Reliability Test Plans for Series Systems in the Presence of Covariates

Abstract With the motivation of developing more realistic test plans, an attempt is made in this paper to construct reliability test plans for the components of series systems under the assumptions that the component lifetimes are independent, identically distributed exponential random variables, the failure rates of these exponential random variables depend on covariates, such as room temperature, humidity etc. through linear and exponential relationships. Our test plans differ from the test plans proposed by Altinel and Özekici (1997) and Alitnel et al. (IIE Transactions 33: 1093-1108, 2001, Reliability Engineering and System Safety 78: 33-43, 2002) in the sense that the former assume dependence on covariates through explicit relationships, while the latter make a very general assumption concerning dependence on covariates. It should be noted that as far as the construction of reliability test plans on component level is concerned, this is the first instance of the use of the penalty function methodology. It should also be highlighted that the numerical results given in this paper illustrate that the use of covariates-related information in the linear case leads to more than 90% savings in total testing cost.