The reliability of exchangeable binary systems

Assuming that the components of a system are Bernoulli and positive dependent by mixture, we can estimate the reliability of a k-out-of-n:F system, a consecutive k-out-of-n:F system and a circular consecutive k-out-of-n:F system by using canonical moments.

[1]  M. Skibinsky The range of the (n + 1)th moment for distributions on [0, 1] , 1967 .

[2]  David R. Brillinger,et al.  The Asymptotic Behaviour of Tukey's General Method of Setting Approximate Confidence Limits (The Jackknife) When Applied to Maximum Likelihood Estimates , 1964 .

[3]  W. J. Studden $D_s$-Optimal Designs for Polynomial Regression Using Continued Fractions , 1980 .

[4]  Jane N. Hagstrom,et al.  System Reliability Analysis in the Presence of Dependent Component Failures , 1987 .

[5]  W. J. Studden Some Robust-Type D-Optimal Designs in Polynomial Regression , 1982 .

[6]  Moshe Shaked,et al.  A Concept of Positive Dependence for Exchangeable Random Variables , 1977 .

[7]  S. Papastavridis,et al.  Formulas for the reliability of a consecutive- K -Out-of- n : F system , 1988 .

[8]  F. Proschan,et al.  A Reliability Bound for Systems of Maintained, Interdependent Components , 1970 .

[9]  K. Liang,et al.  Asymptotic Properties of Maximum Likelihood Estimators and Likelihood Ratio Tests under Nonstandard Conditions , 1987 .

[10]  Jerald F. Lawless,et al.  Statistical Methods in Reliability , 1983 .

[11]  Y. L. Tong,et al.  A rearrangement inequality for the longest run, with an application to network reliability , 1985, Journal of Applied Probability.

[12]  Morris Skibinsky,et al.  Some Striking Properties of Binomial and Beta Moments , 1969 .

[13]  Morris Skibinsky Extreme nth moments for distributions on [0, 1] and the inverse of a moment space map , 1968 .

[14]  J. George Shanthikumar,et al.  Lifetime Distribution of Consecutive-k-out-of-n:F Systems With Exchangeable Lifetimes , 1985, IEEE Transactions on Reliability.