Lifetime testing and sound analytical techniques: A critical investigation of the entropy-based efficiency of censored samples
Kittaneh, Omar El-Kafrawy, Passent
Kittaneh, Omar
El-Kafrawy, Passent
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2026-01-24
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Abstract
Time-series data consist of observations collected at regular time intervals, focusing on how a variable changes over time and allowing for trend analysis and forecasting. Examples include daily stock prices, monthly sales revenue, and temperature recordings. In contrast, life data measures the time until a specific event occurs, such as the failure of a machine or the survival time of patients after treatment. Life data is commonly used in reliability engineering and survival analysis, while time series is essential for predicting future trends in finance, weather, and business analytics. This chapter presents a comprehensive and precise investigation of previous studies on life data with more focus on the entropy-based efficiency of type I right-censored samples obtained from life tests. It offers a compelling rationale for this important concept from both mathematical and practical perspectives. Theoretical results are rigorously proven, and numerous real-world examples from the literature are provided to illustrate different probability models that have been shown to fit standard experimental datasets. Numerical examples show that the efficiency of censored sample has nothing to do with the suitability of models to experimental data, but it tells us how if that stopping time of a life test would be enough to collect data (observing failures) and give acceptable estimates. Thus, certain conceptual insights and computational findings related to this measure, as presented in previous literature, have been rectified.
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Mathematical Modeling for Big Data Analytics