TTT plot for complete data set

• Assume we have n independent and identically distributed time-to-failure observations
  • The items have been operated under approximately the same conditions, and they are as good as new after a repair if we observe several failures for one item
  • If we have several observations for one item, the so-called Nelson Aalen plot should show points approximately on a straight line (not covered here)
• Time-to-failures are denoted t₁,t₂,t₃,..,t_n
• t₍₁₎,t₍₂₎,t₍₃₎,..., t_(n) are the sorted time-to-failure observations
  • i.e., t₍₁₎ ≤ t₍₂₎ ≤ t₍₃₎ ≤..≤ t_(n)
• The so-called TTT observator is defined for each point of time t as the total observed time (Total Time on Test) up to t:
• $ \color{blue}{\mathcal{T}(t) = \sum_{j=1}^i t_{(j)} + (n-i)t} $
  • where i is such that t_(i) ≤ t < t_(i+1)
• The TTT plot is given by plotting the normalized TTT observator againts a normalized index, i.e.,
• $ \left ( \color{blue}{ \frac{i}{n}} , \color{blue}{\frac{\mathcal{T}(t_{(i)})} {\mathcal{T}(t_{(n)})}} \right )$