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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:



Featured Reference:

Statistical Models in Engineering
Statistical Models in Engineering


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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. Nordman, Danial J. and Meeker, William Q., "Weibull Prediction Intervals for a Future Number of Failures" (2000). Statistics Preprints. .
  3. Nelson, W. (2000). Weibull prediction of a future number of failures. Quality and Reliability Engineering International. 16, 23-26.
  4. Abernethy, Robert, The Weibull Analysis Handbook.
  5. Nelson, Wayne, Applied Life Data Analysis
  6. Meeker, William Q.; Escobar, Luis A.Statistical Methods for Reliability Data.
  7. Barringer, Paul, Barringer & Associates, Inc., database of typical Weibull shape and characteristic life parameters (wdbase), Feb. 22, 2010 (no longer available online).