A preventive maintenance policy for a continuously monitored system with correlated wear indicators

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Lévy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive maintenance policy is proposed, which involves a delayed replacement, triggered by the reaching of some preventive zone for the system deterioration level. The preventive maintenance policy is assessed through a cost function on an infinite horizon time. The cost function is provided in full form, and tools are provided for its numerical computation. The influence of different parameters on the cost function is studied, both from a theoretical and/or numerical point of view.     

Modeling past-dependent partial repairs for condition-based maintenance of continuously deteriorating systems

We are interested in the stochastic modeling of a condition-based maintained system subject to continuous deterioration and maintenance actions such as inspection, partial repair and replacement. The partial repair is assumed dependent on the past in the sense that it cannot bring the system back into a deterioration state better than the one reached at the last repair. Such a past-dependency can affect (i) the selection of a type of maintenance actions, (ii) the maintenance duration, (iii) the deterioration level after a maintenance, and (iv) the restarting system deterioration behavior. In this paper, all these effects are jointly considered in an unifying condition-based maintenance model on the basis of restarting deterioration states randomly sampled from a probability distribution truncated by the deterioration levels just before a current repair and just after the last repair/replacement. Using results from the semi-regenerative theory, the long-run maintenance cost rate is analytically derived. Numerous sensitivity studies illustrate the impacts of past-dependent partial repairs on the economic performance of the considered condition-based maintained system.     

Optimal inspection policy for three-state systems monitored by control charts

This paper presents the formulations of the expected long-run cost per time unit for a system monitored by a static control chart and by an adaptive control chart respectively. The static chart has a fixed sampling interval and a fixed sample size. The adaptive chart has a fixed sample size but variable sampling intervals. The system is supposed to have three states, normal working state, failure delay time state, and failed state. Two levels of repair are used to maintain the system. A minor repair is used to restore the system if a detectable defect is confirmed by an inspection. A major repair will be performed if the system fails. The expected cost per time unit for maintaining such a system is obtained. The objective of such analysis is to find an optimal sampling policy for the inspection process. An artificially generated data example and a real data example are used to compare the expected cost per time unit for both the static and adaptive control charts.     

Weakly continuously Urysohn spaces

We study weakly continuously Urysohn spaces, which were introduced in [P.L. Zenor, Continuously extending partial functions, Proc. Amer. Math. Soc. 135 (1) (2007) 305-312]. We show that every weakly continuously Urysohn wΔ-space has a base of countable order, that separable weakly continuously Urysohn spaces are submetrizable, hence continuously Urysohn, that monotonically normal weakly continuously Urysohn spaces are hereditarily paracompact, and that no linear extension of any uncountable subspace of the Sorgenfrey line is weakly continuously Urysohn. These results generalize various results in the literature concerning continuously Urysohn spaces.     

Finely continuously differentiable functions

This paper establishes an explicit characterization of those real-valued functions on a finely open set in Euclidean space which are continuously differentiable with respect to the fine topology of classical potential theory. It improves and extends previous work of several authors. Differentiability of all orders is considered, and some consequences of the characterization are deduced.     

Finely continuously differentiable functions

In Lávi?ka [A remark on fine differentiability, Adv. Appl. Clifford Algebras 17 (2007) 549–554], it is observed that finely continuously differentiable functions on finely open subsets of the plane are just functions which are finely locally extendable to usual continuously differentiable functions on the whole plane. In this note, it is proved that, under a mild additional assumption, this result remains true even in higher dimensions. Here the word “fine” refers to the fine topology of classical potential theory.     

Twice continuously differentiable S-splines

Twice continuously differentiable S-splines consisting of fifth degree polynomials are constructed, uniqueness and existence theorems are proved, stability conditions are established for such splines. The first three coefficients of each polynomial are determined by conditions of smooth gluing, the others are determined by the least squares method. This provides the ability to smooth initial data. The peculiarity of these splines is their semilocal property, i.e., each polynomial implicitly depends on function values determining previous polynomials and does not depend on values determining subsequent polynomials. It turns out that in this case the stability conditions are fulfilled under some very strong restrictions. Under there conditions and other ones ensuring sufficient closeness of the first polynomial and its derivatives to values of the function and its derivatives it is proved that this closeness is retained on the whole given interval.     

On continuously irreducible continua

We study continuously irreducible continua and characterize them as those continua of type λ for which the set function T is continuous. Using results by Mohler and Oversteegen, we present a new family of one-dimensional continua for which the set function T is continuous and no element of the family contains a pseudo-arc. We study the hyperspaces of these continua.     

