How Stable Are Maintenance Priorities

Summary

A single maintenance priority list looks more dependable than it is when its assumptions stay invisible. Using an abstract set of six assets, this report shows how the ranking changes when only a few parameters are varied: the time horizon, a common deterioration factor, and the deterioration rate of a single asset. The report is a document from the scenario, not scientific evidence; numbers and assets are constructed and do not assess any real municipality.

Research question

The project Uncertainty in municipal maintenance models asks which assumptions change a priority list the most. A single model curve hides the fact that initial conditions, deterioration rates and weightings are uncertain. This report confines itself to a sub-question: how stable is the ranking when individual assumptions are changed systematically but only slightly, and which assumptions should be listed explicitly in an assumptions register?

Set-up

The example has four steps. First, a set of six abstract assets A to F is fixed. Second, the assumptions are recorded in a register (see Assumptions register for maintenance models). Third, a baseline run is computed. Fourth, a few parameters are varied one at a time and the rankings are compared. The modelling belongs to the modelling workshop; the project is led by the head of the Simulation and Modelling research area.

Each asset has an initial state s0 on a scale from 0 (good) to 3 (poor), a deterioration rate p (probability per year of dropping one state step) and a consequence weight c from 1 to 5. For a horizon of H years, a simplified expected-value approximation of the discrete state transition is used:

• expected state d = min(3, s0 + H · p);
• priority value = c · d;
• rank 1 has the largest priority value.

Rankings are compared by counting discordant pairs. A pair of assets is discordant if the two lists order it differently. With six assets there are 15 pairs; Kendall’s rank correlation is τ = 1 − 2 · (discordant pairs) / 15.

Assumptions

This report is a document; all values are constructed, uncalibrated and support no statement about real assets. The assumptions register for this example contains:

1. The assets are independent of one another; there are no maintenance budgets and no dependencies.
2. The state scale is equally spaced; a step from 2 to 3 counts the same as one from 0 to 1.
3. Deterioration is constant and independent of age; the expected-value approximation ignores that the state ends at 3.
4. The consequence weight is fixed and treated as known.
5. The horizon is 5 years in the baseline run; it is freely chosen.

Each of these assumptions can change the ranking. In the example only assumptions 3 and 5 are varied.

Illustrative analysis

Constructed worked example, not a measurement. The baseline parameters are given in the first table.

The baseline run (H = 5, factor 1) gives the priority values A 5.00, B 7.50, C 8.00, D 11.25, E 9.00 and F 6.25. The ranking is D, E, C, B, F, A. As a check: for C, d = min(3, 0 + 5 · 0.40) = 2, so 4 · 2 = 8. For D, d = 2 + 5 · 0.05 = 2.25 and the value is 5 · 2.25 = 11.25. Three variants are then computed.

In V1, B and C swap places, as do A and F; short horizons favour assets in a poor initial state. In V2, C moves to rank 1 because its rate is high and it reaches state 3 (the cap: 0 + 5 · 0.60 = 3). Asset D, with a high weight but a small rate, drops to rank 2. In V3, halving p for C alone moves that asset from rank 3 to rank 6. Asset D is first in two of the three variants and E is second or third, while the middle and the end of the list change more. A statement such as “D is the most urgent” therefore depends on assumptions 3 and 5.

The report recommends nothing for real assets on the basis of this example; it shows how a rank change can be documented traceably. The share of rank changes attributable to individual assumptions would be a result of its own in a larger study.

Limitations

The parameters are uncalibrated; there is no comparison with condition data, and the six assets stand for no real municipality. Three variants with one change each capture no interactions between parameters and do not amount to a systematic sensitivity analysis. The expected-value approximation neglects the spread of the discrete transitions. Choosing the priority value as the product of weight and expected state is also a convention that other methods would set differently. Municipal deployment planning cannot be derived from this.

Conclusion

In the constructed example, a few changes to two assumptions shift the ranking noticeably; the Kendall correlation with the baseline lies between 0.60 and 0.73. For the practice of such models this yields mainly a methodological requirement: assumptions should be kept in a register, and a priority list should always be shown together with a variation calculation. Whether and how strongly real lists fluctuate cannot be answered by this report.