Weibull Analysis: Estimating Life and Failure Mode from Failure Data
What Is the Weibull Distribution?
The Weibull distribution is the most commonly used life distribution in reliability engineering, with reliability function R(t) = exp(-(t/eta)^beta), where beta is the shape parameter and eta the scale parameter (characteristic life). From a set of failure times it simultaneously describes how the failure rate changes over time, suiting life analysis and prediction for electronic components, mechanical parts, bearings and batteries - and it is the standard analysis recommended by IEC 61649 and the MIL-HDBK system. The tool estimates the parameters by both least-squares probability plotting and maximum likelihood; the probability plot visually checks the fit and the results feed directly into reliability-metric calculations.
Reading the Shape Parameter beta
Beta is the key to the failure mechanism: beta < 1 indicates early-life (infant mortality) with a decreasing failure rate, typical of manufacturing defects, cold solder joints and poor assembly - remove via screening or burn-in; beta approximately 1 indicates the random-failure period with an approximately constant failure rate, equivalent to the exponential distribution, corresponding to chance failures; beta > 1 indicates the wear-out period with an increasing failure rate, corresponding to wear, fatigue and aging. The three regions map to different product-life stages and decide whether the maintenance strategy is preventive replacement or reliability screening. Beta also drives burn-in schemes, warranty periods and preventive-maintenance intervals - an important input to reliability planning.
Interpreting eta, B10 and MTTF
Eta is the characteristic life - the time at which 63.2% of products fail; a larger scale parameter means a longer life. B10 life is the time at which 10% fail, commonly used as the design-life metric (e.g., bearing L10). MTTF is the mean time to failure, MTTF = eta*Gamma(1 + 1/beta); the closer beta is to 1, the closer MTTF is to eta. The tool gives these indicators automatically and marks the corresponding quantile lives directly on the probability plot, with confidence intervals and point estimates for design reviews, customer contracts and reliability reports.
How to Use It and Notes
After sign-in, paste the failure-time data (including censored data), choose the estimation method and confidence level, and the tool completes parameter estimation, the probability plot and the fit R-squared. An R-squared close to 1 means a good fit; visibly curved data points suggest the data are not a single straight-line Weibull - consider segmented fitting or another distribution. Use at least 8 failure points and interpret cautiously when the censoring ratio is high. With multiple failure modes present, stratify by mode before fitting so the parameters are clearer and the conclusions more reliable.