Oblongix logoOblongixEnterprise AI transformation

Working example 05 Weibull reliability and knapsack optimisation

Prediction without effective action

“We can predict a failure, but cannot prevent it economically.”

A utility runs 40 pumps of different criticality. A model predicts which are likely to fail, but crews are limited and planned work is not free. Acting on every alert costs more than it saves.

How it works

The method in three steps

  1. Predict failureLifetimes follow a Weibull distribution with a 24-month scale. Each asset’s 12-month failure probability depends on its current age.P(fail | age a) = 1 − R(a + 12) / R(a), R(t) = exp(−(t/η)^β)
  2. Find the economic policyThe age-replacement model gives the long-run cost of replacing at age T, or on failure if that comes first.C(T) = [C_p·R(T) + C_f·(1 − R(T))] / ∫₀ᵀ R(t) dt
  3. Choose what to act onDynamic programming selects the set of assets that maximises total net saving within the available crew hours.max Σ saving_i·x_i s.t. Σ hours_i·x_i ≤ H, x_i ∈ {0, 1}

Try it

The working example

Asset economics

Try a shape parameter of 1.0 to see why some predictions cannot be acted on profitably.

Below 1: risk falls with age · above 1: wear-out
Repair, downtime and penalties (scaled by criticality)
Best replacement age–
Risk-ranking plan saves–
Optimised plan saves–

When does prevention pay?

Long-run cost per asset-month for each planned replacement age.

This month’s choices

Each pump by predicted risk and the net saving from servicing it. Larger dots need more crew hours.

Interpretation

From example to engagement

What the example shows

An accurate prediction is not the same as a profitable action. When failures are random (β ≤ 1), replacing a risky asset early buys a new one that is just as likely to fail. When they are not, the best plan weighs risk against the cost of failure and the time each job takes — and sometimes leaves a high-risk asset alone.

With real data

  • Failure and maintenance histories, with censoring for assets that have not yet failed.
  • Covariates such as load, environment and condition monitoring through Cox or Weibull regression.
  • Crew skills, travel and spare parts added as further constraints in the optimisation.