9860

Closed-Form Full Life Cycle Distribution

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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

The first snapshot depicts the effects of infant mortality, random failure, and wear-out on the distribution. The second snapshot demonstrates that when the random failure rate is relatively high, the distribution asymptotically approaches an exponential. The third snapshot shows that when infant mortality and random failures are low, wear-out dominates, and the distribution approaches a Gaussian.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+