A component reliability test plan for a parallel system with failure rate as the exponential function of covariates

  • P N Bajeel
  • M Kumar

Abstract

Consider a parallel system with $ n $ different components. Assume that lifetime of \textit{i}-th component follows exponential distribution with parameter $ \lambda_{i}(x), \ 1\leq i \leq n $, where each $ \lambda_{i}(x), \ 1\leq i \leq n $, is distinct and depends upon k covariates such as temperature, pressure, humidity etc. through exponential relationship. Using data obtained through Type-II censoring, we derive optimal reliability test plan. In most of the reliability studies, acceptable reliability level (ARL) and unacceptable reliability level (URL) are considered as constants. We define a new strategy replacing ARL and URL, as acceptable reliability interval (ARI) and unacceptable reliability interval (URI). This will enhance the possibility of reducing the burden of rejection cost, and thereby accepting the good system (rejecting the bad system) when the estimated reliability belongs to half open intervals ARI (URI). We also use prior information available in the form of upper bounds on $ \lambda_{i}(x) $ in the design. An integer optimization problem is formulated satisfying usual probability requirements. An algorithm is developed to solve the problem. Finally, our approach is illustrated by several numerical examples.

Published
2015-05-23
Section
Articles