Inference on Accelerated Life Testing for One-Shot Device with Competing Risks

Document Type : Original Article

Author

Department of Mathematics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

Abstract
This article deals with modelling and analysis of the competing risks for a one-shot device under a constant stress accelerated life test. In a reliability analysis of a device, it is important to be able to identify the main causes of failure. Therefore, a competing risk model is generally used. We consider this model in two modes: observed and masked causes of failure. The data obtained from one-shot device testing are missing in fact. For this reason, the EM algorithm along with the Fisher scoring method are used to estimate the model parameters. An accelerated life test is also used to shorten the time and cost. In addition, in order to accurately estimate the product reliability, the test design is finally optimized. Based on the simulated study, it is concluded that the EM algorithm and the bootstrap confidence interval are more accurate than the other methods. Also, shortening the test length leads to achieve an optimal test design.

Keywords


[1] Abd El-Raheem, A.M., Hosny, M., & Abu-Moussa, M.H (2021). On Progressive Censored Competing Risks Data: Real Data Application and Simulation Study. Mathematics9(15), 1805.
[2] Abushal, T. A., Soliman, A. A., & Abd-Elmougod, G. A. (2021). Inference of partially observed causes for failure of Lomax competing risks model under type-II generalized hybrid censoring scheme. Alexandria Engineering Journal.
[3] Balakrishnan, N., Castilla, E., Martín, N., & Pardo, L. (2019). Robust estimators and test statistics for one-shot device testing under the exponential distribution. IEEE Transactions on Information Theory65(5), 3080-3096.
[4] Balakrishnan, N., & Ling, M. H. (2013). Expectation maximization algorithm for one shot device accelerated life testing with Weibull lifetimes, and variable parameters over stress. IEEE Transactions on Reliability62(2), 537-551.
[5] Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological)39(1), 1-22.
[6] Escobar, L. A., & Meeker, W. Q. (2006). A review of accelerated test model. Statistical science, 21(4), 552–577.
 [7] Fan, T. H., Balakrishnan, N. & Chang, C. C. (2009). The Bayesian approach for highly reliable electro-explosive devices using one-shot device testing. Journal of Statistical Computation and Simulation, 79(9), 1143-1154.
[8] Farbod, D., Ebrahimpour, M., & Ghayourmoradi, Z. (2010). Maximum likelihood estimation for distribution generated by Cauchy stable law. International Journal of Mathematics & Computation7(J10), 22-28.
[9] Hakamipour, N. (2022). Parameter estimation using EM algorithm and test design optimization of constant stress accelerated life test with non-constant parameters under type-I progressive censoring. Journal of decisions and operations research, 6(4), 570-591. (Persian)
[10] Hakamipour, N. (2021). Comparison between constant-stress and step-stress accelerated life tests under a cost constraint for progressive type I censoring. Sequential Analysis40(1), 17-31.
[11] Hakamipour, N. (2020). Design and analysis of step stress accelerated life tests for censored data. Andishe-ye Amari, 24(2), 55-64. (Persian)
[12] Hakamipour, N. (2019). Time and cost constrained optimal designs of multiple step stress tests under progressive censoring. International Journal of Quality & Reliability Management, 36(10), 1721-1733.
[13] Hermanns, M., Cramer, E., & Ng, H. K. T. (2020). EM algorithms for ordered and censored system lifetime data under a proportional hazard rate model. Journal of Statistical Computation and Simulation90(18), 3301-3337.
[14] Hirano, K. (1986). Rayleigh distribution, Encyclopedia of Statistical Sciences, Vol. 7, 647-649. John Wiley, New York.
[15] Hoffman, D., & Karst, O. J. (1975). The theory of the Rayleigh distribution and some of its applications. Journal of Ship Research19(03), 172-191.
[16] Hoshyar, H. (2007). EM Algorithm. Student Statistical Journal_ NEDA, 5(1), 7-18. (Persian)
[17] Jiang, P. H., Wang, B. X., & Wu, F. T. (2019). Inference for constant-stress accelerated degradation test based on Gamma process. Applied Mathematical Modelling67(2), 123-134.
[18] Kayid, M. (2021). EM Algorithm for Estimating the Parameters of Weibull Competing Risk Model. Applied bionics and biomechanics2021.
[19] Lee, H. L., & Cohen, M. A. (1985). A multinomial logit model for the spatial distribution of hospital utilization. Journal of Business & Economic Statistics3(2), 159-168.
[20] Lindqvist, B. H. (2006). Competing risks. Encyclopedia of Statistics in Quality and Reliability. New York: Wiley10, 9780470061572.
[21] McLachlan, G. J., & Krishnan, T. (2007). The EM algorithm and extensions (Vol. 382). John Wiley & Sons.
[22] Nassar, M., Dey, S., & Nadarajah, S. (2021). Reliability analysis of exponentiated Poisson‐exponential constant stress accelerated life test model. Quality and Reliability Engineering International, 37(6), 2853-2874.
[23] Nelson, W. (1990). Accelerated Testing - Statistical Models, Test Plans, and data Analyses. John Wiley and Sons, New York.
[24] Ng, H. K. T., Chan, P. S., & Balakrishnan, N. (2002). Estimation of parameters from progressively censored data using EM algorithm. Computational Statistics & Data Analysis39(4), 371-386.
[25] Pan, R., Yang, T., & Seo, K. (2015). Planning constant-stress accelerated life tests for acceleration model selection. IEEE Transactions on Reliability64(4), 1356-1366.
[26] Samanta, D., & Kundu, D. (2021). Bayesian inference of a dependent competing risk data. Journal of Statistical Computation and Simulation, 1-18.
[27] Schworer, A. & Hovey, P. “Newton Raphson versus Fisher Scoring Algorithms in Calculating Maximum Likelihood Estimates,” Dayton, 2004.
[28] Wang, L., Tripathi, Y. M., & Lodhi, C. (2020). Inference for Weibull competing risks model with partially observed failure causes under generalized progressive hybrid censoring. Journal of Computational and Applied Mathematics368, 112537.
[29] Widyaningsih, P., Saputro, D. R. S., & Putri, A. N. Fisher scoring method for parameter estimation of geographically weighted ordinal logistic regression (GWOLR) model. Journal of Physics: Conference Series, vol. 855, no. 1, p. 012060. IOP Publishing, 2017.
[30] Zhu, X., & Liu, K. (2021). Reliability of one-shot device with generalized gamma lifetime under cyclic accelerated life-test. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 1748006X211058938.