Estimation of Failure Probabilities using Johnson's Method

Source: R/probability_estimators.R

[Soft-deprecated]

johnson_method() is no longer under active development, switching to estimate_cdf is recommended.

johnson_method(x, status, id = NULL, method = c("benard", "invbeta"))

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.

status

A vector of binary data (0 or 1) indicating whether a unit is a right censored observation (= 0) or a failure (= 1).

id

A vector for the identification of every unit. Default is NULL.

method

Method for the estimation of the cdf. Can be "benard" (default) or "invbeta".

Value

A tibble containing the following columns:

  • id : Identification for every unit.

  • x : Lifetime characteristic.

  • status : Binary data (0 or 1) indicating whether a unit is a right censored observation (= 0) or a failure (= 1).

  • rank : Adjusted ranks, NA if status = 0.

  • prob : Estimated failure probabilities, NA if status = 0.

  • cdf_estimation_method : Specified method for the estimation of failure probabilities (always 'johnson').

Details

This non-parametric approach is used to estimate the failure probabilities in terms of uncensored or (multiple) right censored data. Compared to complete data the correction is done by calculating adjusted ranks which takes non-defective units into account.

Examples

# Vectors:
obs   <- seq(10000, 100000, 10000)
state <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 0)
uic   <- c("3435", "1203", "958X", "XX71", "abcd", "tz46",
           "fl29", "AX23", "Uy12", "kl1a")

# Example 1 - Johnson method for intact and failed units:
tbl_john <- johnson_method(
  x = obs,
  status = state,
  id = uic
)
#> Warning: `johnson_method()` was deprecated in weibulltools 2.0.0.
#> Please use `estimate_cdf()` instead.

# Example 2 - Johnson's method works also if only defective units are considered:
tbl_john_2 <- johnson_method(
  x = obs,
  status = rep(1, length(obs))
)
#> Warning: `johnson_method()` was deprecated in weibulltools 2.0.0.
#> Please use `estimate_cdf()` instead.