Statistical Inference Under Step Stress Partially Accelerated Life Testing for Adaptive Type-II Progressive Hybrid Censored Data

  • Mustafa Kamal Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Dammam, 32256, Kingdom of Saudi Arabia
  • Ahmadur Rahman Department of Statistics and Operations Research, Aligarh Muslim University, India
  • Shazia Zarrin Uttaranchal Unani Medical College and Hospital, Haridwar, India
  • Haneefa Kausar Department of Statistics and Operations Research, Aligarh Muslim University, India
Keywords: Partially Accelerated Life Testing plan, Nadarajah-Haghighi distribution, Adaptive Type-II Progressive Hybrid Censoring, Maximum likelihood estimation, Simulation Study

Abstract

Accelerated life tests (ALTs) are designed to investigate the lifetime of extraordinarily reliable things by exposing them to increased stress levels of stressors such as temperature, voltage, pressure, and so on, in order to cause early breakdowns. The Nadarajah-Haghighi (NH) distribution is of tremendous importance and practical relevance in many real-life scenarios due to its attractive qualities such as its density function always has a zero mode and its hazard rate function can be increasing, decreasing, or constant. In this article, the NH distribution is considered as a lifetime distribution under the step stress partially accelerated life testing (SSPALT) model with adaptive type II progressively hybrid censored samples. The unknown model parameters and acceleration factors are estimated using maximum likelihood estimation (MLE) method assuming that the impact of stress change in SSPALT is explained by a tampered random variable (TRV) model. The Fisher information matrix, which is based on large sample theory, is also constructed and used to produce the approximate confidence intervals (ACIs). Furthermore, two potential optimum test strategies based on the A and D optimality criteria are evaluated. To investigate the performance of the proposed methodologies and statistical assumptions established in this article, extensive simulations using R software have been conducted. Finally, to further illustrate the suggested approach, a real-world example based on the times between breakdowns for a repairable system has been provided.

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Author Biographies

Mustafa Kamal, Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, Dammam, 32256, Kingdom of Saudi Arabia

Mustafa Kamal is an Assistant Professor at Saudi Electronic University’s College of Science and Theoretical Studies. In 2013, he received his Ph.D. (Statistics) from Aligarh Muslim University, India. He authored more than 20 research papers that have been published in a variety of international journals. His main research interests include Accelerated Life testing & Reliability theory. Currently he is working on Bayesian estimation, Artificial intelligence and neural networks techniques, Sustainable Energy, Survey Sampling; Order Statistics; Statistical Inference and Distribution Theory.

Ahmadur Rahman, Department of Statistics and Operations Research, Aligarh Muslim University, India

Ahmadur Rahman is working as Assistant Professor in the department of Statistics and Operations Research, Aligarh Muslim University, Aligarh. He received his Bachelor, Master and PhD degree from Aligarh Muslim University in Statistics. He has published several research papers in national and international reputed journals. His areas of research are Life Testing, Accelerated Life Testing Plans, Reliability Analysis, Survival Analysis, Bayesian inference and Econometrics with R language/software.

Shazia Zarrin, Uttaranchal Unani Medical College and Hospital, Haridwar, India

Shazia Zarrin earned her Ph.D. in “Statistics” from the Department of Statistics and Operations Research, Aligarh Muslim University, India. Her primary research interests are in reliability theory and accelerated life testing. She is currently working on the Bayesian estimation technique in life testing and reliability estimation and applying computational techniques to field reliability and survival data using R software. She is an active reviewer for a number of prestigious international journals.

Haneefa Kausar, Department of Statistics and Operations Research, Aligarh Muslim University, India

Haneefa Kausar earned her Ph.D. in “Operations Research” from the Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India. Her area of research is Mathematical Programming, Bi-level Programming, Multi-level Programming, Linear Fractional Programming, Non Linear Fractional Programming and Accelerated Life Testing plan. She has published number of papers in very good journals.

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Published
2021-12-18
Section
Articles