Reliability models based on bivariate exponential distributions

Abstract Motivated by reliability applications, we derive the exact distributions of R = X + Y and W = X / ( X + Y ) and the corresponding moment properties when X and Y follow five flexible bivariate exponential distributions. The expressions turn out to involve several special functions.

[1]  L. R. Goel,et al.  A two-unit parallel redundant system with three modes and bivariate exponential lifetimes , 1984 .

[2]  L. R. Goel,et al.  A warm standby redundant system with correlated failures and repairs , 1992 .

[3]  L. R. Goel,et al.  Profit analysis of a two-unit redundant system with provision for rest and correlated failures and repairs , 1991 .

[4]  Vinay Kumar Tyagi.  Profit analysis of two-unit standby system with rest period for the operator and correlated failures and repairs , 1995 .

[5]  L. R. Goel,et al.  Analysis of a two unit standby system with preparation time and correlated failures and repairs , 1995 .

[6]  L. R. Goel,et al.  A two unit series system with correlated failures and repairs , 1993 .

[7]  L. R. Goel,et al.  Analysis of a standby system with dependent repair time and slow switching device , 1994 .

[8]  L. R. Goel,et al.  Cost benefit analysis of a complex system with correlated failures and repairs , 1993 .

[9]  L. R. Goel,et al.  A two-unit cold standby system with allowed down-time and correlated failures and repairs , 1992 .

[10]  J P Klein,et al.  Bounds on net survival probabilities for dependent competing risks. , 1988, Biometrics.

[11]  F. Downton.  Bivariate Exponential Distributions in Reliability Theory , 1970 .

[12]  Adrian E. Raftery,et al.  A continuous multivariate exponential distribution , 1984 .

[13]  Mutsumi Kadoya,et al.  Two-variate Exponential Distribution and Its Numerical Table for Engineering Application , 1971 .

[14]  L. R. Goel,et al.  A cold standby system with arrival time of server and correlated failures and repairs , 1995 .

[15]  B. Arnold,et al.  Bivariate Distributions with Exponential Conditionals , 1988 .

[16]  L. R. Goel,et al.  Analysis of a two server-two unit cold standby system with correlated failures and repairs , 1994 .

[17]  L. R. Goel,et al.  An inspection policy for unrevealed failures in a two-unit cold standby system subject to correlated failures and repairs , 1994 .

[18]  Ignacio Rodriguez-Iturbe,et al.  On the probabilistic structure of storm surface runoff , 1985 .

[19]  Nozer D. Singpurwalla,et al.  Specifying interdependence in networked systems , 2004, IEEE Transactions on Reliability.

[20]  N. Ebrahimi.  Analysis of Bivariate Accelerated Life Test Data for the Bivariate Exponential Distribution , 1987 .

[21]  I. Olkin,et al.  A generalized bivariate exponential distribution , 1967 .

[22]  E. W. Hagen,et al.  Common-mode/common-cause failure: A review , 1980 .

[23]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[24]  Shunji Osaki,et al.  Availability theory for two-unit nonindependent series systems subject to shut-off rules , 1989 .

[25]  I. S. Gradshteyn,et al.  Table of Integrals, Series, and Products , 1976 .

[26]  S. Osaki.  A two-unit parallel redundant system with bivariate exponential lifetimes , 1980 .

[27]  Masanori Kodama,et al.  Availability analysis of two-unit warm standby system with inspection time , 1980 .

[28]  A generalization of Freund's model for a repairable paired component based on a bivariate Geiger Muller (G.M.) counter , 1984 .

[29]  Peter A. W. Lewis,et al.  Simple Dependent Pairs of Exponential and Uniform Random Variables , 1983, Oper. Res..

[30]  Akira Kimura,et al.  STATISTICAL PROPERTIES OF SHORT-TERM OVERTOPPING , 1984 .

[31]  J. E. Freund.  A Bivariate Extension of the Exponential Distribution , 1961 .

[32]  Richard E. Barlow,et al.  Techniques for Analyzing Multivariate Failure Data. , 1977 .

[33]  T. Inaba,et al.  Measures of dependence in normal models and exponential models by information gain , 1986 .

[34]  Testing for symmetry and independence in a bivariate exponential distribution , 1985 .

[35]  T. Lai.  Control Charts Based on Weighted Sums , 1974 .

[36]  L. R. Goel,et al.  Availability analysis of a two-unit (dissimilar) parallel system with inspection and bivariate exponential life times , 1985 .

[37]  Chris P. Tsokos,et al.  Theory and Applications of Reliability , 1977 .

[38]  L. R. Goel,et al.  Analysis of an on-surface transit system with correlated failures and repairs , 1994 .

[39]  Ram C. Tiwari,et al.  Comparing cumulative incidence functions of a competing-risks model , 1997 .

[40]  I. Olkin,et al.  A Multivariate Exponential Distribution , 1967 .

[41]  L. R. Goel,et al.  A two-unit standby system with imperfect switch, preventive maintenance and correlated failures and repairs , 1992 .

[42]  Earthquake hazard assessment based on bivariate exponential distributions , 1994 .

[43]  R. Ramanarayanan,et al.  A 2-Unit Cold Standby System with Marshall-Olkin Bivariate Exponential Life and Repair Times , 1981, IEEE Transactions on Reliability.

[44]  L. R. Goel,et al.  A two-unit duplicating standby system with correlated failure-repair/vbreplacement times , 1996 .

[45]  L. R. Goel,et al.  A two-unit cold standby system with three modes and correlated failures and repairs , 1991 .