Is the Weibull Distribution Effective for β < 1 Despite Divergence at t=0?

  • Thread starter Thread starter free_electron
  • Start date Start date
  • Tags Tags
    Divergent Pdf
Click For Summary
SUMMARY

The Weibull distribution is effective for β < 1, despite its divergence at t=0, as it accurately represents early-type failures where the failure rate decreases with age. The probability density function (pdf) is unbounded at t=0, indicating potential issues in production, burn-in processes, or component quality. As time progresses, the failure rate, λ(T), decreases monotonically and approaches zero, making it a valuable tool for analyzing products with early failure characteristics.

PREREQUISITES
  • Understanding of Weibull distribution and its parameters
  • Familiarity with probability density functions (pdf)
  • Knowledge of failure rate analysis in reliability engineering
  • Basic concepts of manufacturing processes and quality control
NEXT STEPS
  • Research the implications of early-type failures in manufacturing
  • Study the application of Weibull distribution in reliability engineering
  • Learn about the impact of production quality on failure rates
  • Explore advanced Weibull analysis techniques for reliability assessment
USEFUL FOR

Reliability engineers, quality control analysts, and manufacturing professionals seeking to understand and apply the Weibull distribution for analyzing early-type failures in products.

free_electron
Messages
27
Reaction score
0
When the weibull shape parameter beta is <1, the pdf is divergent at t=0 due to negative exponent of beta -1. With such a divergent distribution is it meaningful to use Weibull for beta <1?
 
Engineering news on Phys.org
"The Weibull failure rate for 0 < β < 1 is unbounded at T = 0 (or γ). The failure rate, λ(T), decreases thereafter monotonically and is convex, approaching the value of zero as MATH or λ() = 0. This behavior makes it suitable for representing the failure rate of units exhibiting early-type failures, for which the failure rate decreases with age. When encountering such behavior in a manufactured product, it may be indicative of problems in the production process, inadequate burn-in, substandard parts and components, or problems with packaging and shipping."

http://www.weibull.com/LifeDataWeb/characteristics_of_the_weibull_distribution.htm
 

Similar threads

Weibull Distribution Homework: Generating Random Observations from Weibull(k,λ)
  • · Replies 3 ·
Replies
3
Views
1K
Probability Weibull Distribution
  • · Replies 1 ·
Replies
1
Views
2K
How to solve for Weibull distribution parameters using Excel's Solver?
  • · Replies 2 ·
Replies
2
Views
12K
Undergrad Value of beta in Boltzmann Statistics taking degeneracy into account
  • · Replies 19 ·
Replies
19
Views
3K
Mathematica Trying to model red and grey squirrels
  • · Replies 8 ·
Replies
8
Views
3K
Why does (-1)^n(sin(pi/n)) converge when (sin(p/n)) diverges
  • · Replies 2 ·
Replies
2
Views
10K
Prove the mean of the weibull distribution
  • · Replies 4 ·
Replies
4
Views
13K
Questions relating to UMVUE/transformations
  • · Replies 3 ·
Replies
3
Views
3K
Graduate Does Delta Method work for asymptotic distributions?
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Deriving the MGF for the Weibull Distribution
  • · Replies 2 ·
Replies
2
Views
7K