guo_weibull_series_md: Example Data for a Series System (Table 2, Guo 2013)

In queelius/series_system_estimation_masked_data: Estimating Reliability of Components in Series from Masked Data with Relaxed Candidate Set Models

Example Data for a Series System (Table 2, Guo 2013)

Description

The source of this data set comes from "Estimating Component Reliabilities from Incomplete System Failure Data", Table 2: Example Data for a Series System.

Usage

guo_weibull_series_md

Format

A data frame with 30 rows and 4 columns:

t

Time of failure of series system

x1

Indicates whether component 1 is in the candidate set

x2

Indicates whether component 2 is in the candidate set

x3

Indicates whether component 3 is in the candidate set

Details

When you use likelihood model that assumes a Weibull series system and candidate sets represented by Boolean vectors (x1, x2, x3) that satisfy conditions C1, C2, and C3, the MLE of the shape and scale parameters are:

• β1 = 1.2576

• η1 = 994.3661

• β2 = 1.1635

• η2 = 908.9458

• β3 = 1.1308

• η3 = 840.1141

• θ̂ = (β1, η1, β2, η2, β3, η3)

This has a log-likelihood of -228.6851.

Source

H. Guo, F. Szidarovszky, and P. Niu, "Estimating component reliabilities from incomplete system failure data," in 2013 Proceedings Annual Reliability and Maintainability Symposium (RAMS), 2013. Online. Available: https://doi.org/10.1109/rams.2013.6517765

See Also

guo_weibull_series_mle

Examples

head(guo_weibull_series_md)
loglik <- md_loglike_weibull_series_C1_C2_C3(guo_weibull_series_md
    deltavar = NULL) # no right-censoring in this data set
sol <- optim(par = guo_weibull_series_mle$mle,
             fn = loglik,
             hessian = TRUE,
             control = list(parscale = c(1, 1000, 1, 1000, 1, 1000)))
abs(sol$value - guo_weibull_series_mle$loglike) < 1e-4
abs(sol$par - guo_weibull_series_mle$mle) < 1e-4

queelius/series_system_estimation_masked_data documentation built on Jan. 29, 2025, 11:08 a.m.