A Review of Accelerated Test Models
Luis A. Escobar and William Q. Meeker
Source: Statist. Sci. Volume 21, Number 4
(2006), 552-577.
Abstract
Engineers in the manufacturing industries have used accelerated test (AT) experiments for many decades. The purpose of AT experiments is to acquire reliability information quickly. Test units of a material, component, subsystem or entire systems are subjected to higher-than-usual levels of one or more accelerating variables such as temperature or stress. Then the AT results are used to predict life of the units at use conditions. The extrapolation is typically justified (correctly or incorrectly) on the basis of physically motivated models or a combination of empirical model fitting with a sufficient amount of previous experience in testing similar units. The need to extrapolate in both time and the accelerating variables generally necessitates the use of fully parametric models. Statisticians have made important contributions in the development of appropriate stochastic models for AT data [typically a distribution for the response and regression relationships between the parameters of this distribution and the accelerating variable(s)], statistical methods for AT planning (choice of accelerating variable levels and allocation of available test units to those levels) and methods of estimation of suitable reliability metrics. This paper provides a review of many of the AT models that have been used successfully in this area.
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Keywords: Reliability; regression model; lifetime data; degradation data; extrapolation; acceleration factor; Arrhenius relationship; Eyring relationship; inverse power relationship; voltage-stress acceleration; photodegradation
Full-text: Open access
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Permanent link to this document: http://projecteuclid.org/euclid.ss/1177334529
Digital Object Identifier: doi:10.1214/088342306000000321
Mathematical Reviews number (MathSciNet): MR2380715
Zentralblatt MATH identifier: 1129.62090
References
Birnbaum, Z. W. and Saunders, S. C. (1969). A new family of life distributions. J. Appl. Probab. 6 319--327
Mathematical Reviews (MathSciNet): MR0253493
Digital Object Identifier: doi:10.2307/3212003
JSTOR: links.jstor.org
Zentralblatt MATH: 0209.49801
Black, J. R. (1969). Electromigration---a brief survey and some recent results. IEEE Transactions on Electron Devices 16 338--347.
Blum, H. F. (1959). Carcinogenesis by Ultraviolet Light. Princeton Univ. Press.
Boccaletti, G., Borri, F. R., D'Esponosa, F. and Ghio, E. (1989). Accelerated tests. In Microelectronic Reliability 2. Integrity Assessment and Assurance (E. Pollino, ed.) Chapter 11. Artech House, Norwood, MA.
Box, G. E. P. and Cox, D. R. (1964). An analysis of transformations (with discussion). J. Roy. Statist. Soc. Ser. B 26 211--252.
Mathematical Reviews (MathSciNet): MR0192611
JSTOR: links.jstor.org
Boyko, K. C. and Gerlach, D. L. (1989). Time dependent dielectric breakdown of 210 Å oxides. In Proc. 27th Annual International Reliability Physics Symposium 1--8. IEEE Press, New York.
Burch, D., Martin, J. W. and VanLandingham, M. R. (2002). Computer analysis of a polymer coating exposed to field weather conditions. J. Coatings Technology 74 75--86.
d'Heurle, F. M. and Ho, P. S. (1978). Electromigration in thin films. In Thin Films: Interdiffusion and Reactions (J. M. Poate, K. N. Tu and J. W. Mayer, eds.) 243--303. Wiley, New York.
Dowling, N. E. (1993). Mechanical Behavior of Materials. Prentice Hall, Englewood Cliffs, NJ.
Escobar, L. A., Meeker, W. Q., Kugler, D. L. and Kramer, L. L. (2003). Accelerated destructive degradation tests: Data, models and analysis. In Mathematical and Statistical Methods in Reliability (B. H. Lindqvist and K. A. Doksum, eds.) 319--337. World Scientific, River Edge, NJ.
Mathematical Reviews (MathSciNet): MR2031082
Evans, R. A. (1977). Accelerated testing: The only game in town. IEEE Transactions on Reliability 26 241.
