`R/confidence_intervals.R`

`confint_betabinom.Rd`

This function computes the non-parametric beta binomial confidence bounds (BB) for quantiles and failure probabilities.

confint_betabinom(x, ...) # S3 method for wt_model confint_betabinom( x, b_lives = c(0.01, 0.1, 0.5), bounds = c("two_sided", "lower", "upper"), conf_level = 0.95, direction = c("y", "x"), ... )

x | A list with class |
---|---|

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

b_lives | A numeric vector indicating the probabilities \(p\) of the \(B_p\)-lives (quantiles) to be considered. |

bounds | A character string specifying the bound(s) to be computed. |

conf_level | Confidence level of the interval. |

direction | A character string specifying the direction of the confidence
interval. |

A tibble with class `wt_confint`

containing the following columns:

`x`

: An ordered sequence of the lifetime characteristic regarding the failed units, starting at`min(x)`

and ending up at`max(x)`

. With`b_lives = c(0.01, 0.1, 0.5)`

the 1%, 10% and 50% quantiles are additionally included in`x`

, but only if the specified probabilities are in the range of the estimated probabilities.`rank`

: Interpolated ranks as a function of probabilities, computed with the converted approximation formula of*Benard*.`prob`

: An ordered sequence of probabilities with specified`b_lives`

included.`lower_bound`

: Provided, if`bounds`

is one of`"two_sided"`

or`"lower"`

. Lower confidence limits with respect to`direction`

, i.e. limits for quantiles or probabilities.`upper_bound`

: Provided, if`bounds`

is one of`"two_sided"`

or`"upper"`

. Upper confidence limits with respect to`direction`

, i.e. limits for quantiles or probabilities.`cdf_estimation_method`

: Method for the estimation of failure probabilities which was specified in estimate_cdf.

Further information is stored in the attributes of this tibble:

`distribution`

: Distribution which was specified in rank_regression.`bounds`

: Specified bound(s).`direction`

: Specified direction.`model_estimation`

: Input list with class`wt_model`

.

The procedure is similar to the *Median Ranks* method but with the
difference that instead of finding the probability for the *j*-th rank at the
50% level the probability (probabilities) has (have) to be found at the given
confidence level.

# Reliability data preparation: ## Data for two-parametric model: data_2p <- reliability_data( shock, x = distance, status = status ) ## Data for three-parametric model: data_3p <- reliability_data( alloy, x = cycles, status = status ) # Probability estimation: prob_tbl_2p <- estimate_cdf( data_2p, methods = "johnson" ) prob_tbl_3p <- estimate_cdf( data_3p, methods = "johnson" ) prob_tbl_mult <- estimate_cdf( data_3p, methods = c("johnson", "mr") )#># Model estimation with rank_regression(): rr_2p <- rank_regression( prob_tbl_2p, distribution = "weibull" ) rr_3p <- rank_regression( prob_tbl_3p, distribution = "lognormal3", conf_level = 0.90 ) rr_lists <- rank_regression( prob_tbl_mult, distribution = "loglogistic3", conf_level = 0.90 ) # Example 1 - Two-sided 95% confidence interval for probabilities ('y'): conf_betabin_1 <- confint_betabinom( x = rr_2p, bounds = "two_sided", conf_level = 0.95, direction = "y" ) # Example 2 - One-sided lower/upper 90% confidence interval for quantiles ('x'): conf_betabin_2_1 <- confint_betabinom( x = rr_2p, bounds = "lower", conf_level = 0.90, direction = "x" ) conf_betabin_2_2 <- confint_betabinom( x = rr_2p, bounds = "upper", conf_level = 0.90, direction = "x" ) # Example 3 - Two-sided 90% confidence intervals for both directions using # a three-parametric model: conf_betabin_3_1 <- confint_betabinom( x = rr_3p, bounds = "two_sided", conf_level = 0.90, direction = "y" ) conf_betabin_3_2 <- confint_betabinom( x = rr_3p, bounds = "two_sided", conf_level = 0.90, direction = "x" ) # Example 4 - Confidence intervals if multiple methods in estimate_cdf, i.e. # "johnson" and "mr", were specified: conf_betabin_4 <- confint_betabinom( x = rr_lists, bounds = "two_sided", conf_level = 0.99, direction = "y" )