|
[1] Arellano-Valle R. B., Bolfarine, H. and Lachos, V. H. (2005), “Skew-normal linear mixed models,” Journal of Data Science, 3, 415-438. [2] Azzalini, A. (1985), “A class of distributions which includes the normal ones,” Scandinavian Journal of Statistics, 12, 171-178. [3] Azzalini, A. (1986), “Further results on a class of distributions which includes the normal ones,” Statistica, 46, 199-208. [4] Azzalini, A. (2005), “The skew-normal distribution and related multivariate families,” Scandinavian Journal of Statistics, 32, 159-188. [5] Azzalini A. and Capitanio A. (1999), “Statistical applications of the multivariate skew-normal distributions,” Journal of the Royal Statistical Society. B, 61, 579-602. [6] Azzalini, A. and Dalla Valle, A. (1996), “The multivariate skew-normal distribution,” Biometrika, 83, 715-726. [7] Bae, S. J. and Kvam, P. H. (2004), “A nonlinear random coefficients model for degradation testing,” Technometrics, 46, 460-469. [8] Bagdonavicius, V. and Nikulin, M. (2000), “Estimation in degradation models with explanatory variables,” Lifetime Data Analysis, 7, 85-103. [9] Bagdonavicius, V. and Nikulin, M. (2002), Accelerated Life Models: Modeling and Statistical Analysis, Chapman & Hall/CRC, New York. [10] Boulanger, M. and Escobar, L. A. (1994), “Experimental design for a class of accelerated degradation tests,” Technometrics, 36, 260-272. [11] Chao, M. T. (1999), “Degradation analysis and related topics: Some thoughts and a review,” The Proceedings of the National Science Council. A, 23, 555-566. [12] Chhikara, R. S. and Folks, L. (1989), The Inverse Gaussain Distribution. Theory, Methodology, and Applications, Marcel Dekker, New York. [13] Chow, Y. S. and Teicher, H. (1997), Probability Theory: independence, in- terchangeability, martingales, 3rd ed, Springer-Verlag, New York. [14] Dempster, A. P., Laird, N. M. and Rubin, D. B. (1977), “Maximum likelihood from incomplete data via the EM algorithm,” Journal of the Royal Statistical Society. B, 39, 1-22. [15] Di Nardo, E., Nobile, A. G., Pirozzi, E. and Ricciardi, L. M. (2001), “A computational approach to first-passage-time problems for Gauss-Markov processes,” Advances in Applied Probability, 33, 453-482. [16] Di Nardo, E., Nobile, A. G., Pirozzi, E. and Ricciardi, L. M. (2003), “On the asymptotic behavior of first passage time densities for stationary Gaussian processes and varying boundaries,” Methodology and Computing in Applied Probability, 5, 211-233. [17] Doksum, K. A. and H´oyland, A. (1992), “Model for variable-stress accelerated life testing experiments based on Wiener processes and the inverse Gaussian distribution,” Technometrics, 34, 74-82. [18] Durham, S. D. and Padgett, W. J. (1997), “A cumulative damage model for system failure with application to carbon fibers and composites,” Techno- metrics, 39, 34-44. [19] Ellison, B. E. (1964), “Two theorems for inferences about the normal distribution with applications in acceptance sampling,” Journal of the American Statistical Association, 59, 89-95. [20] Feller, W. (1971), An Introduction to Probability Theory and Its Application, Vol. 2, John Wiley & Sons, New York. [21] Gertsbakh, I. B. and Kordonskiy, Kh. B. (1969), Models of Failure, Springer- Verlag, New York. [22] Gill, P. E., Murray, W. and Wright, M. H. (1981), Practical Optimization, Academic Press, London. [23] Gourieroux, C. and Monfort, A. (1995), Statistics and Econometric Models: Volumn 1-2, Cambridge University Press, New York. [24] Harville, D. A. (1977), “Maximum likelihood approaches to variance component estimation and to related problems,” Journal of the American Statistical Association, 72, 320-338. [25] Hendry, D. F. (1995), Dynamic