From Resistor Theory and Technology

OVERVIEW

A statistical model for accelerated lifetime testing includes the following elements:

  1. A distribution curve for lifetime as a function of time, representing the dispersion among the sampled components.

  2. A mathematical equation relating component lifetime to the magnitude of the applied stress.

Typically the mean value and variance of lifetime distribution are expressed as a function of the stress or acceleration parameter: temperature, pressure, humidity, etc.

The most common distributions used are exponential, normal, Gaussian, log-normal, Weibull, and Arrhenius.

A.1 EXPONENTIAL DISTRIBUTION [1]

A cumulative probability distribution function F(t) represents that fraction of the population to which we apply one or more constraints of known origin and magnitude, and which fails in time t. This population has the following mathematical properties:

  1. It is a continuous function for all values of t > 0.

  2. Lim F(t) = 0 for t - ? and lim F(t) = 1 for t => ?

  3. F(t) ? F(t ?) for all values of t < t ?.

The exponential distribution function is given by the following formula:


in which ? is the mean time to failure (MTTF). ? is expressed in units of time, for example, hours, months, years, cycles, etc. We can also define the ratio ? = 1/ ? as the mean rate of failure. [2] The relation between MTTF and failure rate is valid only for an exponential distribution. The probability density is equal to:


This...


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