β.
loc_sc_coefficients
: Estimated location-scale parameters.
loc_sc_confint
: Confidence interval for location-scale parameters.
loc_sc_vcov
: Estimated Variance-Covariance matrix of the used
location-scale distribution.
logL
: The log-likelihood value.
aic
: Akaike Information Criterion.
bic
: Bayesian Information Criterion.
Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | # Example 1: Fitting a two-parameter Weibull:
obs <- seq(10000, 100000, 10000)
state <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0)
mle <- ml_estimation(x = obs, event = state,
distribution = "weibull", conf_level = 0.90)
# Example 2: Fitting a three-parameter Weibull:
# Alloy T7987 dataset taken from Meeker and Escobar(1998, p. 131)
cycles <- c(300, 300, 300, 300, 300, 291, 274, 271, 269, 257, 256, 227, 226,
224, 213, 211, 205, 203, 197, 196, 190, 189, 188, 187, 184, 180,
180, 177, 176, 173, 172, 171, 170, 170, 169, 168, 168, 162, 159,
159, 159, 159, 152, 152, 149, 149, 144, 143, 141, 141, 140, 139,
139, 136, 135, 133, 131, 129, 123, 121, 121, 118, 117, 117, 114,
112, 108, 104, 99, 99, 96, 94)
state <- c(rep(0, 5), rep(1, 67))
mle_weib3 <- ml_estimation(x = cycles, event = state,
distribution = "weibull3", conf_level = 0.95)
|
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