What question did this study set out to answer?

The research aims to develop a method for computing confidence bands that capture the variability of predicted cumulative failure event curves for engine fleets.

February 8, 2026

Confidence bands for cumulative event number evolution curves

Key Points

The research aims to develop a method for computing confidence bands that capture the variability of predicted cumulative failure event curves for engine fleets.
Developed a predictor using historical failure data and an inspection strategy.
Estimated average curves from numerous predicted curves.
Computed confidence bands to capture variability around average predictions with specified probabilities.
Confidence bands successfully reflected variability in predicted cumulative failure curves.
Statistical guarantees were maintained using a finite number of curves.

Abstract

For a fleet of engines to remain in service, the cumulative number of failures must be kept under a threshold set by the authorities. If the cumulative number of said event reaches a critical level during a fleet's service, a statistical study is conducted to predict the evolution of that number. This study integrates the fleet's history, a scenario describing the occurrence of the event, and an inspection strategy put in place to prevent the occurrence of said event. This results in a predictor capable of predicting possible curves describing the evolution of the cumulative number of events under these specifications. To interpret this predictor, only the average curve is estimated using a sample of predicted curves. Although the average curve is informative, it alone does not reflect the variability of possible curves. The aim of this work is to describe a generic method for computing bands that "contain" the generated curves with a probability higher than a specified threshold. An important aspect of these bands is that they ensures these statistical guarantees only using a finite number of predicted curves.

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