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Statistical Estimation of Occurrence Rates in Alpha-Series Process using Maxwell Inter-Arrival Times |
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PP: 717-729 |
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doi:10.18576/jsap/140615
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Author(s) |
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Ameena K. Essa,
Marwah A. Maklef,
Husam M. Sabri,
Mohammad A. Tashtoush,
Hasanain J. Alsaedi,
Abdullah M. S. Ajlouni,
Adel S. Hussain,
Sufyan A. Wuhaib,
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Abstract |
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| In this study, we investigate the Alpha Series Process (ASP) as a flexible stochastic model for describing event
occurrences in reliability and scheduling systems when the assumption of a constant hazard rate is not appropriate. The first inter-arrival time of the ASP is assumed to follow the Maxwell distribution, which is widely used in engineering to model system failure times. Three parameter estimation methods are developed and compared: Maximum Likelihood Estimation (MLE), Modified Moment Estimation (MME), and an intelligent optimization-based approach using the Artificial Bee Colony (ABC) algorithm. The ABC estimator performs objective-function maximization through its swarm-intelligence design, eliminating the need for restrictive analytical assumptions. A Monte Carlo simulation study is conducted under multiple parameter settings and different sample sizes, with Mean Squared Error (MSE) used as the main performance criterion. The simulation results show that the ABC algorithm provides higher estimation accuracy and greater stability than the classical MLE and MME methods. To demonstrate the practical applicability of the proposed approach, the methodology is applied to real failure-time data from the Mosul Dam power station. The empirical results indicate that the ASP with Maxwell-distributed inter-arrival times provides a better model fit than traditional renewal process models. Overall, the findings highlight the effectiveness of combining flexible stochastic models with swarm-intelligence
optimization techniques for robust occurrence-rate estimation in degrading systems.
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