Comparing confidence limits for short-run process incapability index Cpp

Process incapability index C_pp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for C_pp is missing. In this paper, six bootstrap methods are applied to construct upper confidence bounds (UCBs) of C_pp for short-urn production processes where sample size is small; standard bootstrap (SB), Bayesian bootstrap (BB), bootstrap pivotal (BP), percentile bootstrap (PB), bias-corrected percentile bootstrap (BCPB), and bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods.     

Eigenvalues Estimate for the Neumann Problem of a Bounded Domain

In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete (not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric  ^g ≥−(n−1)a ², a≥0, then there exist constants A _n >0,B _n >0 only depending on the dimension, such that

The upper bound revisited

The empirical upper bound relationship for membrane separation of gases initially published in 1991 has been reviewed with the myriad of data now presently available. The upper bound correlation follows the relationship , where P_i is the permeability of the fast gas, α_ij (P_i/P_j) is the separation factor, k is referred to as the “front factor” and n is the slope of the log–log plot of the noted relationship. Below this line on a plot of log α_ij versus log P_i, virtually all the experimental data points exist. In spite of the intense investigation resulting in a much larger dataset than the original correlation, the upper bound position has had only minor shifts in position for many gas pairs. Where more significant shifts are observed, they are almost exclusively due to data now in the literature on a series of perfluorinated polymers and involve many of the gas pairs comprising He. The shift observed is primarily due to a change in the front factor, k, whereas the slope of the resultant upper bound relationship remains similar to the prior data correlations. This indicates a different solubility selectivity relationship for perfluorinated polymers compared to hydrocarbon/aromatic polymers as has been noted in the literature. Two additional upper bound relationships are included in this analysis; CO₂/N₂ and N₂/CH₄. In addition to the perfluorinated polymers resulting in significant upper bound shifts, minor shifts were observed primarily due to polymers exhibiting rigid, glassy structures including ladder-type polymers. The upper bound correlation can be used to qualitatively determine where the permeability process changes from solution-diffusion to Knudsen diffusion.     

An upper bound for the restrained domination number of a graph with minimum degree at least two in terms of order and minimum degree

Let G=(V,E) be a graph. A set S⊆V is a restrained dominating set if every vertex in V−S is adjacent to a vertex in S and to a vertex in V−S. The restrained domination number of G, denoted γ_r(G), is the smallest cardinality of a restrained dominating set of G. We will show that if G is a connected graph of order n and minimum degree δ and not isomorphic to one of nine exceptional graphs, then .     

Long-Time Behavior for Second Order Lattice Dynamical Systems

Many researchers examined the existence of global attractors for various types of first and second order lattice dynamical systems. Here we prove the existence of a global attractor for a new type of second order lattice dynamical systems in the Hilbert space l ²×l ². For specific choices of the linear operators this system can be regraded as a spatial discretization of a continuous damped nonlinear Boussinesq equation on ℝ ^m ,m≥1.      

Calculus Rules for Derivatives of Multimaps

In this paper, by virtue of two intermediate derivative-like multifunctions, which depend on an element in the intermediate space, some exact calculus rules are obtained for calculating the derivatives of the composition of two set-valued maps. Similar rules are displayed for sums. Moreover, by using these calculus rules, the solution map of a parametrized variational inequality and the variations of the feasible set of a parametrized mathematical programming problem are studied. This research was partially supported by the National Natural Science Foundation of China (Grant numbers: 10871216 and 60574073).     

Spaces of type BLO on non-homogeneous metric measure

Let (, d, μ) be a metric measure space satisfying the so-called upper doubling condition and the geometrically doubling condition. In this paper, we introduce the space RBLO(μ) and prove that it is a subset of the known space RBMO(μ) in this context. Moreover, we establish several useful characterizations for the space RBLO(μ). As an application, we obtain the boundedness of the maximal Calderón-Zygmund operators from L ^∞(μ) to RBLO(μ).     

Strain field and extrusion load in ECAE process of bi-metal circular cross section

In this paper the previous velocity field proposed by the authors for the prediction of strain field and deformation load of circular cross section billet in ECAE process has been extended to take into account the deformation behavior of bimetal circular billet in the same process. Accordingly, using Bezier method, as a robust method for determining the geometry of the streamlines, the strain field developed in the circular bimetal billet is calculated. Then, based on the kinematically admissible velocity and strain fields and using the upper bound theorem the ECAE load is predicted. It was found that at constant inner corner angle of ECAE die, with decreasing of outer curve corner the inhemogenity of strain distribution is decreased and the ECAE force is increased. Also, at a constant outer curve corner, by decreasing the inner corner angle, the extrusion load is increased. A good agreement was found between the predicted and experimental results.