R/ttt.R

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

#' Total Time on Test for Repairable Systems
#'
#' \code{ttt} calculates the scaled total time on test (TTT) as described in
#' \href{http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.46.974&rep=rep1&type=pdf}{Tests for trend in more than one repairable system}
#' and \href{www.dtic.mil/dtic/tr/fulltext/u2/a043573.pdf}{Analysis of Time Between Failures for Repairable Components} \cr \cr
#' As indicated in \href{www.dtic.mil/dtic/tr/fulltext/u2/a043573.pdf}{Analysis of Time Between Failures for Repairable Components}
#' this can be used to create a TTT plot. \cr \cr
#' A TTT plot that follows the line \eqn{y = x}
#' indicates a Homogeneous Poisson Process (HPP) (constant failure rate),
#' while a concave TTT plot indicates a Nonhomogeneous Poisson Process (NHPP).
#' Concave up indicates decreasing failure rate,
#' while concave down indicates increasing failure rate. See:
#' \href{http://www.pinzhi.org/Minitab/Reliability_and_Survival_Analysis/RS_Growth_Curves/Total_time_on_test_plot.htm}{Minitab TTT Plot}
#'
#' @param t A list of failure time vectors. Each vector should indicate
#'   a different system, i.e. if you have multiple systems each
#'   systems' failure times should be in it's own vector.
#' @param T A list of Total Time on Test (TTT) (i.e. test duration) vectors.
#'   The vectors in the list should be of length 1, and each vector should
#'   indicate a different system, i.e. if you have multiple systems each
#'   systems' TTT should be in it's own vector.
#' @param fail.trunc Logical indicating if the test was failure terminated.
#'
#' @return The output will be a data.frame with the sorted supplied time
#'   values (\code{t}), the total time on test (\code{ttt}), and the
#'   scaled total time on test (\code{scaled_ttt}).
#'   A plot of \code{scaled_ttt} vs \code{ttt} would be a TTT plot.
#'
#' @seealso \code{\link{power_law_process}}, \code{\link{power_law_mcf}},
#'   \code{\link{mcf}}, \code{\link{trend_test}}, \code{\link{common_beta}}
#'
#' @examples
#' data(amsaa)
#'
#' # Three systems all time truncated at 200 hours
#' ttt_df <- ttt(
#'   t = split(amsaa$Time, amsaa$System),
#'   T = list(200,200,200),
#'   fail.trunc = FALSE)
#'
#' theme_set(theme_bw())
#' ggplot(ttt_df, aes(x = ttt, y = scaled_ttt)) +
#'   geom_line(colour = "red") + geom_point() +
#'   geom_abline(intercept = 0, slope = 1) +
#'   labs(
#'     x = "Total Time on Test",
#'     y = "Scaled Total Time on Test")
#'
#'  rm(list = c("amsaa", "ttt_df"))
#'
#' @export
ttt <- function(t, T, fail.trunc = FALSE){

  if(fail.trunc == TRUE){

    T <- unlist(T)
    tsort <- sort(unlist(t))
    test_time_accrued <- NULL
    N <- length(tsort)

    for(i in seq_along(tsort)){
      n <- length(which(T >= tsort[i]))
      test_time_accrued[i] <- tsort[i]*n
      if(i > 1){
        if(test_time_accrued[i] < test_time_accrued[i-1]){
          test_time_accrued[i] <- test_time_accrued[i] + sum(T[which(T < tsort[i])])
        }
      }
    }
    scaled_ttt <- test_time_accrued / max(test_time_accrued)

    df <- data.frame(t = tsort, ttt = (1:N)/N, scaled_ttt = scaled_ttt)
  }
  if(fail.trunc == FALSE){
  
    T <- unlist(T)
    tsort <- sort(unlist(t))
    test_time_accrued <- NULL
    N <- length(tsort)

    for(i in seq_along(tsort)){
      n <- length(which(T >= tsort[i]))
      test_time_accrued[i] <- tsort[i]*n
      if(i > 1){
        if(test_time_accrued[i] < test_time_accrued[i-1]){
          test_time_accrued[i] <- test_time_accrued[i] + sum(T[which(T < tsort[i])])
        }
      }
    }

    # Add the final times (when all the systems stopped testing)
    test_time_accrued <- c(test_time_accrued, sum(T))

    scaled_ttt <- test_time_accrued / max(test_time_accrued)

    df <- data.frame(t = tsort, ttt = (1:N)/N, scaled_ttt = scaled_ttt[-(N+1)])
  }

  return(df)
}