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All Journal Jurnal Teknologi Riset Terapan Jurnal Studi Multidisiplin Ilmu
Avishek Shah
Rajarshi Janak University, Janakpurdham, Nepal
Computer Science & IT Economics, Econometrics & Finance Education Electrical & Electronics Engineering Engineering Industrial & Manufacturing Engineering Mechanical Engineering Social Sciences Other

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Generalized Summability Methods for Failure Rate and Maintainability Analysis Avishek Shah; Prem Kumar Nayak; Suresh Kumar Sahani
Jurnal Teknologi Riset Terapan Vol 4 No 1 (2026): Januari
Publisher : Penerbit Goodwood

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35912/jatra.v4i1.7805

Abstract

Purpose: This study develops a transparent framework for applying generalized summability methods to sequences of failure-rate and maintainability estimates produced from finite, irregular and noisy operational records.Research Methodology: Cesàro, weighted, Nörlund and exponential means are compared as regularizing transformations rather than as substitutes for a reliability model. The framework specifies exposure-aware rate construction, treatment of censoring and missing intervals, regularity and stability checks, delay diagnostics and a validation design based on simulated sequences, illustrated with model-based curves and a worked calculation.Results: Averaging reduced high-frequency variation in the illustrative sequences but introduced lag and blurred change points. In the worked example, the unweighted mean of interval rates was 0.0167 per hour while the exposure-pooled rate was 0.0133 per hour, showing that the weighting rule can silently redefine the target quantity.Conclusions: Summability is useful as a monitoring layer only after the estimand, exposure and censoring have been defined correctly, and raw values and uncertainty must remain visible.Limitations: No field dataset is used, and all curves are illustrative.Contributions: The study joins classical summability theory with reliability practice through a reproducible decision framework, selection criteria and validation safeguards.
Summability-based Reliability Modelling With Laplace Transforms: Numerical Methods and Optimization Avishek Shah; Prem Kumar Nayak; Suresh Kumar Sahani
Jurnal Teknologi Riset Terapan Vol 4 No 2 (2026): July
Publisher : Penerbit Goodwood

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35912/jatra.v4.n2.p1-19.2026

Abstract

Purpose: This study develops a summability-aware workflow that links reliability modelling, Laplace-domain analysis, numerical inversion and constrained optimization for time-dependent reliability and availability.Research Methodology: The framework covers survival and hazard functions, series and parallel structures, a two-state repair model, transform-domain representations, numerical inversion checks and a reliability-cost optimization formulation. Cesàro averaging is treated as a sequence-smoothing and convergence diagnostic rather than a substitute for a valid inverse transform. A worked example uses stated hypothetical rates.Results: For two components with failure rates of 0.0005 and 0.0010 per hour, reliability at 400 hours was 0.5488 in series and 0.9402 in parallel. Fixed-Talbot and de Hoog inversion of the availability transform converged to round-off error, while Gaver-Stehfest converged more slowly, and the lowest-cost design meeting a 0.90 reliability threshold was not the most reliable one.Conclusions: Summability can help interpret oscillatory numerical sequences, but reliable decisions require sound assumptions, independent checks and validation before optimization.Limitations: All rates and design options are hypothetical, and the models assume independence and constant rates.Contributions: The study offers a reproducible verification protocol and a model-to-decision workflow for student research and early-stage industrial reliability studies.
Transforms and Runge-Kutta Methods: Error Bounds and Convergence Acceleration in Reliability Models Using Summability Methods Avishek Shah; Prem Kumar Nayak; Suresh Kumar Sahani
Jurnal Studi Multidisiplin Ilmu Vol 4 No 3 (2026): September
Publisher : Penerbit Goodwood

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.35912/jasmi.v4.n3.p63-84.2026

Abstract

Purpose: This study develops a practical framework that combines Laplace transforms, Runge-Kutta (RK) integration, error assessment and summability-based convergence acceleration for computing transient reliability and availability.Methodology: The methods are treated as complementary. Laplace transforms reduce linear time-invariant state equations, RK methods approximate dynamics when closed forms are unavailable, and Cesàro averaging or Richardson extrapolation is used only when the sequence has a defensible asymptotic structure. A two-state failure-repair model supplies exact benchmarks, and a smooth quadrature problem illustrates extrapolation.Results: Classical RK4 reproduced the exact availability with an observed order of about 4.06, and successive error ratios approached 16 as the step size was halved, while Euler and midpoint RK2 gave observed orders of 1.01 and 2.10. Richardson extrapolation raised the trapezoidal rule from second to fourth order on the smooth benchmark.Conclusions: Acceleration cannot repair an unstable or biased numerical solution, so the model, base solver and error estimator must be validated before any summability procedure is applied.Limitations: The worked model has two states and constant rates, and all results are analytical illustrations rather than field data.Contributions: The study offers a global error bound under Lipschitz assumptions, an exactly solvable benchmark, a verification checklist and decision rules for reproducible reliability computation.
Co-Authors Prem Kumar Nayak Suresh Kumar Sahani