For each vehicle query, the engine runs 10,000 simulated ownership periods. In each iteration, every component is evaluated for failure probability based on the log-normal cumulative distribution function:
P(fail) = [CDF(future_mi) - CDF(current_mi)] / [1 - CDF(current_mi)]
This gives the conditional probability of failure in the projection window, given that the component has survived to the current mileage. If a random draw triggers failure, a repair cost is sampled uniformly from the component's cost range.
Results are aggregated across all iterations to produce percentile-based cost projections (P10, P25, P50, P75, P90).
┌────────────────────┬──────────────────────────────┐ │Parameter │Value │ ├────────────────────┼──────────────────────────────┤ │Iterations │10,000 per query │ │Failure model │Log-normal CDF │ │Cost sampling │Uniform (low..high) │ │Projection │1-5 years, 8000mi/yr default │ └────────────────────┴──────────────────────────────┘
Each component has a log-normal failure distribution characterised by mean failure mileage and standard deviation. These are derived from real MOT failure data:
Component Mean mi Std dev Source ───────────────────────────────────────────────── Ball joints 80,000 30,000 MOT data Coil springs 85,000 32,000 MOT data Shock absorbers 90,000 28,000 MOT data Brake pads 55,000 20,000 MOT data Timing chain 120,000 35,000 Estimated Turbo 100,000 30,000 Estimated
MOT-derived values use actual mileage-at-failure distributions from 4.9M test records. Non-MOT items use industry estimates calibrated per model.
Market valuation uses an exponential decay model with segment-specific parameters. Year 1 has a larger drop, subsequent years decay at a reducing rate. A value floor prevents estimates below scrap value.
Mileage adjustments apply a per-mile penalty/reward for deviation from expected mileage. High mileage is penalised more heavily than low mileage is rewarded.
┌────────────────────┬────────────┬────────────┬────────────┐ │Parameter │Budget │Mainstream │Premium │ ├────────────────────┼────────────┼────────────┼────────────┤ │Year 1 drop │25% │22% │20% │ │Annual rate │12% │14% │16% │ │Value floor │5% │8% │10% │ └────────────────────┴────────────┴────────────┴────────────┘
TCO projections estimate annual running costs including:
Category Source ────────────────────────────────── VED (road tax) CO2 band / flat rate Fuel MPG + DfT fuel prices MOT Fixed £54.85/yr (3+ yrs) Insurance Group-based estimate Servicing Model-specific annual cost Repair risk Monte Carlo P50 amortised