Closed-Form Full Life Cycle Distribution

end of life mean, μ

10.

end of life standard deviation, σ

1.

random failure rate, λ

0.1

infant mortality failure rate, Λ

10.

infant mortality defective proportion, α

0.2

This Demonstration features an approximation of the closed-form full life cycle distribution. It updates the probability density function, cumulative density function, and hazard function for the distribution as you change the five input parameters. This distribution models the three basic types of failure—infant mortality, random, and end-of-life. It is a rigorous improvement over the empirically observed and modeled "bathtub curve". Like the related Weibull distribution, it is closed-form and continuous; unlike the Weibull, it can simultaneously model infant mortality and wear-out. This distribution closely approximates the closed-form full life cycle distribution when the wear-out mean is significantly larger than the wear-out standard deviation.