Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32131
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


In this paper, we propose a method to model the relationship between failure time and degradation for a simple step stress test where underlying degradation path is linear and different causes of failure are possible. It is assumed that the intensity function depends only on the degradation value. No assumptions are made about the distribution of the failure times. A simple step-stress test is used to shorten failure time of products and a tampered failure rate (TFR) model is proposed to describe the effect of the changing stress on the intensities. We assume that some of the products that fail during the test have a cause of failure that is only known to belong to a certain subset of all possible failures. This case is known as masking. In the presence of masking, the maximum likelihood estimates (MLEs) of the model parameters are obtained through an expectation-maximization (EM) algorithm by treating the causes of failure as missing values. The effect of incomplete information on the estimation of parameters is studied through a Monte-Carlo simulation. Finally, a real example is analyzed to illustrate the application of the proposed methods.

Keywords: Expectation-maximization (EM) algorithm, cause of failure, intensity, linear degradation path, masked data, reliability function.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 664


[1] V. Bagdonavicius, A. Bikelis and V. Kazakevicius, ” Statistical analysis of linear degradation and failure time data with multiple failure modes,” Lifetime data analysis, vol. 1, no. 10, pp. 65-81, 2004.
[2] V. Bagdonavicius, F. Haghighi and M. Nikulin, ” Statistical analysis of general degradation path model and failure time data with multiple failure modes,” Communications in statistics-Theory and methods, vol. 34, no. 8, pp. 1771-1791, 2005.
[3] G. Bhattacharyya and Z. Soejoeti, ” A tampered failure rate model for step-stress accelerated life test,” Communications in statistics- Theory and methods, vol. 18, no. 5, pp. 1627-1643, 1989.
[4] R. V. Craiu and T. Duchesne,” Inference based on the EM algorithm for the competing risk model with masked causes of failure,” Biometrika, vol. 91, no. 3, pp. 543558, 2004.
[5] R. V. Craiu and B. Reiser,” Inference for the dependent competing risks model with masked causes of failure,” Lifetime data analysis, vol. 12, no. 1, pp. 2133, 2006.
[6] R. V. Fan and B. Wang,” Accelerated Life Tests for Weibull Series Systems With Masked Data,” IEEE Transactions on Reliability, vol. 60, no. 3, pp. 557569, 2011.
[7] F. Haghighi and S. J. Bae, ” Reliability estimation from linear degradation and failure time data with competing risks under a step-stress accelerated degradation test,” IEEE Trans. Reliability, vol.64, no. 3, pp.960-971 , 2015.
[8] M. Hamada, ” Bayesian analysis of step-stress accelerated life tests and its use in planning,” Quality Engineering, vol. 27, no. 3, pp. 276-282, 2015.
[9] W. Q. Meeker and L. A. Escobar, Statistical methods for reliability data. John Wiley and Sons, 1998.
[10] W. B. Nelson, Accelerated testing: statistical models, test plans, and data analyses. John Wiley and Sons, 2004.
[11] C. Park, ” Parameter estimation of incomplete data in competing risks using the EM algorithm , ” IEEE Transactions on reliability, vol. 54, no. 2, pp. 282-290, 2005.
[12] A. Xu, S. Basu, and Y.A. Tang, A Full Bayesian Approach for Masked Data in Step-Stress Accelerated Life Testing, IEEE Transactions on Reliability, vol. 63, no. 3, pp. 798–806, 2014.
[13] A. Xu, Y. Tang, and Q. Guan, Bayesian Analysis of Masked Data in Step-Stress Accelerated Life Testing, Communications in Statistics- Simulation and Computation, vol. 43, no. 8, pp. 2016–2030, 2014.