Evans, R. A. (1991). Accelerated testing. IEEE Transactions on Reliability 40 497.
Eyring, H. (1980). Basic Chemical Kinetics. Wiley, New York.
Fisher, R. and Tippett, L. H. (1928). Limiting forms of the frequency distribution of the largest and smallest member of a sample. Proc. Cambridge Philos. Soc. 24 180--190.
Ghate, P. B. (1982). Electromigration-induced failures in VLSI interconnects. In Proc. 20th Annual International Reliability Physics Symposium 292--299. IEEE Press, New York.
Gillen, K. T. and Mead, K. E. (1980). Predicting life expectancy and simulating age of complex equipment using accelerated aging techniques. Available from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA 22151.
Glasstone, S., Laidler, K. J. and Eyring, H. (1941). Theory of Rate Processes. McGraw-Hill, New York.
Hahn, G. J., Meeker, W. Q. and Doganaksoy, N. (2003). Accelerated testing for speedier reliability analysis. Quality Progress 36(6) 58--63.
Hooper, J. H. and Amster, S. J. (1990). Analysis and presentation of reliability data. In Handbook of Statistical Methods for Engineers and Scientists (H. M. Wadsworth, ed.). McGraw Hill, New York.
James, T. H., ed. (1977). The Theory of the Photographic Process, 4th ed. Macmillan, New York.
Jensen, F. (1995). Electronic Component Reliability: Fundamentals, Modelling, Evaluation and Assurance. Wiley, New York.
Johnston, D. R., LaForte, J. T., Podhorez, P. E. and Galpern, H. N. (1979). Frequency acceleration of voltage endurance. IEEE Transactions on Electrical Insulation 14 121--126.
Joyce, W. B., Liou, K.-Y., Nash, F. R., Bossard, P. R. and Hartman, R. L. (1985). Methodology of accelerated aging. AT&T Technical J. 64 717--764.
Kalkanis, G. and Rosso, E. (1989). The inverse power law model for the lifetime of a mylar--polyurethane laminated dc hv insulating structure. Nuclear Instruments and Methods in Physics Research A281 489--496.
Klinger, D. J. (1991). On the notion of activation energy in reliability: Arrhenius, Eyring and thermodynamics. In Annual Reliability and Maintainability Symposium 295--300. IEEE, New York.
Klinger, D. J. (1991). Humidity acceleration factor for plastic packaged electronic devices. Quality and Reliability Engineering International 7 365--370.
Klinger, D. J. (1992). Failure time and rate constant of degradation: An argument for the inverse relationship. Microelectronics Reliability 32 987--994.
Klinger, D. J., Nakada, Y. and Menendez, M. A., eds. (1990). AT&T Reliability Manual. Van Nostrand Reinhold, New York.
Lawless, J. F. (1986). A note on lifetime regression models. Biometrika 73 509--512.
Mathematical Reviews (MathSciNet): MR0855912
Zentralblatt MATH: 0595.62104
Digital Object Identifier: doi:10.1093/biomet/73.2.509
JSTOR: links.jstor.org
LuValle, M. J., Copeland, L. R., Kannan, S., Judkins, J. and Lemaire, P. (1998). A strategy for extrapolation in accelerated testing. Bell Labs Technical J. 3(3) 139--147.
LuValle, M. J., Lefevre, B. and Kannan, S. (2004). Design and Analysis of Accelerated Tests for Mission Critical Reliability. Chapman and Hall/CRC, Boca Raton, FL.
Zentralblatt MATH: 1053.62115
LuValle, M. J., Welsher, T. L. and Mitchell, J. P. (1986). A new approach to the extrapolation of accelerated life test data. In Proc. Fifth International Conference on Reliability and Maintainability 620--635. Biarritz, France.
LuValle, M. J., Welsher, T. L. and Svoboda, K. (1988). Acceleration transforms and statistical kinetic models. J. Statist. Phys. 52 311--330.