Locally continuously perfect groups of homeomorphisms

The notion of a locally continuously perfect group is introduced and studied. This notion generalizes locally smoothly perfect groups introduced by Haller and Teichmann. Next, we prove that the path connected identity component of the group of all homeomorphisms of a manifold is locally continuously perfect. The case of equivariant homeomorphism group and other examples are also considered.     

Fields with continuously distributed mass

We describe local field theories with continuously distributed mass. Such models can be realized as models in d > 4 space-time with Poincaré invariance only in four-dimensional space-time. We discuss some possible phenomenological consequences. Namely, we show that the Higgs boson phenomenology in the Standard Model extension with continuously distributed Higgs boson mass can differ in a drastic way from the standard Higgs boson phenomenology that makes the Higgs boson discovery at the Large Hadron Collider (LHC) an extremely difficult task. We also study the LHC discovery potential for Z′ models with continuously distributed mass for √2 = 7, 10 and 14 TeV center-of-mass energies. One of possible LHC signatures for such models is the existence of a broad resonance structure in the Drell-Yan reaction pp → Z′ + … → l ⁺ l ⁻ + ….     

More on continuously Urysohn spaces

We study the properties of weakly continuously Urysohn and continuously Urysohn spaces. We show that being a (weakly) continuously Urysohn space is not a multiplicative property, and that this property is not preserved under perfect maps. However, being a weakly continuously Urysohn space is preserved under perfect open maps. By using the scattering process, we show that the class of protometrizable spaces is also contained in the class of continuously Urysohn space. We also give a characterization of the continuously Urysohn property for well-ordered spaces, and prove that a paracompact locally continuously Urysohn ordered space is continuously Urysohn.     

Twice continuously differentiable semilocal smoothing spline

Twice continuously differentiable periodic local and semilocal smoothing splines, or S-splines from the class C ² are considered. These splines consist of polynomials of 5th degree, first three coefficients of each polynomial are determined by values of the previous polynomial and two its derivatives at the point of splice, coefficients at higher terms of the polynomial are determined by the least squares method. These conditions are supplemented by the periodicity condition for the spline function on the whole segment of definition or by initial conditions. Uniqueness and existence theorems are proved. Stability and convergence conditions for these splines are established.     

Filling an area discretely and continuously

The literature dealing with student understanding of integration in general and the Fundamental Theorem of Calculus in particular suggests that although students can integrate properly, they understand little about the process that leads to the definite integral. The definite integral is naturally connected to the antiderivative, the area under the curve and the limit of Riemann sums; these three conceptualizations of the definite integral are useful in different contexts and provide students with what it takes to interpret the definite integrals. Research shows that students rarely invoke the multiplicatively-based summation conception of the definite integral although it is essential for evaluating line integrals, surface integrals and volumes. This paper describes a teaching module that promotes understanding as well as activating all three conceptualizations of the definite integral through motivating the accumulation area function and the results in the Fundamental Theorems of Calculus.     

Green's functions for continuously supported plates

The Green's functions for an infinite elastic plate, attached respectively to a Pasternak or a Kerr base model, and subjected to a concentrated force, are obtained in terms of Bessel functions. It is shown, that for each base model, depending on the plate and base parameters, the solutions may be of different form. The method of images is then utilized to generate closed form solutions for the semi-infinite and quarter plates with simply supported boundaries. Paper also presents a generalization of Bessel functions of the Kelvin type and a discussion of their properties. They were needed for the solution of some of the equations under consideration.Research supported by National Science Foundation Grant MSM-8308919.     

Bayesian modeling of continuously marked spatial point patterns

Many analyses of continuously marked spatial point patterns assume that the density of points, with differing marks, is identical. However, as noted in the seminal paper of Goulard et al. (Scand J Stat 23:365–379, 1996), such an assumption is not realistic in many situations. For example, a stand of forest may have many more small trees than large, hence the model should allow for a higher density of points with small marks. In addition, as suggested by Ogata and Tanemura (Biometrics 41:421–433, 1985), the interaction between points should be a function of their mark, allowing, for example, the range of interaction for large trees to exceed that of smaller trees. The aforementioned articles use frequentist inferential techniques, but interval estimation presents difficulties due to the extremely complex distributional properties of the estimates; it might be possible, however, to use parametric bootstrap methodology for such inferences (Baddeley et al. in J Roy Stat Soc Ser B 67:617–666, 2005). We suggest the use of Bayesian inferential techniques. Although a Bayesian approach requires a complex, computational implementation of (reversible jump) Markov Chain Monte Carlo methodology, it enables a wide variety of inferences (including interval estimation). We demonstrate our approach by analyzing the well known Norway spruce dataset.     

Cube formulas on spaces of continuously differentiable functions

Siberian Mathematical Journal -