## THERMAL SCIENCE

International Scientific Journal

### STATISTICAL INFERENCE ON THE ACCELERATED COMPETING FAILURE MODEL FROM THE INVERSE WEIBULL DISTRIBUTION UNDER PROGRESSIVELY TYPE-II CENSORED DATA

**ABSTRACT**

In this paper, the parameter estimation is discussed by using the maximum likelihood method when the available data have the form of progressively censored sample from a constant-stress accelerated competing failure model. Normal approximation and bootstrap confidence intervals for the unknown parameters are obtained and compared numerically. The simulation results show that bootstrap confidence intervals perform better than normal approximation. A thermal stress example is discussed.

**KEYWORDS**

PAPER SUBMITTED: 2019-12-26

PAPER REVISED: 2020-05-10

PAPER ACCEPTED: 2020-05-10

PUBLISHED ONLINE: 2021-03-27

**THERMAL SCIENCE** YEAR

**2021**, VOLUME

**25**, ISSUE

**Issue 3**, PAGES [2127 - 2134]

- Wang, L., et al., Inference for Weibull Competing Risks Model with Partially Observed Failure Causes under Generalized Progressive Hybrid Censoring, Journal of Computational and Applied Mathematics, 368 (2020), Apr., pp. 423-431
- Yang, L., et al., Hybrid Preventive Maintenance of Competing Failures under Random Environment, Reliability Engineering and System Safety, 174 (2018), June., pp. 130-140
- Han, D., Balakrishnan, N., Inference for a Simple Step-Stress Model with Competing Risks for Failure from the Exponential Distribution under Time Constraint, Computational Statistics and Data Analysis, 54 (2010), 9, pp. 2066-2081
- Pareek, B., et al., On Progressively Censored Competing Risks Data for Weibull Distributions, Computational Statistics and Data Analysis, 53 (2009), 12, pp. 4083-4094
- Wu, M., et al., Inference for Accelerated Competing Failure Model from Weibull Distribution under Type-I Progressively Hybrid Censoring, Journal of Computational and Applied Mathematics, 263 (2014), June, pp. 423-431
- EI-Raheem, A. M. A., Optimal Plans and Estimation of Constant-Stress Accelerated Life Tests for the Extension of the Exponential Distribution under Type-I Censoring, Journal of Testing and Evaluation , 47 (2018), 5, pp. 3781-3821
- Nassar, M., Dey S., Different Estimation Methods for Exponentiated Rayleigh Distribution under Constant-Stress Accelerated Life Test, Quality and Reliability Engineering International, 34 (2018), 8, pp. 1633-1645
- Han, D., Time and Cost Constrained Optimal Designs of Constant-Stress and Step-Stress Accelerated Life Tests, Reliability Engineering and System Safety, 140 (2015), Aug., pp. 1-14
- Kohansal, A., On Estimation of Reliability in a Multi-component Stress-Strength Model for a Kumaras-wamy Distribution based on Progressively Censored Sample, Statistical Papers, 60 (2019), 6, pp. 2185-2224
- Zhang Z., Gui, W. H., Statistical Inference of Reliability of Generalized Raleigh Distribution under Progressively Type-II Censoring, Journal of Computational and Applied Mathematics, 361 (2019), Dec., pp. 295-312
- Han, D., Kundu, D., Inference for a Step-Stress Model with Competing Risks for Failure from the Generalized Exponential Distribution under Type-I Censoring, IEEE Transactions on Reliability, 64 (2015), 1, pp. 31-43
- Zheng, G. Y., Shi, Y. M., Statistical Analysis in Constant-Stress Accelerated Life Tests for Generalized Exponential Distribution based on Adaptive Type-II Progressive Hybrid Censored Data, Chinese Journal of Applied Probability and Statistics, 29 (2013), 4, pp. 363-380
- Ismail, A. A., Bayesian Estimation under Constant-Stress Partially Accelerated Life Test for Pareto Distribution with Type-I Censoring, Strength of Materials, 47 (2015), 4, pp. 633-641
- Singh, S., Tripathi, Y. M., Estimating the Parameters of an Inverse Weibull Distribution under Progressive Type-I Interval Censoring, Statistical Papers, 59 (2018), 1, pp. 21-56
- Nassar, M., Abo-Kasem, O. E., Estimation of the Inverse Weibull Parameters under Adaptive type-II Progressive Hybrid Censoring Scheme, Journal of Computational and Applied Mathematics, 315 (2017), May, pp. 228-239
- Akgul, F. G., et al., An Alternative Distribution to Weibull for Modeling the Wind Speed Da-ta:InverseWeibull Distribution, Energy Conversion and Management, 114 (2016), Apr., pp. 234-240
- Balakrishnan, N., Sandu, R. A., A Simple Simulation Algorithm for Generating Progressive Type-II Censored Samples, The American Statistician, 49 (1995), 2, pp. 229-230
- Balakrishnan, N., Aggarwala, A., Progressive Censoring: Theory, Methods, and Applications, Birkhauser, Boston, Mass., USA, 2000
- Nelson W., Accelerated Testing: Statistical Models, Test Plans, and Data Analysis, Wiley, New York, USA, 1990