Econometrics, Oxford University Press, New York. [26] Henze, N. (1986), “A probabilistic representation of the skew-normal distribution,” Scandinavian Journal of Statistics, 13, 271-275. [27] Hoel, P. G., Port, S. C. and Stone, C. J. (1972), Introduction to Stochastic Processes, Waveland Press, Illinois. [28] Lawless, J. F. (2002), Statistical Models and Methods for Lifetime Data, John Wiley & Sons, New York. [29] Lawless, J. F. and Crowder, M. J. (2004), “Covariates and random effects in a gamma process model with application to degradation and failure,” Lifetime Data Analysis, 10, 213-227. [30] LeCam, L. (1953), “On some asymptotic properties of maximum likelihood estimates and related Bayes’ estimates,” University of California Publica- tions in Statistics, 1, 277-330. [31] Li, Q. and Kececioglu, D. B. (2004), “Optimal design of accelerated degradation tests,” International Journal of Materials and Product Technology, 20, 73-90. [32] Liao, C. M. and Tseng, S. T. (2006), “Optimal design for step-stress accelerated degradation tests,” IEEE Transactions on Reliability, 55, 59-66. [33] Lu, J. (1995), “Degradation processes and related reliability models,” Un- published Ph.D. Thesis, McGill University, Canada. [34] Lu, C. J. and Meeker, W. Q. (1993), “Using degradation measures to estimate a time-to-failure distribution,” Technometrics, 35, 161-174. [35] Lu, J. C., Park, J. and Yang, Q. (1997), “Statistical inference of a time-tofailure distribution derived from linear degradation data,” Technometrics, 39, 391-400. [36] Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods for Reliability Data, John Wiley & Sons, New York. [37] Meeker, W. Q., Escobar, L. A. and Lu, C. J. (1998), “Accelerated degradation tests: modeling and analysis,” Technometrics, 40, 89-99. [38] Meng, X. L. and Rubin, D.B. (1993), “Maximum likelihood estimation via the ECM algorithm: a general framework,” Biometrika, 80, 267-278. [39] Nelson, W. (1990), Accelerated Testing: Statistical Models, Test Plans, and Data Analyses, John Wiley & Sons, New York. [40] Ng, T. S. (2008), “An application of the EM algorithm to degradation modeling,” IEEE Transactions on Reliability, 57, 2-13. [41] O’Hagan, A. and Leonard, T. (1976), “Bayes estimation subject to uncertainty about parameter constraints,” Biometrika, 63, 201-203. [42] Onar, A. and Padgett, W. J. (2000), “Inverse Gaussian accelerated test models based on cumulative damage,” Journal of Statistical Computation and Simulation, 66, 233-247. [43] Owen, D. B. (1980), “A table of normal integrals,” Communications in Statistics: Part B - Simulation and Computation, 9, 389-419. [44] Park, S. J., Yum, B. J. and Balamurali, S. (2004), “Optimal design of stepstress degradation tests in the case of destructive measurement,” Quality Technology & Quantitative Management, 1, 105-124. [45] Padgett, W. J. (1998), “A multiplicative damage model for strength of fibrous composite materials,” IEEE Transactions on Reliability, 47, 46-52. [46] Padgett, W. J. and Tomlinson, M. A. (2002), “A cumulative damage model for strength of materials when initial damage is a gamma process,” Journal of Statistical Theory and Applications, 1, 1-14. [47] Park, C. and Padgett, W. J. (2005a), “Accelerated degradation models for failure based on geometric Brownian motion and gamma processes,” Lifetime Data Analysis, 11, 511-527. [48] Park, C. and Padgett, W. J. (2005b), “New cumulative damage models for failure using stochastic processes as initial damage,” IEEE Transactions on Reliability, 54, 530-540. [49] Park, C. and Padgett, W. J. (2006), “Stochastic degradation models with several accelerating variables,” IEEE Transactions on