Weibull Analysis: Predicting Equipment Life from Failure Data

Scenario

Your factory replaced a batch of new bearings. Over the past 6 months, 15 failure records were received, with failure times ranging from 300 hours to 2,800 hours.

Your supervisor asked: "What is the actual life of these bearings? When should they be replaced?"

Mean Time Between Failures (MTBF) only gives you a single number. Weibull analysis tells you whether these bearings are "more likely to fail the longer they are used," "fail randomly," or "fail only when their life expectancy is reached"—the maintenance strategies for these three situations are completely different.

Two Parameters of the Weibull Distribution

β (Beta, Shape Parameter)

β determines the direction of change in the failure rate over time:

• β < 1: Failure rate decreases over time (Infant Mortality)

→ Represents: Manufacturing defects, installation issues

→ Countermeasure: Burn-in test (run for a period before shipping to screen out infant mortality items)

• β = 1: Failure rate is constant (Exponential Distribution, Random Failure)

→ Represents: External shocks, random stresses

→ Countermeasure: Reliability calculation based on MTBF

• β > 1: Failure rate increases over time (Wear-out Failure)

→ Represents: Wear and tear, fatigue, aging

→ Countermeasure: Preventive replacement (replace before the failure rate sharply increases)

η (Eta, Characteristic Life)

η = The point in time when 63.2% of the parts have failed.

(Why 63.2%? Because the Weibull reliability function R(η) = e^(-1) = 36.8%, meaning the cumulative failure rate = 63.2%)

B10 Life

B10 Life = The point in time when 10% of the parts have failed.

In engineering, B10 is often used as the replacement time point:

• Replacing parts at B10 means only 10% of the parts have failed.
• If B50 is used (replace only when 50% fail) = Half of the parts have already failed, which is likely to cause significant downtime.

Bearing product specifications often indicate L10 (equivalent to B10).

Interpretation of the Weibull Plot

The X-axis of a Weibull plot is log (time), and the Y-axis is log (log (1/R(t))).

If the data conforms to a Weibull distribution, the failure data will form a straight line on this double logarithmic coordinate system.

Slope of the line = β (Shape Parameter)

Intersection of the line with the 63.2% failure rate = η (Characteristic Life)

Maintenance Strategies for Different Failure Modes

Golden Quote

"The greatest value of Weibull analysis is telling you which lifecycle stage your equipment is in—this determines what you should do. Performing PM for infant mortality is a waste, and implementing redundant backup for wear-out failures is also a waste. Diagnose first, then treat."