Survival Analysis – Reliability Theory / Human Life – Transistor’s Life (Final Part)

Some Mathematics of Reliability Theory – Survival Analysis

In this blog I am trying to explain mathematical concepts with real life metaphors and examples. The discussion on similarities between reliability theory and survival analysis is concluded in today’s blog with explanation on mathematics behind this concept. This mathematics summarizes the discussion conducted in previous five parts.

Denoting the life of a device/ human by a random variable T, t denotes the specific value taken by this random variable.

R(t) = Reliability of device at time t = P( T greater than equal to t)  = Probability that the life time of device is greater than t

S(t)= Survival of an individual at least till time t = P( T greater than equal to t) = Probability that an individual survives at time t

Cumulative distribution function = F(t) = 1 - R(t) = Probability that the device fails before t

Cumulative distribution function = F(t) = 1 - S(t) = Probability that an individual dies before t

 h(t) = hazard rate = Probability (the device fails between time t and t + Δ t|The device has survived till t)

= -R’(t)/R(t)

h(t)= instantaneous force of mortality = Probability ( an individual dies between time t and t + Δ t|The individual survived till t) = -S’(t)/S(t)

h(t) = λ=constant  for electronic device – memory less property and independent of time-Reliability Theory

h(t) = λ(t) = function of time for human life – Survival Analysis