Algebraic Relationship Between Symmetrical and Asymmetrical Capability Indices

There have been many investigations on the capability indices C_p, C_pk, C_pm, and C_pmk, for the common situation in which the target is the midpoint of the tolerance interval. However, only a few investigations deal with the specific case of asymmetrical tolerances. In that particular case, a number of symmetrical and asymmetrical indices are put forward, but there is no full literature treatment or synthesis showing the similarity between those indices and the common ones. We intend here, to demonstrate that the algebraic links between the indices C_p, C_pk, C_pm, and C_pmk, are similar to the ones which relate the symmetrical indices proposed in the case of asymmetrical tolerances. In that case, the algebraic structure allows us to propose asymmetrical indices families. An example based on a pharmaceutical filling operation is used to illustrate the application.     

Effect of Testing Normality on Estimating Process Capability Indices

Process capability indices are used to measure whether a manufacturing process meets the specifications. The studies of these indices are usually based on the assumption that the process follows a normal distribution. These include the indices C_p, C_pk, C_pm, and C_pmk. When the investigator is uncertain whether the process follows a normal distribution, a test of normality may be used to resolve the uncertainty. If the test accepts the null hypothesis that the process follows a normal distribution, the investigator uses C_p, C_pk, C_pm, or C_pmk. If the test rejects the null hypothesis, the investigator uses indices under non-normal distributions. Therefore the test of normality is a preliminary test that determines the form of the distribution and the index to use. In this paper we study the effect of the preliminary test of normality on the estimation of the four process capability indices mentioned above.     

Assessing Capability for Hole Location

This paper introduces a procedure for assessing the capability of a process to locate hole centers within a circular tolerance zone. By being able to calculate both a C_P and C_PK index, practitioners can compare these two metrics and determine whether process capability is lacking due to poor centering, excessive variation, or a combination of both factors.     

Bootstrap Confidence Limits for Short-Run Capability Indices

The capability indices are widely used by quality professionals as an estimate of process capability. Recently, techniques and tables were developed to construct confidence limits for each index. These techniques are based on the assumption that the underlying process is normally distributed. In industries it may not be possible to get large samples, and, hence, the normality assumption is often violated. For the short-run production processes where sample size is small, appropriate indices can be developed. In this article, the capability indices such as C_p, C_pk, and C_pm are modified, and appropriate capability indices are constructed. A further bootstrap technique is used to define the confidence intervals. A simulation using two distributions (one normal and the other nonnormal) is conducted, and a comparison is made to show the performances of the three nonparametric confidence intervals.     

Statistical Reason for the 1.5σ Shift

Ever since Motorola, Inc. introduced its Six Sigma quality initiative, quality practitioners have questioned why followers of this philosophy add a 1.5σ shift to the average before estimating process capability. Six Sigma advocates claim such an adjustment is necessary but offer only empirical studies as justification for this decision. By examining the sensitivity of control charts to detect changes of various magnitudes, this article provides a statistically based reason for including such a shift in the process average. A new capability index, called dynamic C_pk, incorporating this shift is introduced.     

Two C60O Structures and Their Relative Stabilities: AM1 Computations

C₆₀O is studied by means of the AM1 quantum-chemical method. Full geometry optimization of its C_s and C_2v structures, and harmonic vibrational analysis, are employed in the evaluation of the temperature dependence of their relative stabilities. The C_2v structure remains a minor component of the equilibrium gas-phase mixture even at high temperatures.     

Evaluating Measurement Systems and Manufacturing Processes Using Three Quality Measures

Manufacturers and suppliers use quality measures calculated from dimensional data to make informed decisions regarding measurement systems and product quality. Many manufacturers and suppliers use the precision-to-tolerance ratio—scaling the standard deviation of gage error (σ_g) by the design tolerance—to approve a measurement system. Manufacturers and suppliers also use one or more measures of process capability, such as C_p that scales the tolerance by the standard deviation of the product (σ_p), to approve a manufacturing process. A measure used to assess the ability for two parties to communicate via dimension data is the correlation in repeat measurements that we derive as a function of σ_g and σ_p. By plotting the precision-to-tolerance ratio and the correlation in repeat measurements on the σ_g and σ_p axes, acceptable and nonacceptable regions for measurement systems are defined. When we add C_p (a measure of process capability) to the mix, a relationship between the three measures suggests a method for determining an acceptable level for the correlation criterion and defines additional regions. This approach of plotting the quality measurement criteria in the σ_g and σ_p axes precisely defines the quality situation and lends to improvement suggestions.     

Highly conducting Langmuir-Blodgett films of the TMTTF-CnTCNQ system

Highly conducting Langmuir-Blodgett (LB) films of the tetramethyltetrathia-fulvalene- alkyltetracyanoquinodimethane (TMTTF-C_n TCNQ, where C_n represents C_nH_2n+1) system are reported. The electron affinities of the acceptors C_nTCNQ (n=14, 18 or 22) in solution are almost the same and lie between those of TCNQ and dimethylTCNQ. These TCNQ derivatives form solid charge transfer complexes with TMTTF. The limiting areas of the complexes, normalized to the number of TCNQ derivatives at the air-water interface, are almost the same irrespective of the donor-to-acceptor ratio and of the length of the alkyl chain, indicating that the areas are governed by the TCNQ moiety. The monolayers of TMTTF-C_n TCNQ (n=14 or 18) are transferred onto solid substrates as LB films. Polarized UV-visible absorption spectra indicate that the long axis of TCNQ is parallel to the film surface. These LB films exhibit lateral conductivities as high as 0.4 S cm^-1 and 0.1 S cm^-1 when n=14 and n=18 respectively.     

