R/exp_oc.R

In jjw3952/mcotear: Contains helpful functions for use within MCOTEA

#' Exponential Operating Characteristic (OC) Function
#'
#' \code{exp_oc} the OC function for exponential reliability tests
#'   (probability of passing test as a function of true MTBF). See pg. 67
#'   for the OC formula in MIL-HDBK-781A.
#'
#' @param accept A vector with the allowable number of failures.
#' @param duration A vector of test durations.
#' @param mtbf A vector of the true MTBFs.
#'
#' @return The probability of passing the test of a given duration with an
#'   allowable number of failures, given the true MTBF. (The probability of
#'   accepting items with an MTBF = \code{mtbf}.)
#'
#' @seealso \code{\link{exp_mtbf_req}}, \code{\link{exp_reliability_req}},
#'   \code{\link{exp_test_duration}}, \code{\link{exp_mean_lcb}},
#'   \code{\link{exp_fixed_duration_tests}}
#'
#' @examples
#' theta <- seq(250, 5000, 50)
#' prob_pass <- exp_oc(accept = 0, duration = 804.719, mtbf = theta)
#' prob_pass[1:5]
#'
#' ggplot(data.frame(prob_pass = prob_pass, theta = theta)) +
#'   geom_line(
#'     aes(x = theta, y = prob_pass),
#'     linewidth = 1, colour = "blue"
#'   ) +
#'   scale_y_continuous(limits = c(0,1), breaks = seq(0,1,.2))
#'
#' # Using stat_function()
#' ggplot(data.frame(x=c(250,5000))) +
#'   stat_function(
#'     aes(x=x), fun = exp_oc, args = list(accept = 0, duration = 804.719),
#'     linewidth = 1, colour = "blue"
#'   ) +
#'   scale_y_continuous(limits = c(0,1), breaks = seq(0,1,.2)) +
#'   labs(x = "MTBF", y = "Prob of Passing Demonstration")
#'
#' # See: example(exp_fixed_duration_tests)
#' 
#' rm(list = c("theta", "prob_pass"))
#'
#' @references
#' Mil-Hdbk-781A
#'
#' @export
exp_oc <- function(accept, duration, mtbf){
  prob_pass <- ppois(accept, duration/mtbf, lower.tail=TRUE)
  prob_pass
}