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.     

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.     

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.     

Evaluating Process Capability for Geometrically Toleranced Parts: A Practical Approach

The practice of geometric tolerancing has gained in industry popularity since the 1990s. This approach has advantages over conventional tolerancing in defining both geometry and associated tolerance and, thus, generating a more realistic “acceptable design space.” There have been a number of highly mathematical treatments of the subject over the years which have not found their way into popular usage. We look at a specific example of geometric tolerancing and derive a simple approach based on the geometry of the situation and standard C_p and C_pk calculations. The study describes an approach based on understanding the limiting conditions of acceptable operation. In the example of a pin and clearance hole, we derive the limiting condition as a zero radial gap for a hole and a perfectly centered pin at maximum metal condition. We then performed a standard C_pk calculation with the limiting condition acting as the effective tolerance limit. Because we are dealing with radial gaps, we have an effective one-sided tolerance with a minimum acceptable value of 0 for the radial gaps. We tested the approach using Normally distributed simulated data and found that it provides an accurate evaluation of process capability and projected scrap levels. With minor cautions, we conclude that this methodological approach could be extrapolated to other geometrically toleranced situations.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Bromination of [60]Fullerene. II. Crystal and Molecular Structure of [60]Fullerene Bromides, C60Br6, C60Br8, and C60Br24

The crystal and molecular structures of the bromofullerene solvates C₆₀Br₆·0.5C₆H₅Cl·0.5Br₂, C₆₀Br₈·1.5(o-C₆H₄Cl₂), C₆₀Br₈·Br₂, C₆₀Br₈·0.5C₆H₅Br·0.5Br₂, and C₆₀Br₂₄·2Br₂ have been determined by single crystal X-ray diffraction. The molecular species C₆₀Br₆, C₆₀Br₈, and C₆₀Br₂₄ which have idealized C_s, C_2v , and T_h symmetries, respectively, have several different types of C-Br and C-C bonds. A comparison between different solvates of the same bromofullerenes revealed a larger stability of the packing modes for the C₆₀Br₆ and C₆₀Br₂₄ solvates, whereas the C₆₀Br₈ solvates showed different packing motifs dependent on the nature and amount of the solvent molecules.     

Low temperature UV/ozone oxidation formation of HfSiON gate dielectric

Physical and electrical properties of hafnium silicon oxynitride (HfSi_xO_yN_z) dielectric films prepared by UV ozone oxidation of hafnium silicon nitride (HfSiN) followed by annealing to 450 °C are reported. Interfacial layer growth was minimized through room temperature deposition and subsequent ultraviolet/ozone oxidation. The capacitance–voltage (C–V) and current–voltage (I–V) characteristics of the as-deposited and annealed HfSi_xO_yN_z are presented. These 4 nm thick films have a dielectric constant of 8–9 with 12 at.% Hf composition, with a leakage current density of 3×10⁻⁵ A/cm² at V_fb+1 V. The films have a breakdown field strength >10 MV/cm.     

Statistical evaluation of fatigue crack propagation properties including threshold stress intensity factor

The relationship between fatigue crack propagation rate, da/dn, and range of stress intensity factor, ΔK, including threshold stress intensity factor, ΔK_th, is analyzed statistically. A non-linear equation, da/dn = C{(ΔK)^m-(ΔK_th)^m}, is fitted to the data by regression method to evaluate the 99% confidence intervals. Several experimental results on fatigue crack propagation properties of welded joints are compared by using these confidence intervals.     

The theory of non-steady state fracture kinetics analysis—1: General theory of crack propagation

The kinetics theory of thermally activated time dependent crack propagation is extended to describe the crack size distribution in non-steady state. The distribution is represented by a series of n differential equations, each expressing the rate of crack tip concentration change over the system of n consecutive energy barriers. The general solution for the set of homogeneous linear first order differential equations developed in this report is of the form ρ_i = Σ_jc_i,je^{−λj_t + C_i}, where ρ_i is the crack tip concentration in the ith valley. The theory takes into consideration the discrete character of solids in contrast with the usual continuum models of fracture studies. The analysis is readily applicable to Regions I and II of stress corrosion cracking.     

