Create 07_lesson.R

code/07_lesson.R

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+#' @name lesson_7
+#' @author Tim Fraser
+#' @title Lesson 7 - Exponential Distribution!
+#' @note more info here: https://timothyfraser.com/sigma/ 
+
+
+library(dplyr)
+library(readr)
+library(mosaicCalc)
+
+masks <- read_csv("workshops/masks.csv")
+
+masks %>% glimpse()
+
+# Let's write some functions!
+# failure function (CDF)
+f = function(t, lambda){ 1 - exp(-1*t*lambda)}
+# reliability function
+r = function(t, lambda){ exp(-1*t*lambda) }
+
+
+
+stat <- masks %>%
+  summarize(
+    # The literal mean time to fail 
+    # in our observed distribution is this
+    mttf = mean(left_earloop),
+    # And lambda is this...
+    lambda = 1 / mttf,
+    # The observed median is this....
+    median = median(left_earloop),
+    # But if we assume it's an exponential distribution
+    # and calculate the median from lambda,
+    # we get t50, which is very close.
+    t50 = log(2) / lambda)
+
+masks$left_earloop %>% hist()
+
+stat$lambda
+
+r(t = 10 + 5, lambda = stat$lambda) / r(t = 10, lambda = stat$lambda)
+
+
+
+
+
+cr = function(t, x, lambda){
+  # We can actually nest functions inside each other, 
+  # to make them easier to write
+  r = function(t, lambda){ exp(-1*t*lambda)}
+
+  # Calculate R(x + t) / R(t) 
+  output <- r(t = t + x, lambda) / r(t = t, lambda)
+
+  # and return the result!
+  return(output)
+}
+
+cr(t = 10, x = 5, lambda = stat$lambda)
+
+
+
+
+# Calculate Mean Residual Life
+mu = function(t, lambda){
+
+  # Get the Reliability Function for exponential distribution
+  r = function(t, lambda){ exp(-1*t*lambda)}
+
+  # Get the MTTF (integral of reliability function)
+  mttf = antiD(tilde = r(t, lambda) ~ t)
+
+  # Now calculate mu(), the Mean Residual Life function at time t
+  output <- mttf(t = Inf, lambda = lambda) / r(t = t, lambda = lambda)
+
+  return(output)
+}
+
+# Get the MTTF (integral of reliability function)
+r = function(t, lambda){ exp(-1*t*lambda)}
+r(t = 100, lambda = 0.01)
+
+mttf = antiD(tilde = r(t, lambda) ~ t)
+
+# mttf(t = 1000, lambda = 0.001)
+mttf(t = Inf, lambda = 0.001)
+
+1 / 0.001