The TTT transform

• The TTT transform is a parametric analogue to the TTT-plot given by:
• $ \color{blue}{\phi_F(v) = \frac{\int_0^{F^{-1}(v)} R(u)du}{\mathrm{MTTF}}} $
  • where $ \color{blue}{F^{-1}(v)} $ is the inverse cumulative distribution function for the time-to-failures
• For The Weibull distribution:
  • $ \color{blue}{\phi_W(v,\alpha) = \mathrm{CDFGamma}(-\mathrm{ln}(1-v), 1/\alpha, 1)} $
  • CDFGamma() is the cummulative distribution fuction in the gamma distribution, and is found in MS Excel by =GAMMADIST(-LN(1-v),1/Alpha,1,TRUE)
• By trial and error, we could find the "best" value for α, and compare the TTT transform with the TTT plot.