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Weibull Prediction of Future Failures

Background:

This tool is based on work described in references 1 and 2. For a population of N items placed on test, this tool calculates the expected number of failures for some future time interval based on the following two inputs:
1. the estimated Weibull shape parameter and
2. some number of failures (X>=1) during the initial time interval (t1).

Weibull Prediction of Future Failures

Inputs 1 - 5 below are pre-filled with example data from references 1 and 2 for 20,000 items and the discovery of 8 failures at the 3 year inspection point. Additional expected failures during years 3 through 10 are predicted based on Weibull shape parameters in the range of 3.0 to 3.6. Note, ensure consistency of time units for inputs 3 and 5.

Calculation Inputs:

1. Weibull shape parameter (β):

To perform sensitivity analysis for multiple βs, separate input values with a comma.

2. Initial number of units (N):
3. First inspection time (t1):
4. Cumulative number of failures at t1:
5. Second inspection time (t2):
6. Confidence level:
7. Decimal places:
8. Chart/equation options:

Equations
Chart
Title:



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References:

  1. Nordman, D. J., & Meeker, W. Q. (2002). Weibull Prediction Intervals for a Future Number of Failures. Technometrics. 44, 15-23. .
  2. Nelson, W. (2000). Weibull prediction of a future number of failures. Quality and Reliability Engineering International. 16, 23-26.
  3. Abernethy, Robert, The New Weibull Handbook Fifth Edition, Reliability and Statistical Analysis for Predicting Life, Safety, Supportability, Risk, Cost and Warranty Claims
  4. Nelson, Wayne, Applied Life Data Analysis (Wiley Series in Probability and Statistics)
  5. http://www.barringer1.com/wdbase.htm, database of typical Weibull shape and characteristic life parameters.