Application of Arithmetic-Geometric Mean Inequality for Construction of Reliability Test Plan for Parallel Systems in the Presence of Covariates

Most of the component level reliability test plans that are available in literature have been developed for series and parallel systems under the assumption that components have constant failure rates. Here an attempt is made to construct a test plan for a parallel system with the failure rates of the corresponding exponential distributions depending upon covariates such as room temperature, pressure etc. In this note, unlike in the works of Altinel and others [Computational Statistics & Data Analysis 14: 281-292, 1992, European Journal of Operational Research 78: 318-333, 1994, Naval Research Logistics 44: 187-197, 1997, European Journal of Operational Research 111: 175-186, 1998, IIE Transactions 33: 1093-1108, 2001, Reliability Engineering and System Safety 78: 33-43, 2002], component failure rates are explicitly expressed in terms of covariates via exponential relationship. The development of this note parallels that of Yan and Mazumdar [IEEE Transactions on Reliability 36: 419-424, 1987], except that it involves the use of Arithmetic-Geometric Mean inequality. The obtained numerical results highlight the importance of this note by distinctly showing economic advantages in using covariates related information.