Summability-based Remaining Useful Life Estimation for Industrial Equipment

Purpose: This study develops a mathematically explicit summability-assisted framework for Remaining Useful Life (RUL) estimation, in which causal weighted means stabilize noisy degradation indicators before a prognostic model estimates RUL.Methodology: Moving, Cesàro-type and exponential means are formulated as normalized causal weighted means, and their variance, bias and lag are derived. A threshold-crossing model maps the smoothed index to RUL with delta-method uncertainty. The framework is illustrated with a synthetic motor-driven pump, a synthetic replica of the NASA/IMS bearing record and a Monte Carlo experiment.Results: In the pump example, a smoothed index of 0.723, a threshold of 1.00 and a slope of 0.0045 per hour gave an RUL of about 61.6 hours. Over 2,000 Monte Carlo runs, the first alarm of the raw feature was false in 78.2% of runs, against 0.6% for a 15-point moving mean and 2.0% for an exponential mean.Conclusions: Summability is a low-cost, interpretable preprocessing option when noise obscures slow degradation, but it can delay warnings and must be validated against baselines.Limitations: All numerical examples are synthetic or simulated.Contributions: The study provides equations, an algorithm and a validation protocol linking classical summability to prognostics.