power_law_mcf: The Mean Cumulative Function for a Power Law Process

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

The Mean Cumulative Function for a Power Law Process

Description

power_law_mcf implements the mean cumulative function (expected number of failures at time t) for a Nonhomogeneous Poisson Process (NHPP) with Power Law Intensity Function (Crow-AMSAA model) given lambda (scale) and beta (shape) parameters/parameter estimates.

Usage

power_law_mcf(t, lambda, beta)

Arguments

t	A vector or list of failure times. As with t in power_law_process, t could be a list of vectors such that each vector indicates a different system, i.e. if you have multiple systems each systems' failure times could be in it's own vector.
lambda	the scale parameter or parameter estimate for a Power Law NHPP. Can be calculated using power_law_process.
beta	the shape parameter or parameter estimate for a Power Law NHPP. Can be calculated using power_law_process.

Value

The output will be a data.frame containing, the ordered failure times ("t") and corresponding Power Law mcf values ("power_mcf").

See Also

power_law_process, mcf, rocof, power_law_intensity, trend_test, ttt, common_beta

Examples

data(amsaa)
data(cbPalette)

# Three systems all time truncated at 200 hours
 # fit a NHPP Power Law (AMSAA-Crow) Model
(m <- power_law_process(
  t = split(amsaa$Time, amsaa$System),
  T = list(200,200,200),
  alpha = 0.05,
  fail.trunc = FALSE,
  iter = 10))

# Get the nonparametric mcf estimates
 # and change the name of "t" to "Time"
 # so it matches with the name in the 
 # amsaa data set
df_mcf <- mcf(
  t = split(amsaa$Time, amsaa$System),
  T = list(200,200,200))
names(df_mcf)[1] <- "Time"

# Merge the nonparametric mcf estimates
# with amsaa into a new data.frame amsaa1
amsaa1 <- merge(amsaa, df_mcf, by = "Time")
head(amsaa1)

# Either one of the following works
power_law_mcf(t = amsaa$Time, m$est[1], m$est[2])
power_law_mcf(t = split(amsaa$Time, amsaa$System), m$est[1], m$est[2])

# Mean Cumulative Function Plot
theme_set(theme_bw())
ggplot(amsaa1, aes(x = Time, y = mcf)) +
  geom_point() +
  labs(
    x = "Operating Hours", y = "MCF",
    title = "Mean Cumulative Function") +
  stat_function(
    fun = function(x){
      power_law_mcf(t = x, lambda = m$e[[1]], beta = m$e[[2]])$power_mcf
    },
    mapping = aes(colour = "Power-Law NHPP")
  ) +
  scale_colour_manual("Functions:",
    breaks = c("Power-Law NHPP"),
    values = c("Power-Law NHPP" = cbPalette[2]),
    guide = guide_legend(
      override.aes = list(
        linetype = c("solid")
    ))
  ) +
  theme(legend.position = c(.175,.80),
    legend.background = element_rect(fill="grey95"),
    legend.key = element_rect(fill="grey95")
  )

rm(list = c("amsaa", "cbPalette", "m", "df_mcf", "amsaa1"))

jjw3952/mcotear documentation built on Sept. 2, 2023, 10:30 a.m.