c  Heldermann Verlag Economic Quality Control ISSN 0940-5151 Vol 21 (2006), No. 2, 219 – 230 Application of Arithmetic-Geometric Mean Inequality for Construction of Reliability Test Plan for Parallel Systems in the Presence of Covariates S.V. Sabnis and G. Agnihothram Abstract: 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 [1, 2, 3, 4, 5, 6], component failure rates are explicitly expressed in terms of covariates via exponential relationship. The development of this note parallels that of Yan and Mazumdar [14], 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. Keywords: Optimization, reliability. 1 Introduction Early work in the construction of component level reliability test plans for systems such as series, parallel, series systems with redundant subsystems has been done by Gal [8], Mazumdar [10, 11], Rajgopal and Mazumdar [12], Yan and Mazumdar [14], Altinel et.al [1, 2, 4]. These reliability test plans are developed under the assumption that component lifetimes have constant failure rates. Altinel et.al [3] proposed a reliability test plan in which failure rates change in dynamic fashion with respect to time. More precisely, components are assumed to have piecewise constant failure rates. A similar reliability test plan was proposed by Altinel et.al [5] for a series system with redundant subsystems. In another article, Altinel et.al [6] proposed a reliability test plan for a series system with constant failure rates that depend on the mission performed. This paper deals with the construction of component level reliability test plans for a paral- lel system with the component lifetimes being independent exponential random variables. The parameters of these exponential distributions are assumed to depend on covariates such as room temperature, pressure, humidity etc. The work presented in this paper differs from the afore-mentioned work of Altinel and others in the sense that failure rates of components of parallel system are explicitly expressed in terms of covariates via Brought to you by | Simon Fraser University Authenticated Download Date | 6/4/15 12:00 AM