Table 6 Point and 95% interval estimates for system reliability (\(\zeta _{2,5}\)) for Dataset 2 (River Floods).

Frequentist Estimates

MLE

\(\hat{\zeta }_{MLE}\)

0.8803

–

–

–

ACI

–

–

0.8015

0.9591

0.1576

Bootstrap-p

–

–

0.8144

0.9412

0.1268

Bootstrap-t

–

–

0.8197

0.9399

0.1202

Bayesian Estimates (via TK)

SE Loss

\(\hat{\zeta }_{TK-SE}\)

0.8825

–

-

–

LINEX (\(c=1.5\))

\(\hat{\zeta }_{TK-L}\)

0.8753

–

–

–

LINEX (\(c=-1.5\))

\(\hat{\zeta }_{TK-L}\)

0.8895

–

–

–

Bayesian Estimates (via MCMC)

SE Loss (Mean)

\(\hat{\zeta }_{MCMC-SE}\)

0.8829

–

–

–

LINEX (\(c=1.5\))

\(\hat{\zeta }_{MCMC-L}\)

0.8759

–

–

–

LINEX (\(c=-1.5\))

\(\hat{\zeta }_{MCMC-L}\)

0.8901

–

–

–

HPD Interval

–

–

0.8185

0.9351

0.1166