Mathematical Reviews (MathSciNet): MR0968588
Digital Object Identifier: doi:10.1007/BF01016417
Zentralblatt MATH: 1082.82517
Mann, N. R., Schafer, R. E. and Singpurwalla, N. D. (1974). Methods for Statistical Analysis of Reliability and Life Data. Wiley, New York.
Mathematical Reviews (MathSciNet): MR365976
Zentralblatt MATH: 0339.62070
Martin, J. W. (1982). Time transformation functions commonly used in life testing analysis. Durability of Building Materials 1 175--194.
Martin, J. W., Saunders, S. C., Floyd, F. L. and Wineburg, J. P. (1996). Methodologies for Predicting the Service Lives of Coating Systems. Federation of Societies for Coatings Technology, Blue Bell, PA.
Meeker, W. Q. and Escobar, L. A. (1998). Statistical Methods for Reliability Data. Wiley, New York.
Zentralblatt MATH: 0949.62086
Meeker, W. Q. and Escobar, L. A. (2004). Reliability: The other dimension of quality. Quality Technology and Quantitative Management 1 1--25.
Mathematical Reviews (MathSciNet): MR2190374
Meeker, W. Q., Escobar, L. A. and Lu, C. J. (1998). Accelerated degradation tests: Modeling and analysis. Technometrics 40 89--99.
Meeker, W. Q., Escobar, L. A. and Zayac, S. (2003). Use of sensitivity analysis to assess the effect of model uncertainty in analyzing accelerated life test data. In Case Studies in Reliability and Maintenance (W. R. Blischke and D. N. Prabhakar Murthy, eds.) 135--162. Wiley, New York.
Mathematical Reviews (MathSciNet): MR1959772
Meeker, W. Q. and Hahn, G. J. (1977). Asymptotically optimum over-stress tests to estimate the survival probability at a condition with a low expected failure probability (with discussion). Technometrics 19 381--404.
Meeker, W. Q. and Hahn, G. J. (1985). How to Plan an Accelerated Life Test: Some Practical Guidelines. American Society for Quality Control, Milwaukee, WI.
Zentralblatt MATH: 0609.62138
Meeker, W. Q. and Hamada, M. (1995). Statistical tools for the rapid development and evaluation of high-reliability products. IEEE Transactions on Reliability 44 187--198.
Meeker, W. Q. and LuValle, M. J. (1995). An accelerated life test model based on reliability kinetics. Technometrics 37 133--146.
Nelson, W. (1984). Fitting of fatigue curves with nonconstant standard deviation to data with runouts. J. Testing and Evaluation 12 69--77.
Nelson, W. (1990). Accelerated Testing: Statistical Models, Test Plans and Data Analyses. Wiley, New York.
Pascual, F. G., Meeker, W. Q. and Escobar, L. A. (2006). Accelerated life test models and data analysis. In Handbook of Engineering Statistics (H. Pham, ed.) Chapter 22. Springer, New York.
Peck, D. S. (1986). Comprehensive model for humidity testing correlation. In Proc. International Reliability Physics Symposium 44--50. IEEE Press, New York.
Peck, D. S. and Zierdt, C. H., Jr. (1974). The reliability of semiconductor devices in the Bell System. In Proc. IEEE 62 185--211.
Phadke, M. S. (1989). Quality Engineering Using Robust Design. Prentice Hall, Englewood Cliffs, NJ.
Smith, J. S. (1996). Physics of failure. In Handbook of Reliability Engineering and Management, 2nd ed. (W. G. Ireson, C. F. Coombs and R. Y. Moss, eds.) Chapter 14. McGraw Hill, New York.
Tobias, P. A. and Trindade, D. C. (1995). Applied Reliability, 2nd ed. Van Nostrand Reinhold, New York.
Mathematical Reviews (MathSciNet): MR876075
Tweedie, M. C. K. (1956). Some statistical properties of inverse Gaussian distributions. Virginia J. Sci. 7 160--165.
Mathematical Reviews (MathSciNet): MR84957
Weston, R. and Schwarz, H. A. (1972). Chemical Kinetics. Prentice Hall, Englewood Cliffs, NJ.
