Optimization of Leased Equipment Maintenance Policy Based on History Failure Data

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

The Exponential Power-Law Process for the Nonhomogeneous Poisson Process and Bathtub Data

Recently, Bar-Lev, Bshouty and Van der Duyn Schouten [Math. Methods Stat. 25 (2016) 79–980] developed a systematic method, called operator-based intensity function, for constructing huge classes of nonmonotonic intensity functions (convex or concave) for the nonhomogeneous Poisson process, all of which are suitable for modeling bathtub data. Each class is parametrized by several parameters (as scale and shape parameters) in addition to the operator index parameter [Formula: see text]. For the sake of demonstration only, we focus in this paper on a special subclass called the exponential power law process (EXPLP[Formula: see text]) whose base function is the intensity function of the power-law process. We describe various properties of such a subclass and use one of its special case, namely EXPLP[Formula: see text] intensity function, to analyze failure data which lack monotonicity. Maximum likelihood estimation of the parameters involved and relevant functions thereof is discussed with respect various aspects as existence, uniqueness, asymptotic behavior and statistical inference facets. Using two real datasets from the literature we provide evidence that the EXPLP[Formula: see text] intensity function is well suited to analyze data which exhibit a bathtub behavior.