Advances on the Stress Interaction Model

In a reliability experiment, a combination of temperature cycling (TC) and temperature humidity bias (THB) stress was applied. The outcome varied significantly with the sequence of the stress tests. It made a difference whether first TC-stress was performed and then THB-stress, or the other way round. A statistical model is created for this effect. It is called the Stress Interaction Model. The stress sequence is given as a path in \BBR2. The hazard function is set up as a vector field. Unless the hazard function is a potential of a vector field, the path integral depends on the way from point A to point B. In this setup, the sequence of the applied stress tests, say the stress history, is reflected in the reliability function. In this paper, the Stress Interaction Model is extended by a shape factor.

[1]  M. Malek Vector Calculus , 2014 .

[2]  J. Klein,et al.  Statistical Models Based On Counting Process , 1994 .

[3]  Loon Ching Tang,et al.  A Distribution-Based Systems Reliability Model Under Extreme Shocks and Natural Degradation , 2011, IEEE Transactions on Reliability.

[4]  Peng Huang,et al.  Stochastic Models in Reliability , 1999, Technometrics.

[5]  Philip Hougaard,et al.  Analysis of Multivariate Survival Data , 2001 .

[6]  E. Lehmann Testing Statistical Hypotheses , 1960 .

[7]  Vijay Nair Advances in statistical modeling and inference , 2013 .

[8]  Alessandro Birolini Reliability Engineering: Theory and Practice , 1999 .

[9]  Maxim Finkelstein,et al.  Burn-in for Systems Operating in a Shock Environment , 2011, IEEE Transactions on Reliability.

[10]  J. Cha,et al.  On a Terminating Shock Process with Independent Wear Increments , 2009, Journal of Applied Probability.

[11]  Zhengqiang Pan,et al.  Bivariate Degradation Modeling Based on Gamma Process , 2010 .

[12]  Neil Genzlinger A. and Q , 2006 .

[13]  G. Grimmett,et al.  Probability and random processes , 2002 .

[14]  L. Fahrmeir,et al.  Multivariate statistische Verfahren , 1984 .

[15]  Jin Qin,et al.  Non-Arrhenius Temperature Acceleration and Stress-Dependent Voltage Acceleration for Semiconductor Device Involving Multiple Failure Mechanisms , 2006, 2006 IEEE International Integrated Reliability Workshop Final Report.

[16]  Toshio Nakagawa,et al.  Stochastic Processes: with Applications to Reliability Theory , 2011 .

[17]  Toshio Nakagawa,et al.  Shock and Damage Models in Reliability Theory , 2006 .

[18]  J. G. Kalbfleisch Probability and Statistical Inference , 1977 .

[19]  A. Wienke Frailty Models in Survival Analysis , 2010 .

[20]  M. Jacobsen Point Process Theory and Applications: Marked Point and Piecewise Deterministic Processes , 2005 .

[21]  Elisa Lee,et al.  Statistical Methods for Survival Data Analysis: Lee/Survival Data Analysis , 2003 .

[22]  Dimitri Kececioglu,et al.  Reliability engineering handbook , 1991 .

[23]  Rosemary A. Roberts,et al.  Probability and Statistical Inference: Volume 2: Statistical Inference , 2011 .

[24]  Laurence L. George,et al.  The Statistical Analysis of Failure Time Data , 2003, Technometrics.

[25]  J. Kalbfleisch,et al.  The Statistical Analysis of Failure Time Data: Kalbfleisch/The Statistical , 2002 .

[26]  Hong-Zhong Huang,et al.  An Approach to Reliability Assessment Under Degradation and Shock Process , 2011, IEEE Transactions on Reliability.

[27]  D. Cox,et al.  Analysis of Survival Data. , 1986 .

[28]  K. Srikrishnan,et al.  Handbook of Semiconductor Interconnection Technology, Second Edition , 2006 .

[29]  Chanseok Park,et al.  Stochastic degradation models with several accelerating variables , 2006, IEEE Transactions on Reliability.