Bayes and classical estimation of environmental factors for the binomial distribution

An environmental factor converts reliability test results at one environmental condition into equivalent "failure" information at other environments. This paper studies environmental-factor estimation for the binomial distribution. Under general conditions, Bayes point estimates and credibility limits for environmental factors are derived. Classical point and confidence interval estimates are introduced and compared with the Bayes estimators. The characteristics of Bayes and classical estimators for the binomial distribution are summarized through numerical computation and theoretical analysis. A numerical example of reliability assessment by means of environmental factors is presented.

[1]  G. Apostolakis,et al.  Some Properties of Distributions Useful in the Study of Rare Events , 1982, IEEE Transactions on Reliability.

[2]  Harry F. Martz,et al.  Bayesian reliability analysis of series systems of binomial subsystems and components , 1988 .

[3]  S P Azen,et al.  OBTAINING CONFIDENCE INTERVALS FOR THE RISK RATIO IN COHORT STUDIES , 1978 .

[4]  D G Thomas,et al.  The performance of three approximate confidence limit methods for the odds ratio. , 1982, American journal of epidemiology.

[5]  B. Bailey,et al.  Confidence limits to the risk ratio. , 1987, Biometrics.

[6]  Walter W. Hauck,et al.  On the asymptotic inefficiency of certain noniterative estimators of a common relative risk or odds ratio , 1983 .

[7]  J J Gart,et al.  Approximate interval estimation of the ratio of binomial parameters: a review and corrections for skewness. , 1988, Biometrics.

[8]  P. Chiou,et al.  An information-theoretic approach to incorporating prior information in binomial sampling , 1984 .

[9]  P. A. R. Koopman,et al.  Confidence intervals for the ratio of two binomial proportions , 1984 .

[10]  H. Weiler,et al.  The Use of Incomplete Beta Functions for Prior Distributions in Binomial Sampling , 1965 .

[11]  E J Bedrick,et al.  A family of confidence intervals for the ratio of two binomial proportions. , 1987, Biometrics.

[12]  H. Martz.  Bayesian reliability analysis , 1982 .

[13]  Hongzhou Wang,et al.  Estimation of environmental factors for the inverse Gaussian distribution , 1992 .

[14]  M Nurminen,et al.  Comparative analysis of two rates. , 1985, Statistics in medicine.

[15]  Gottfried E. Noether,et al.  Two Confidence Intervals for the Ratio of Two Probabilities and Some Measures of Effectiveness , 1957 .

[16]  Hongzhou Wang,et al.  A research study of environmental factors for the gamma distribution , 1992 .

[17]  S. Walter.  The estimation and interpretation of attributable risk in health research. , 1976, Biometrics.