Given a stochastic process Xt, t b T CR, and s ~ R, then a) iff b): a) For every probability measure p on there is a stopping time T for Xt with law L(T) = p: b) If At is the smallest a-algebra for which Xu are measurable for all u ~ t, then P restricted to At is nonatomic for all t > s. This note began with a question of G. Shiryaev, connected with the following example. Let Wt be a standard W...

A fundamental problem in statistics is to develop models based on a sample of observations and drawing inferences using the model so developed. In growth modeling, data are usually collected over time. One characteristic of such data is that the successive observations are dependent. Each observation of the observed data series Yt may be considered as a realization of a stochastic process {Yt},...

We establish weak convergence of partial sums of tempered fractional time series (TFTS) to a stochastic process which we call a tempered Gaussian Hermite process (TGHP). We also introduce the Wiener integral with respect to TGHP, and establish weak convergence of weighted sums of TFTS to this Wiener integral.

This paper presents a method to find the optimal production, repair/replacement and preventive maintenance policies for a degraded manufacturing system. The system is subject to random machine failures and repairs. The status of the system is deemed to degrade with repair activities. When a failure occurs, the machine is either repaired or replaced, and a replacement action renews the machine, ...

Apart from important but particular cases, such as state-dependent exponential distributions, for example, [1, 4] or an arbitrary repair time distribution [12], the reliability analysis of multiple cold standby systems is far from complete. We present a general reliability analysis of a basic multiple cold standby system attended by a single repairman, henceforth called a K-system. The K-system...

abstract background: renal insufficiency is a potential complication after infrarenal abdominal aortic aneurysm repair and is a significant risk factor for postoperative mortality and morbidity. the aim of this study was to analyze the effect of this risk factor, before and during operation. methods: in this prospective study, between 2003 and 2006, 45 patients underwent repair of an infrarenal...

This paper presents a method of fault prognostics and reliability estimation for DC motor using time series modeling procedure based on DC motor performance degradation data. DC motor performance degradation data are treated as a time series data and stochastic process are utilized to describe the degradation process for predicting long-term trend. A degradation test is processed for DC motor u...

This article presents an analytical continuous-time Markov chain approach to model a repair system with rotable components for resource allocation. As an important type of repair service system, this repair system with rotable components demonstrated that rotable components can be repaired to an as-new condition and then assembled circularly with rotable-component inventories after a piece of e...

The chloride corrosion of reinforcing steel in reinforced concrete (RC) structures is a significant reason for premature deterioration and failure of RC structures in aggressive environments such as Persian Gulf region. This is one of the most important sources of engineering and economic problems in developed countries. So, the repair and maintenance of RC structures exposed to corrosive envir...