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.     

Calculation of the ferrite volume in some dual phase steels

The relation between the γ/γ + boundary temperature, T, and the equivalent values of [Cr] and [Ni], as well as the variation of the ferrite volume, V_f, with the temperature in + γ dual-phase steels have been studied. With the aid of a computer, the regressive expressions derived from the experimental results are: T (°C) = T₃ + 21.2 [Cr] − 15.8 [Ni] + 223; V_f (%) = 0.715 exp [0.015(T − T_δ)] − exp[0.015(T_c − T_δ)] + 1.85 exp [0.0083(T − T_c]).     

The occurence of transcrystallization or row-nucleated cylindritic crystallization as a result of shearing in a glass-fiber-reinforced polypropylene

The formation and build-up of transcystalline-like superstructures produced by pulling a glass fiber (GF) from an isothermal crystallizing (T_c = 130−140°C) isotactic polypropylene (iPP) melt has been studied by thermo-optical methods. It was found that these morphological structures are caused by row-nucleation (self-nucleation), and that they should therefore be termed cylindrites instead of transcrystalline layers. The build-up of the cylindrites depends on whether the pulling and crystallization temperatures (T_pull and T_c, respectively) are above or below the upper threshold temperature of the possible β crystallization (T_β). The thermal stability and β nucleation ability of the primary row-nuclei at T_pull = T_c < T_β depend on their molecular orientation, caused by the shear stress field accommodated during pulling. In addition, the thermal stability of the row-nuclie is also affected by T_pull. It is suggested that the observed -β bifurcation at T_pull = T_c < T_β, which is the main argument for cylindritic crystallization, may be related to epitaxial growth.     

Quasicrystal films: numerical optimization as a solar selective absorber

Selective absorbers for solar thermal energy applications have to show high solar absorptance _s and low thermal emittance ε_h. Stability against oxidation and diffusion is indispensable, especially at high absorber temperatures. The new class of quasicrystalline materials seems to have favourable properties regarding stability. With a genetic algorithm a thin film stack based on dielectric and quasicrystal films was optimized as a selective absorber. A sandwich system dielectric/quasicrystal/dielectric on copper has highly selective properties: _s = 0.86 and ε_h (400 °C) = 0.051. Even better results can be achieved, at least in theory, by the use of a cermet. The optical constants of cermets with the quasicrystalline material as the metal were calculated with the Bruggeman theory. A system of a cermet film and an additional antireflective coating on copper shows _s = 0.92 and ε_h (400 °C) = 0.048.     

水热法制备锂离子二次电池用球形Li4Ti5O12负极材料及其电化学性能

以LiOH溶液和不同粒径的自制球形TiO₂为反应物, 通过水热法快速地合成了尖晶石型结构的球形Li₄Ti₅O₁₂, 并考察了材料合成的水热反应机理和电化学性能。TiO₂在100℃、5 mol/L LiOH溶液中经水热反应20 h得到前驱体, 再经800℃热处理2 h便可得到粒径大小不同(0.5~1.5 µm)且分布均匀的球形尖晶石Li₄Ti₅O₁₂材料。LiOH在水热反应条件下扩散到球形TiO₂内部, 得到在分子水平混合均匀的Li-Ti-O中间体, 利于高温下生成纯相的尖晶石Li₄Ti₅O₁₂。所得粒径大小不同的Li₄Ti₅O₁₂材料均表现出稳定的电化学循环充放电性能, 其中, 粒径为0.5 µm 的Li₄Ti₅O₁₂材料的电化学性能最好: 室温下, 以0.2 C的倍率进行充放电, 其可逆容量达到158 mAh/g, 70周后容量保持率高于99%; 同时还表现出优异的高温循环稳定性, 55℃下以0.2 C的倍率进行充放电, 50次循环后其可逆放电比容量仍能达到125 mAh/g。