weibulltools (version 2.0.0)

r_squared_profiling.default: R-Squared-Profile Function for Parametric Lifetime Distributions with Threshold

Description

This function evaluates the coefficient of determination with respect to a given threshold parameter of a three-parametric lifetime distribution. In terms of Rank Regression this function can be optimized (optim) to estimate the threshold parameter.

Usage

# S3 method for default
r_squared_profiling(
  x,
  y,
  thres,
  distribution = c("weibull3", "lognormal3", "loglogistic3"),
  ...
)

Value

Returns the coefficient of determination with respect to the threshold parameter thres.

Arguments

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.

y

A numeric vector which consists of estimated failure probabilities regarding the lifetime data in x.

thres

A numeric value for the threshold parameter.

distribution

Supposed three-parametric distribution of the random variable.

...

Further arguments passed to or from other methods. Currently not used.

References

Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998

See Also

r_squared_profiling

Examples

# Vectors:
cycles <- alloy$cycles
status <- alloy$status

# Probability estimation:
prob_tbl <- estimate_cdf(
  x = cycles,
  status = status,
  method = "johnson"
)

# Determining the optimal coefficient of determination:
## Range of threshold parameter must be smaller than the first failure:
threshold <- seq(
  0,
  min(cycles[status == 1]) - 0.1,
  length.out = 100
)

## Coefficient of determination with respect to threshold values:
profile_r2 <- r_squared_profiling(
  x = prob_tbl$x[prob_tbl$status == 1],
  y = prob_tbl$prob[prob_tbl$status == 1],
  thres = threshold,
  distribution = "weibull3"
)

## Threshold value (among the candidates) that maximizes the
## coefficient of determination:
threshold[which.max(profile_r2)]

## plot:
plot(
  threshold,
  profile_r2,
  type = "l"
)
abline(
  v = threshold[which.max(profile_r2)],
  h = max(profile_r2),
  col = "red"
)