This is an example of a recently published in the Reliability Analytics Toolkit called Weibull Prediction of Future Failures. 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 (t_{1}).

For example, if there are 20,000 items that have started operation at “time 0” and 8 have found to be in a failed state at the 3 year point. It is desired to estimate how many additional items will fail between the 3 and 10 year point. The figure below shows the inputs required. Although a single value could be entered for input #1, beta, three values separated by commas are entered for purposes of performing sensitivity analysis. It is estimated that the Weibull shape parameter is in the range of 3.0 to 3.6, with a typical value of 3.3.

The resulting estimated number of failures is 413, assuming a Weibull shape parameter of 3.3, with a lower 90% bound of 206 failures and an upper bound of 753.

The calculation of confidence limits in the above table depends on p and q being small. If p + q is greater than 0.10, confidence limits are not shown (references provide examples with p+q=0.03). p is the probability of item failure up to t_{1}. Given that an item survives to t_{1}, q is the probability of item failure from t_{1} to t_{2}. r is the probability of item survival to t_{2}.

p + q + r = 1.0

References:

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