Weibull Parameter Estimation and Life Prediction
How Are the Parameters Estimated?
Regress ln[-ln(1-F(t))] against ln t with a double-log transform; the slope is beta and eta follows from the intercept. Maximum likelihood estimation (MLE) solves directly and handles censored data better. The tool gives both least-squares and MLE estimates with the fit R-squared for cross-checking stability - close agreement means robust estimation, while large differences warrant checking the data quality and censoring assumptions.
beta and the Failure Period
Beta < 1 means early-life failure with a decreasing failure rate, typical of manufacturing defects - remove with screening or burn-in; beta approximately 1 means random failure with a constant rate, equivalent to the exponential distribution, corresponding to chance failures; beta > 1 means wear-out with an increasing rate, corresponding to wear, fatigue and aging. The beta region tells you the product's life-cycle stage and whether to choose screening or preventive maintenance. For batch-delivered products, beta also directly drives burn-in schemes and warranty settings.
eta, B10 and MTTF
Eta is the characteristic life - the time at which 63.2% of products fail - reflecting the overall life level; B10 life is the time at which 10% fail, the most common engineering design-life metric (bearing L10); MTTF = eta*Gamma(1 + 1/beta) is the mean time to failure. The tool computes these automatically and marks the quantile life points on the probability plot for direct reading, with confidence intervals and point estimates for design and contract clauses.
Reliability Prediction and Notes
The reliability function R(t) = exp(-(t/eta)^beta) gives the reliability and failure rate at any time point. Use at least 8 failure points; visibly curved probability data suggest the data are not a single Weibull distribution - consider segmented fitting or another distribution; extrapolating beyond the data range requires caution. For planned maintenance and spares, the reliability curve directly suggests replacement intervals, avoiding both premature and overdue maintenance.