Sequential Tests of Hypotheses for System Reliability Modeled by a 2-Parameter Weibull Distribution

For the 2-parameter Weibull distribution, truncated sequential tests are developed for the null hypothesis R = R₀ against the alternative hypothesis R = R₁ which are based on the logarithm of the likelihood ratio. Wald upper and lower bounds for a sequential test are modified by Monte Carlo methods using a Monte Carlo sample size of 2000 to yield the desired α and ß errors. Results are given for null hypothesis R₀ = 0.9 vs. an alternative hypothesis R₁ = 0.729, 0.81, 0.854 for (μ, ß) = (0.2, 0.2), (0.1, 0.2) and (0.1, 0.1). Monte Carlo verification of the boundaries, again based on a Monte Carlo sample size of 2000 runs, yielded μ and ß values consistent with Monte Carlo sampling error. The average sample size of the sequential tests result in a saving of about 40% of the values needed for the corresponding fixed sample test. Therefore we have developed and verified a useful sequential test for the reliability of systems whose failure are modeled by the 2-parameter Weibull distribution.