Interval Estimation of Stress-Strength Reliability Based on Lower Record Values from Inverse Rayleigh Distribution

Table 1

Expected lengths and coverage rates (in parentheses) of the confidence intervals with .

			ML	Bayes	J.B	E.B	Norm	Basic	Perc
5	5	0.1	0.277 (0.942)	0.406 (0.520)	0.272 (0.944)	0.190 (0.847)	0.284 (0.933)	0.276 (0.822)	0.276 (0.940)
5	5	0.25	0.451 (0.951)	0.422 (0.791)	0.453 (0.951)	0.336 (0.862)	0.461 (0.908)	0.449 (0.812)	0.449 (0.949)
5	5	0.5	0.537 (0.947)	0.434 (0.988)	0.540 (0.956)	0.414 (0.868)	0.549 (0.886)	0.536 (0.798)	0.536 (0.941)
5	10	0.1	0.220 (0.952)	0.339 (0.645)	0.217 (0.947)	0.172 (0.883)	0.257 (0.957)	0.250 (0.857)	0.250 (0.947)
5	10	0.25	0.386 (0.948)	0.377 (0.871)	0.388 (0.949)	0.314 (0.879)	0.421 (0.929)	0.413 (0.841)	0.413 (0.942)
5	10	0.5	0.482 (0.956)	0.403 (0.976)	0.482 (0.949)	0.390 (0.883)	0.489 (0.903)	0.480 (0.833)	0.480 (0.937)
5	15	0.1	0.203 (0.946)	0.300 (0.777)	0.202 (0.943)	0.164 (0.873)	0.248 (0.964)	0.241 (0.856)	0.241 (0.927)
5	15	0.25	0.367 (0.947)	0.352 (0.902)	0.365 (0.953)	0.301 (0.887)	0.410 (0.931)	0.402 (0.866)	0.402 (0.933)
5	15	0.5	0.460 (0.956)	0.386 (0.981)	0.459 (0.947)	0.375 (0.873)	0.466 (0.907)	0.458 (0.844)	0.458 (0.936)
10	5	0.1	0.235 (0.946)	0.361 (0.502)	0.236 (0.943)	0.164 (0.856)	0.209 (0.905)	0.204 (0.825)	0.204 (0.935)
10	5	0.25	0.406 (0.961)	0.377 (0.721)	0.403 (0.935)	0.299 (0.846)	0.383 (0.911)	0.375 (0.833)	0.375 (0.945)
10	5	0.5	0.482 (0.958)	0.388 (0.982)	0.480 (0.945)	0.374 (0.855)	0.489 (0.903)	0.480 (0.829)	0.480 (0.942)
10	10	0.1	0.178 (0.947)	0.292 (0.650)	0.175 (0.950)	0.144 (0.905)	0.181 (0.939)	0.178 (0.858)	0.178 (0.950)
10	10	0.25	0.326 (0.958)	0.328 (0.828)	0.327 (0.955)	0.275 (0.913)	0.330 (0.928)	0.326 (0.872)	0.326 (0.955)
10	10	0.5	0.405 (0.943)	0.352 (0.969)	0.405 (0.949)	0.346 (0.895)	0.409 (0.900)	0.404 (0.854)	0.404 (0.940)
10	15	0.1	0.157 (0.955)	0.252 (0.735)	0.156 (0.952)	0.135 (0.913)	0.167 (0.952)	0.164 (0.875)	0.164 (0.950)
10	15	0.25	0.297 (0.951)	0.300 (0.864)	0.296 (0.949)	0.258 (0.913)	0.307 (0.938)	0.304 (0.891)	0.304 (0.947)
10	15	0.5	0.374 (0.943)	0.333 (0.968)	0.374 (0.947)	0.328 (0.913)	0.377 (0.908)	0.373 (0.868)	0.373 (0.935)
15	5	0.1	0.224 (0.946)	0.339 (0.490)	0.221 (0.935)	0.151 (0.840)	0.189 (0.898)	0.185 (0.829)	0.185 (0.934)
15	5	0.25	0.386 (0.951)	0.355 (0.706)	0.386 (0.947)	0.283 (0.871)	0.353 (0.894)	0.346 (0.835)	0.346 (0.931)
15	5	0.5	0.459 (0.946)	0.367 (0.979)	0.459 (0.943)	0.354 (0.855)	0.463 (0.888)	0.455 (0.832)	0.455 (0.919)
15	10	0.1	0.160 (0.952)	0.270 (0.614)	0.162 (0.956)	0.134 (0.911)	0.154 (0.933)	0.152 (0.865)	0.152 (0.948)
15	10	0.25	0.300 (0.943)	0.304 (0.776)	0.302 (0.950)	0.256 (0.909)	0.295 (0.911)	0.291 (0.869)	0.291 (0.937)
15	10	0.5	0.374 (0.948)	0.327 (0.967)	0.375 (0.950)	0.323 (0.911)	0.378 (0.919)	0.374 (0.873)	0.374 (0.947)
15	15	0.1	0.138 (0.946)	0.229 (0.658)	0.139 (0.947)	0.122 (0.919)	0.140 (0.936)	0.138 (0.881)	0.138 (0.948)
15	15	0.25	0.266 (0.953)	0.274 (0.847)	0.267 (0.951)	0.236 (0.920)	0.268 (0.929)	0.266 (0.884)	0.266 (0.950)
15	15	0.5	0.339 (0.952)	0.305 (0.965)	0.339 (0.948)	0.303 (0.915)	0.342 (0.931)	0.339 (0.899)	0.339 (0.952)