Project: select a fault-count model from exposure, zeros and burst behavior

Last updated: 7 Oct 20265 min read

project

Audit machine-hour exposure, compare count distributions, and publish only the predictive quantities maintenance can act on.

Freeze the machine-week frame

A factory wants to forecast maintenance work from logged device faults. Define eligible machine-weeks, powered-on hours, fault deduplication, site and machine type, and the outcome maturity cutoff. Separate powered-off weeks from active weeks with no faults. If a device was down and its fault log was unavailable, mark missing observation rather than zero. The exposure lesson supplies the denominator; the missingness lesson handles absent logs.

Diagnose before fitting

Compare observed zeros with Poisson expectations for exposed rows, inspect count variance among comparable exposure bands, and examine high-fault machine-weeks. Check whether site or device age explains spread before considering latent classes. The simple Poisson, negative binomial, zero-inflated and hurdle candidates answer different data stories; candidate selection must reflect the maintenance decision. Zero diagnostics, extra variance and two-part modeling connect to these checks.

Validate on a later period

For each model, predict chance of any fault, mean count per machine-week and probability of a costly burst on a later time window. Report calibration by site and machine type with denominators. A likelihood advantage on the training set is insufficient if a simpler count model predicts the maintenance inventory better. Preserve exposure and model versions so a logging update cannot be mistaken for a risk shift.

Gate the operational packet

The packet contains uptime reconciliation, zero-exposure rules, missing-log counts, candidate assumptions, later-period calibration, uncertainty and a staffing loss measure. The gate below refuses a published recommendation if inactive machines were counted as safe exposed weeks or burst validation is missing. Passing it permits operations review; it does not establish that changing maintenance will causally change the observed fault rate.

Implementation

def device_fault_gate(audit):
    if audit["zero_exposure_as_safe"]:
        return "hold:exposure-definition"
    if audit["missing_logs_as_zero"]:
        return "hold:missing-faults"
    if not audit["later_window_validated"]:
        return "hold:forecast-validation"
    if not audit["burst_calibration_reviewed"]:
        return "hold:high-count-tail"
    return "review:maintenance-model"

audit = {"zero_exposure_as_safe": True, "missing_logs_as_zero": False,
         "later_window_validated": True, "burst_calibration_reviewed": True}
assert device_fault_gate(audit) == "hold:exposure-definition"
assert device_fault_gate({**audit, "zero_exposure_as_safe": False})        == "review:maintenance-model"

Performance and operating cost

The gate is O(1). Frame reconstruction and group summaries are O(n) over machine-weeks, while fitting several count models and validating rare bursts take more time. Wrong uptime exposure is a data fault that no model comparison can cheaply fix.

Common Mistakes

Treating powered-off machines as exposed zero-fault evidence.
Replacing unavailable fault logs with zero counts.
Choosing the most complex count model from training likelihood alone.
Reporting total fault accuracy without checking burst-week calibration.