{"title":"A Partially Accelerated Life Test Planning with Competing Risks and Linear Degradation Path under Tampered Failure Rate Model","authors":"Fariba Azizi, Firoozeh Haghighi, Viliam Makis","volume":126,"journal":"International Journal of Industrial and Manufacturing Engineering","pagesStart":1252,"pagesEnd":1256,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/10007544","abstract":"In this paper, we propose a method to model the
\r\nrelationship between failure time and degradation for a simple step
\r\nstress test where underlying degradation path is linear and different
\r\ncauses of failure are possible. It is assumed that the intensity function
\r\ndepends only on the degradation value. No assumptions are made
\r\nabout the distribution of the failure times. A simple step-stress test
\r\nis used to shorten failure time of products and a tampered failure
\r\nrate (TFR) model is proposed to describe the effect of the changing
\r\nstress on the intensities. We assume that some of the products that
\r\nfail during the test have a cause of failure that is only known to
\r\nbelong to a certain subset of all possible failures. This case is known
\r\nas masking. In the presence of masking, the maximum likelihood
\r\nestimates (MLEs) of the model parameters are obtained through an
\r\nexpectation-maximization (EM) algorithm by treating the causes of
\r\nfailure as missing values. The effect of incomplete information on the
\r\nestimation of parameters is studied through a Monte-Carlo simulation.
\r\nFinally, a real example is analyzed to illustrate the application of the
\r\nproposed methods.","references":"[1] V. Bagdonavicius, A. Bikelis and V. Kazakevicius, \u201d Statistical analysis\r\nof linear degradation and failure time data with multiple failure modes,\u201d\r\nLifetime data analysis, vol. 1, no. 10, pp. 65-81, 2004.\r\n[2] V. Bagdonavicius, F. Haghighi and M. Nikulin, \u201d Statistical analysis of\r\ngeneral degradation path model and failure time data with multiple failure\r\nmodes,\u201d Communications in statistics-Theory and methods, vol. 34, no.\r\n8, pp. 1771-1791, 2005.\r\n[3] G. Bhattacharyya and Z. Soejoeti, \u201d A tampered failure rate model for\r\nstep-stress accelerated life test,\u201d Communications in statistics- Theory and\r\nmethods, vol. 18, no. 5, pp. 1627-1643, 1989.\r\n[4] R. V. Craiu and T. Duchesne,\u201d Inference based on the EM algorithm\r\nfor the competing risk model with masked causes of failure,\u201d Biometrika,\r\nvol. 91, no. 3, pp. 543558, 2004.\r\n[5] R. V. Craiu and B. Reiser,\u201d Inference for the dependent competing risks\r\nmodel with masked causes of failure,\u201d Lifetime data analysis, vol. 12, no.\r\n1, pp. 2133, 2006.\r\n[6] R. V. Fan and B. Wang,\u201d Accelerated Life Tests for Weibull Series\r\nSystems With Masked Data,\u201d IEEE Transactions on Reliability, vol. 60,\r\nno. 3, pp. 557569, 2011.\r\n[7] F. Haghighi and S. J. Bae, \u201d Reliability estimation from linear degradation\r\nand failure time data with competing risks under a step-stress accelerated\r\ndegradation test,\u201d IEEE Trans. Reliability, vol.64, no. 3, pp.960-971 ,\r\n2015.\r\n[8] M. Hamada, \u201d Bayesian analysis of step-stress accelerated life tests and\r\nits use in planning,\u201d Quality Engineering, vol. 27, no. 3, pp. 276-282,\r\n2015.\r\n[9] W. Q. Meeker and L. A. Escobar, Statistical methods for reliability data.\r\nJohn Wiley and Sons, 1998.\r\n[10] W. B. Nelson, Accelerated testing: statistical models, test plans, and\r\ndata analyses. John Wiley and Sons, 2004.\r\n[11] C. Park, \u201d Parameter estimation of incomplete data in competing risks\r\nusing the EM algorithm , \u201d IEEE Transactions on reliability, vol. 54, no.\r\n2, pp. 282-290, 2005.\r\n[12] A. Xu, S. Basu, and Y.A. Tang, A Full Bayesian Approach for Masked\r\nData in Step-Stress Accelerated Life Testing, IEEE Transactions on\r\nReliability, vol. 63, no. 3, pp. 798\u2013806, 2014.\r\n[13] A. Xu, Y. Tang, and Q. Guan, Bayesian Analysis of Masked Data\r\nin Step-Stress Accelerated Life Testing, Communications in Statistics-\r\nSimulation and Computation, vol. 43, no. 8, pp. 2016\u20132030, 2014.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 126, 2017"}