Open Access

ARTICLE

Robust and Efficient Reliability Estimation for Exponential Distribution

by Muhammad Aslam Mohd Safari¹, Nurulkamal Masseran^2,*, Muhammad Hilmi Abdul Majid²

1 Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, UPM Serdang, 43400, Selangor, Malaysia
2 Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, UKM Bangi, 43600, Selangor, Malaysia

* Corresponding Author: Nurulkamal Masseran. Email:

(This article belongs to the Special Issue: Emerging Applications of Artificial Intelligence, Machine learning and Data Science)

Computers, Materials & Continua 2021, 69(2), 2807-2824. https://doi.org/10.32604/cmc.2021.018815

Received 22 March 2021; Accepted 29 April 2021; Issue published 21 July 2021

Abstract

In modeling reliability data, the exponential distribution is commonly used due to its simplicity. For estimating the parameter of the exponential distribution, classical estimators including maximum likelihood estimator represent the most commonly used method and are well known to be efficient. However, the maximum likelihood estimator is highly sensitive in the presence of contamination or outliers. In this study, a robust and efficient estimator of the exponential distribution parameter was proposed based on the probability integral transform statistic. To examine the robustness of this new estimator, asymptotic variance, breakdown point, and gross error sensitivity were derived. This new estimator offers reasonable protection against outliers besides being simple to compute. Furthermore, a simulation study was conducted to compare the performance of this new estimator with the maximum likelihood estimator, weighted likelihood estimator, and M-scale estimator in the presence of outliers. Finally, a statistical analysis of three reliability data sets was conducted to demonstrate the performance of the proposed estimator.

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Keywords

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