One-, Two- and Three-Dimensional Structures of C20

The aggregates C₂₀ have been studied by the AM1 quantum-chemical method and at least three different local energy minima found. The located planar cyclic ground state exhibits C_10h symmetry, being followed by two triplet linear structures, a spheroidal C₁ structure, and a bowl-shaped C_5v structure.     

The research on aggregation structure of PP materials under different condition and the influence on mechanical properties

In this article, the study of the aggregation structure of PP material with the IAS4 Image Analysis System is reported. The result indicates that the morphology of spherulite or filling particle in the matrix of crystalline polymer can be quantitatively described by the IAS4 Image Analysis System. Through the measurement of the aggregation structure, the transformation of mechanical properties was explained. With the increase of filling quantity of nucleating agent, the crystallinity (X_c) tends to increase, the spherulite size (D_n) and its distribution (C_d) tends towards decline. The different heat treatment technology influenced only the crystallinity but not the spherulite size or its distribution. The effects of X_c, D_n and C_d on mechanical properties were investigated. It was shown that, with the decrease of X_c, D_n or C_d, the notch impact strength increases. To the PP/talc composite, the aggregation of talc particle has relation with the original size of particle, filling quantity and the surface treatment level. With the decrease of particle size or uniform distribution, the notch impact strength rises up.     

Information geometry in functional spaces of classical and quantum finite statistical systems

Statistical states and bounded random variables (observables) of finite physical systems can be represented in real Banach spaces L_s¹ and L_s^∞, respectively. Since both norms are Krein-weak, the solution of the estimation problem in these spaces is not necessarily unique. The latter property occurs on the Hilbert-Schmidt space L_s² which is connected with the Onicescu information energy and the method of least squares. The square information is only an approximation of the “true” logarithmic Shannon information which induces a “logarithmic” asymmetric geometry by means of the concept of relative information (gain of information). This geometry was known in the classical case as the asymmetric Pythagorean geometry (Chentsov [10]) and is approximated by the Riemannian geometry of Fisher's information (Kullback and Leibler [45]). This paper shows that a similar geometric construction is also possible in the quantum case. The fundamental formulae of the quantum case are given (they differ in some details from the classical ones), and possible physical applications are shortly sketched.     

The influence of the stress state on the plastic zone size

“Linear elastic” fracture mechanics is based on the “plane strain” condition which means dε_zz = 0. Really stress states can occur in structures or components where dε_zz > 0. Two examples are discussed. Using the v. Mises criterion and the Sneddon equations the influence of an external stress σ^e_zz acting parallel to the crack front on the plastic zone size is calculated and demonstrated by examples.     

Generalization and evaluation of vectorial tolerances

In recent years, vectorial tolerancing has emerged as a new alternative for representing workpiece tolerances. In contrast to conventional geometric tolerances which originated from hard gauging practices, vectorial tolerancing follows the working principle of coordinate measuring machines and CAD/ CAM systems. Moreover it provides feedback from measurement directly to manufacturing process control. Many believe it is a better tolerancing method to tie design, manufacuturing, and measurement together. However, the current proposal of vectorial tolerancing has some limitations. First, the currently adopted orientation vector is not sufficient for representing true 3D orientations. As a result, the orientation of a free form surface cannot be properly established. Second, there is lacking a unified and consistent method for the evaluation of vectorial tolerances. This paper proposes a new orientation vector which provides a more general mathematical basis for representing vectorial tolerances. It enables true 3D orientation representation and relates tolerances to the functional requirement. With the improved mathematical definition, a systematic tolerance evaluation approach becomes possible for both analytical geometric elements and free-form surfaces. Computer simulations and real-world applications are studied to validate this new approach.     

Driver age, car mass and accident exposure— A synthesis of available data

The tendency of younger drivers to be more likely than older drivers to drive smaller cars has been an important consideration in a number of prior investigations of the relation between car size and traffic safety. The purpose of the present study is to quantify this effect on a firmer basis than hitherto by fitting data from seven independent sources to a unified general model. More specifically, when the exposure measures “per unit distance of travel” or “per registered car” are used in studies of car mass effects on traffic safety, the exposure information often does not contain the variable driver age. This work develops a general procedure for disaggregating such exposure data into three driver (or owner) age categories; A₁: 16–24; A₂: 25–34; and A₃: 35 years. Data from the seven sources are fined to the equation

f(i,m) = H_i[1 + G _i(m/900 − 1)]

where m is the ear mass in kg, and f(i,m) is the fraction of cars of mass m which are driven (owned) by persons in the A_i, (i = 1, 2, 3) age category. The form of this equation permits easy comparison of 900 and 1800 kg cars. Those particular masses that have been chosen for illustrative comparisons in earlier work. The seven sets of data are used to derive overall average values of the parameters H₁ and G₁. The data from all seven sources show consistent effects which are summarized in one analytical expression which is well suited for use in future studies of car size effects because it reflects a synthesis of much prior data and it permits sensitivity analyses to be performed conveniently.     

