Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products' lifetime distribution

A dynamic auto-adaptive predictive maintenance policy for degradation with unknown parameters

International audienceWith the development of monitoring equipment, research on condition-based maintenance (CBM) is rapidly growing. CBM optimization aims to find an optimal CBM policy which minimizes the average cost of the system over a specified duration of time. This paper proposes a dynamic auto-adaptive predictive maintenance policy for single-unit systems whose gradual deterioration is governed by an increasing stochastic process. The parameters of the degradation process are assumed to be unknown and Bayes' theorem is used to update the prior information. The time interval between two successive inspections is scheduled based on the remaining useful life (RUL) of the system and is updated along with the degradation parameters. A procedure is proposed to dynamically adapt the maintenance decision variables accordingly. Finally, different possible maintenance policies are considered and compared to illustrate their performance

ON THE AVERAGE NUMBER OF SHARP CROSSINGS OF CERTAIN GAUSSIAN RANDOM POLYNOMIALS Communicated by Fraydoun Rezakhanlou

Abstract. Let Qn(x) = n i=0 Aix i be a random algebraic polynomial where the coefficients A0, A1, · · · form a sequence of centered Gaussian random variables. Moreover, assume that the increments ∆j = Aj − Aj−1, j = 0, 1, 2, · · · , are independent, assuming A−1 = 0. The coefficients can be considered as n consecutive observations of a Brownian motion. We obtain the asymptotic behaviour of the expected number of u-sharp crossings, u > 0, of polynomial Qn(x). We refer to u-sharp crossings as those zero upcrossings with slope greater than u, or those down-crossings with slope smaller than −u. We consider the cases where u is unbounded and increasing with n, say u = o(n 5/4 ), and u = o(n 3/2 )

Fluid biomarkers in cerebral amyloid angiopathy

Cerebral amyloid angiopathy (CAA) is a type of cerebrovascular disorder characterised by the accumulation of amyloid within the leptomeninges and small/medium-sized cerebral blood vessels. Typically, cerebral haemorrhages are one of the first clinical manifestations of CAA, posing a considerable challenge to the timely diagnosis of CAA as the bleedings only occur during the later disease stages. Fluid biomarkers may change prior to imaging biomarkers, and therefore, they could be the future of CAA diagnosis. Additionally, they can be used as primary outcome markers in prospective clinical trials. Among fluid biomarkers, blood-based biomarkers offer a distinct advantage over cerebrospinal fluid biomarkers as they do not require a procedure as invasive as a lumbar puncture. This article aimed to provide an overview of the present clinical data concerning fluid biomarkers associated with CAA and point out the direction of future studies. Among all the biomarkers discussed, amyloid β, neurofilament light chain, matrix metalloproteinases, complement 3, uric acid, and lactadherin demonstrated the most promising evidence. However, the field of fluid biomarkers for CAA is an under-researched area, and in most cases, there are only one or two studies on each of the biomarkers mentioned in this review. Additionally, a small sample size is a common limitation of the discussed studies. Hence, it is hard to reach a solid conclusion on the clinical significance of each biomarker at different stages of the disease or in various subpopulations of CAA. In order to overcome this issue, larger longitudinal and multicentered studies are needed.</p