Simulated Annealing for Mixture Distribution Analysis and its Applications to Reliability Testing

Reliability is a very important field of study in today’s era of technology. It is essential to quantitatively estimate the reliability of a product or device before it is mass produced and sold in the market through accelerated life tests. In reliability testing and data analysis, global optimization of the log-likelihood function plays a key role. An effective technique for this optimization is Simulated Annealing (SA). The objective of this chapter is to illustrate the applicability of SA to reliability data analysis. In particular, this optimization technique is very useful for mixture distribution analysis which will be described in detail later. The flow of the chapter goes as follows. A brief introduction to reliability statistics will be provided, intended to provide a b asic outlook into this fascinating field to readers who are new to it. The role of SA in reliability statistics will be made clear through the developed log-likelihood function which needs to be optimized. This is followed by an insight into the need for mixture distribution analysis in reliability testing and assessment. The origin and methodology underlying the SA algorithm is then described in detail. The application of SA to mixt ure distribution analysis is presented and two practical examples of this application are provided from the microelectronics industry where electronic device reliability for gate oxide breakdown and electromigration phenomenon is assessed. Towards the end, techniques proposed in the literature to improve the efficiency of search for SA is presented and a conclu ding section directs the reader on the path to pursue further research investigations in simulated annealing. 1.2 Scope The most fundamental form of the SA algori thm is employed in the reliability analysis presented in this chapter. Although more efficient designs of the SA algorithm have been made, they are not utilized in this work. The application case studies illustrate the application of SA for reliability analysis only in the field of microelectronics. The approach presented in this paper is nevertheless applicable to all practical reliability studies.

[1]  Cher Ming Tan,et al.  Electromigration in ULSI Interconnections , 2010, International Series on Advances in Solid State Electronics and Technology.

[2]  William H. Press,et al.  Numerical recipes in C. The art of scientific computing , 1987 .

[3]  Ulrich W. Thonemann,et al.  Optimizing simulated annealing schedules with genetic programming , 1996 .

[4]  Cher Ming Tan,et al.  Statistical Analysis of Multi-Censored Electromigration Data using the EM Algorithm , 2007, 2007 14th International Symposium on the Physical and Failure Analysis of Integrated Circuits.

[5]  Cher Ming Tan,et al.  Unveiling the electromigration physics of ULSI interconnects through statistics , 2007 .

[6]  H. Akaike.  A new look at the statistical model identification , 1974 .

[7]  Cher Ming Tan,et al.  An approach to statistical analysis of gate oxide breakdown mechanisms , 2007, Microelectron. Reliab..

[8]  Matija Fajdiga,et al.  Reliability approximation using finite Weibull mixture distributions , 2004, Reliab. Eng. Syst. Saf..

[10]  R. Degraeve,et al.  A new model for the field dependence of intrinsic and extrinsic time-dependent dielectric breakdown , 1998 .

[11]  S. Brooks,et al.  Optimization Using Simulated Annealing , 1995 .

[12]  William L. Goffe,et al.  SIMANN: FORTRAN module to perform Global Optimization of Statistical Functions with Simulated Annealing , 1992 .

[13]  Yuan Taur,et al.  Fundamentals of Modern VLSI Devices , 1998 .

[14]  Cher Ming Tan,et al.  Application of gamma distribution in electromigration for submicron interconnects , 2007 .

[15]  Xin Yao,et al.  A new simulated annealing algorithm , 1995, Int. J. Comput. Math..

[16]  Edgar N. Reyes,et al.  Optimization using simulated annealing , 1998, Northcon/98. Conference Proceedings (Cat. No.98CH36264).

[17]  Dimitri Kececioglu,et al.  Maximum likelihood estimates, from censored data, for mixed-Weibull distributions , 1992 .

[18]  Ephraim Suhir.  Accelerated life testing (ALT) in microelectronics and photonics: its role, attributes, challenges, pitfalls, and interaction with qualification tests , 2002, SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring.

[19]  A. F. Smith,et al.  Statistical analysis of finite mixture distributions , 1986 .

[20]  Charles E Ebeling,et al.  An Introduction to Reliability and Maintainability Engineering , 1996 .

[21]  P. A. Bennett.  Practical Reliability Engineering , 1982 .

[22]  B. Suman,et al.  A survey of simulated annealing as a tool for single and multiobjective optimization , 2006, J. Oper. Res. Soc..

[23]  William Q. Meeker,et al.  Pitfalls of accelerated testing , 1998 .