Doping and electrical characteristics of in-situ heavily B-doped Si1−x−yGexCy films epitaxially grown using ultraclean LPCVD

Doping and electrical characteristics of in-situ heavily B-doped Si_1−x−yGe_xC_y (0.22<x<0.6, 0<y<0.02) films epitaxially grown on Si(100) were investigated. The epitaxial growth was carried out at 550°C in a SiH₄–GeH₄–CH₃SiH₃–B₂H₆–H₂ gas mixture using an ultraclean hot-wall low-pressure chemical vapor deposition (LPCVD) system. It was found that the deposition rate increased with increasing GeH₄ partial pressure, and only at high GeH₄ partial pressure did it decrease with increasing B₂H₆ as well as CH₃SiH₃ partial pressures. With the B₂H₆ addition, the Ge and C fractions scarcely changed and the B concentration (C_B) increased proportionally. The C fraction increased proportionally with increasing CH₃SiH₃ partial pressures. These results can be explained by the modified Langmuir-type adsorption and reaction scheme. In B-doped Si_1−x−yGe_xC_y with y=0.0054 or below, the carrier concentration was nearly equal to C_B up to approximately 2×10²⁰ cm⁻³ and was saturated at approximately 5×10²⁰ cm⁻³, regardless of the Ge fraction. The B-doped Si_1−x−yGe_xC_y with high Ge and C fractions contained some electrically inactive B even at the lower C_B region. Resistivity measurements show that the existence of C in the film enhances alloy scattering. The discrepancy between the observed lattice constant and the calculated value at the higher Ge and C fraction suggests that the B and C atoms exist at the interstitial site more preferentially.     

Point defects and diffusion mechanisms pertinent to the Ga sublattice of GaAs

For the Ga sublattice of GaAs, the recent understanding of the impurity and self-diffusion mechanisms and the nature of the point defects responsible are discussed. Analyses of doping enhanced AlAs/GaAs superlattice disordering data and impurity diffusion data have led to the conclusion that, under thermal equilibrium and intrinsic conditions, the triply-negatively-charged Ga vacancy ((V_Ga³⁻) governs Ga self-diffusion and Al---Ga interdiffusion in As-rich crystals, while the doubly-positively-charged Ga self-interstitial (I_Ga²⁺) dominates in Ga-rich crystals. When doped sufficiently, dominates in n-type crystals, while I_Ga²⁺ dominates in p-type crystals, irrespective of the crystal composition. The V_Ga³⁻ species also contributes to the diffusion of the main donor species Si, while I_Ga²⁺ also governs the diffusion of the main acceptor species Zn and Be via the kick-out mechanism. The thermal equilibrium concentration of V_Ga³⁻ (C_VGa³⁻) has been found to exhibit a temperature independence or even a small negative temperature dependence in that, when the temperature is lowered, C_VGa³⁻; is either unchanged or even slightly increases. This C_VGa³⁻ behavior is consistent with many outstanding experimental results.     

Analysis of cracks emanating from a circular hole in [0n/90m]s laminates under various boundary conditions

This paper investigates the problem of cracks emanating from a circular hole in an orthotropic finite plate under various boundary conditions. Three types of boundary conditions, that is, stress conditions, displacement conditions and their combinations are considered. Analysis is based on stress functions satisfying the stress free conditions along the crack. The coefficients of stress functions are determined from boundary conditions by using a modified mapping-collocation method. Then, the stress intensity factors are detennined from the coefficients of stress function. Numerical calculations are performed for various finite configurations of [0_n/90_m]_s laminates. The results indicate a strong dependence of the stress intensity factor on the material orthotropy, geometry and boundary conditions.     

Systematic search for energetically favored isomers of large fullerenes C122–C130 and C162–C180

Based on the methodology by Cioslowski et al. [J. Cioslowski, N. Rao, D. Moncrieff, J. Am. Chem. Soc. 122 (2000) 8265–8270], two empirical fit equations to predict the standard enthalpy of formation are obtained over large number of calculation results at B3LYP/6-31G* theory level for fullerene isomers, which can be used as a preliminary and second-level screening tool, respectively, for large fullerenes. By applying these equations in screening the whole isolated pentagon rule (IPR) isomers, the energetically favored isomers of large fullerenes C₁₂₂–C₁₃₀ and C₁₆₂–C₁₈₀ were predicted at the B3LYP/6-31G* density functional theory level for the first time. Our results show that the lowest energy isomers of C₁₇₄ (2473259: C_3v) and C₁₈₀ (4071832: I_h) possess much lower relative energy and larger HOMO–LUMO gaps. Moreover, the ionization energy and electron affinity of the lowest energy isomers were also investigated.