Weibull in five minutes

The Weibull distribution earns its place as the workhorse of life-data analysis because two numbers — a shape and a scale — describe a remarkable range of failure behaviour.

The shape parameter (β) is the story

The scale parameter just sets the time axis. The shape parameter, β, tells you how things are failing:

• β < 1 — failures are decreasing over time. This is infant mortality: manufacturing defects, bad installs, weak units dying early. Burn-in helps.
• β ≈ 1 — a constant failure rate. Failures arrive randomly, independent of age (the Weibull collapses to the Exponential). Replacing on a schedule won't help much.
• β > 1 — failures increase with age: wear-out. Bearings, seals, fatigue. This is exactly where preventive replacement pays off.

Why it matters for maintenance

If β is at or below 1, a time-based replacement policy is wasted effort — you're swapping good parts for ones just as likely to fail. If β is comfortably above 1, there's a cost-optimal interval to be found, balancing the price of planned replacement against the cost of failure.

In Reliafy, fit a Weibull to your data, read β off the results, and then take it straight to the optimal replacement tool to turn that shape into a schedule.

Rule of thumb: don't schedule replacements until you've confirmed β > 1.