An age model is proposed for modelling imperfect repairable systems operating under a non-homogeneous Poisson framework. The imperfect repair model investigated here effectively includes good-as-new, imperfect repair and bad-as-old regimes that have appeared separately in reliability engineering literature. To incorporate the impact of the equipment's operating environment, proportional intensities assumptions are integrated into the age model. Maximum likeihood estimates are derived for the parameters of interest.

Statistical analysis of an age model for imperfectly repaired systems

Trend analysis of the power law process using Expectation–Maximization algorithm for data censored by inspection intervals

For decades, reliability engineering techniques have been successfully applied in many industries to improve the performance of equipment maintenance management. Numerous inspection and optimization models are developed and widely used to achieve maintenance excellence, i.e. the balance of performance, risk, resources and cost to reach to an optimal solution. However, the application of all these techniques and models to medical devices is new. Hospitals, due to possessing a large number of difference devices, can benefit significantly if the optimization techniques are used properly in the equipment management processes. Most research in the area of reliability engineering for medical equipment mainly considers the devices in their design or manufacturing stage and suggests some techniques to improve the reliability. To this point, best maintenance strategies for medical equipment in their operating context have not been considered. We aim to address this gap and propose methods to improve current maintenance strategies in the healthcare industry. More specifically, we first identify or propose the criteria

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Reliability and Maintenance of Medical Devices

Simulating nonhomogeneous poisson processes with proportional intensities

https://www.isid.ac.in/~statmath/2004/isid200423.pdf

Likelihood ratio tests for and against ordering of the cumulative incidence functions in multiple competing risks and discrete mark variable models

Tests are considered for the hypothesis of a constant intensity against the alternative of an intensity which increases with time in a nonhomogeneous Poisson process. Attention is focused on step-function alternatives and tests designed for such alternatives. One application is testing for abrupt changes in equipment following scheduled overhauls. The authors recommend the order-restricted likelihood-ratio test over an ordered chi-square test for such situations, provided the points at which jumps can occur are known. Otherwise, they recommend the test based on the Laplace statistic. The performance of these tests is evaluated for smooth alternatives, with the result that the smallest relative power of the order-restricted likelihood-ratio test is 73%, while for the Laplace test it is 82%. A numerical example based on failure times for a main-propulsion diesel engine is presented. The result is that the order-restricted likelihood-ratio test corresponds to the lowest statistical significance level. >

Tests for positive jumps in the intensity of a Poisson process: a power study

The likelihood-ratio test statistic for testing homogeneity of exponential means with an ordered alternative has a rather complex null distribution. Expressions for the mean and variance of its null distribution are derived, and the accuracy of a two-moment chi-squared approximation is studied. The coefficients needed to implement the approximation are tabled. The application of these results in testing for a constant versus a nondecreasing intensity in a nonhomogeneous Poisson process is also discussed.



La statistique du rapport de vraisemblance pour tester l'egalite des moyennes de lois exponentielles, contre une hypothese d'ordre, suit une loi plutot compliquee sous l'hypothese nulle. On trouve des expressions pour la moyenne et la variance de cette loi et on etudie la precision d'une approximation de celle-ci par une loi du chi-deux. On donne le tableau des coefficients necessaires pour calculer l'approximation. On discute aussi comment on peut utiliser ces resultats pour tester si l'intensite d'un processus de Poisson non-homogene est constante ou non-decroissante.

Testing for a trend in exponential means: A two-moment approximation to the null distribution of the likelihood-ratio statistic*

Testing for monotonicity in the intensity of a nonhomogeneous Poisson process

/pdf/the-impact-of-comprehensive-institutional-assessment-on-2r07cpi8oa.pdf

The Impact of Comprehensive Institutional Assessment on Faculty

Hollander and Proschan (1974) studied nonhomogeneous Poisson processes as models for systems subject to overhauls. They did not postulate a functional form for the intensity, but showed that certain basic assumptions about the deterioration of the system implied that the mean function is superadditive. They studied tests of the null hypothesis that the intensity is constant with the alternative restricted to superadditive mean functions. For estimation purposes, the class of superadditive mean functions is too broad. We assume that the intensity is nondecreasing between overhauls and that at an overhaul it does not fall below its average prior to the overhaul. These two assumptions imply that the mean function is star-shaped. We obtain the restricted maximum-likelihood estimates under these two assumptions and under the star-shaped restriction. The two estimates are compared on a data set.

James M. Guffey

Papers

Tests for positive jumps in the intensity of a Poisson process: a power study

Testing for a trend in exponential means: A two-moment approximation to the null distribution of the likelihood-ratio statistic*

Testing for monotonicity in the intensity of a nonhomogeneous Poisson process

The Impact of Comprehensive Institutional Assessment on Faculty

Nonhomogeneous poisson processes as overhaul models