Damaged IGBT
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Reliability Formulae — The Usual Suspects
 
F Cumulative distribution function
(CDF)
F(t) = 1 – R(t)
F(t) = ∫ f(τ) dτ
F(t) = 1 – exp(–∫ h(τ) dτ)
 
f Probability density function
(pdf)
f(t) = F'(t)
f(t) = h(t) exp(–∫ h(τ) dτ)
f(t) = –R'(t)
 
h Failure rate function h(t) = f(t) / R(t)
h(t) = F'(t) / (1 – F(t))
h(t) = f(t) / (1 – ∫ f(τ) dτ)
h(t) = –R'(t) / R(t)
 
R Reliability function R(t) = 1 – F(t)
R(t) = exp(–∫ h(τ) dτ)
R(t) = 1 – ∫ f(τ) dτ
 
MTTF Mean time to failure MTTF = ∫ 1 – F(τ) dτ
MTTF = ∫ τ F(τ) dτ
MTTF = ∫ R(τ) dτ
 
Integration intervals of F, f, h, R → [0, t]
Integration interval of MTTF → [0, ∞)