Reliability, 55, 379- 390. [50] Pascual, F. G. (2006), “Theory for accelerated life test plans robust to misspecification of stress-life relationship,” Technometrics, 48, 11-25. [51] Pascual, F. G. and Montepiedra, G. (2005), “Accelerated life testing under distribution misspecification: biased estimation and test planning,” IEEE Transactions on Reliability, 54, 43-52. [52] Patel, R. C. (1965), “Estimates of parameters of truncated inverse Gaussian distribution,” Annals of the Institute of Statistical Mathematics, 17, 29-33. [53] Peng, C. Y. (2008), “The first negative moment in the sense of the Cauchy principal value,” Statistics & Probability Letters, in press. [54] Peng, C. Y., and Tseng, S. T. (2008), “Mis-specification analysis of linear degradation models,” Submitted for publication. [55] Quenouille, M. H. (1956), “Notes on bias in estimation,” Biometrika, 43, 353-360. [56] Schott, J. R. (2005), Matrix Analysis for Statistics, 2nd ed, John Wiley & Sons, New York. [57] Seshadri, V. (1999), The Inverse Gaussian Distribution: Statistical Theory and Applications, Springer-Verlag, New York. [58] Tseng, S. T. and Liao, C. M. (1998), “Optimal design for a degradation test,” International Journal of Operations and Quantitative Management, 4, 293-301. [59] Tseng, S. T. and Peng, C. Y. (2004), “Optimal burn-in policy by using integrated Wiener process,” IIE Transactions, 36, 1161-1170. [60] Tseng, S. T. and Peng, C. Y. (2007), “Stochastic diffusion modeling of degradation data,” Journal of Data Science, 5, 315-333. [61] Tseng, S. T. and Wen, Z. C. (2000), “Step-stress accelerated degradation analysis for highly reliable products,” Journal of Quality Technology, 32, 209-216. [62] Tseng, S. T. and Yu, H. F. (1997), “A termination rule for degradation experiment,” IEEE Transactions on Reliability, 46, 130-133. [63] Voinov, V. G. (1985), “Unbiased estimation of powers of the inverse of mean and related problems,” Sankhy‾a, B, 47, 354-364. [64] Wald, A. (1949), “Note on the consistency of the maximum likelihood estimate,” Annals of Mathematical Statistics, 60, 595-603. [65] White, H. (1982), “Maximum likelihood estimation of misspecified models,” Econometrica, 50, 1-25. [66] Whitmore, G. A. (1986), “Normal-gamma mixtures of inverse Gaussian distributions,” Scandinavian Journal of Statistics, 13, 211-220. [67] Whitmore, G. A. (1995), “Estimating degradation by a Wiener diffusion process subject to measurement error,” Lifetime Data Analysis, 1, 307-319. [68] Whitmore, G. A., Crowder, M. I. and Lawless, J. F. (1998), “Failure inference from a marker process based on a bivariate model,” Lifetime Data Analysis, 4, 229-251. [69] Whitmore, G. A. and Schenkelberg, F. (1997), “Modeling accelerated degradation data using Wiener diffusion with a scale transformation,” Lifetime Data Analysis, 3, 27-45. [70] Wu, C. F. J. (1983), “On the convergence properties of the EM algrithm,” Annals of Statistics, 11, 95-103. [71] Wu, S. J. and Chang, C. T. (2002), “Optimal design of degradation tests in presence of cost constraint,” Reliability Engineering and System Safety, 76, 109-115. [72] Yu, H. F. and Tseng, S. T. (1998), “On-line procedure for terminating an accelerated degradation test,” Statistica Sinica, 8, 207-220. [73] Yu, H. F. and Tseng, S. T. (1999), “Designing a degradation experiment,” Naval Research Logistics, 46, 689-706. [74] Yu, H. F. and Tseng, S. T. (2004), “Designing a degradation experiment with a reciprocal Weibull degradation rate,” Quality Technology & Quantitative Management, 1, 47-63. [75] Zacks, S. (1971), The Theory of Statistical Inference, John Wiley & Sons, New York.
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