A Bayesian Approach to Capability Testing Based on Cpk with Multiple Samples

Process capability indices provide numerical measures to compare the output of a process to client's expectations. However, most of the existing researches have used traditional distribution frequency method by using a single sample due to assess process capability. An alternative to this approach is to use the Bayesian method. In this paper, we utilize a Bayesian approach based on subsamples to check process capability via capability index C_pk. As a new suggestion, we used the informative normal prior distribution and the characteristics of sufficient statistic of the parameter to drive the posterior distribution. The capability test is done, and the posterior probability p, for which the process under investigation is capable, is derived both based on the most popular index C_pk. Finally, a numerical example is given to clarify the method. Copyright © 2013 John Wiley & Sons, Ltd.     

Paraconductivity in type-II superconductors

The additional conductivity due to the fluctuation of the order parameter in dirty type-II superconductors is reconsidered. It is shown that in a magnetic fieldH slightly above the upper critical field the electric conductivity is strongly anisotropic depending on the relative direction of the magnetic field and the electric current. In the parallel case (i.e.,H J) the conductivity diverges like(H–H _c2)^–3/2, while in the perpendicular case (H J) it diverges like(H–H _c2)^–1/2.     

History effects in low-field magnetoresistance of BPSSCO polycrystals

Low-field (H<40 G) magnetoresistance measurements have been made on Bi_1·6Pb_0·4Sr₂Ca₂Cu₃O₁₀ polycrystals at several temperatures between 80 and 105 K. Considerable hysteresis in ρ(H) is found in a zero-field-cooled sample when the applied field is increased from 0 to a maximum value and then lowered back to 0 at all temperatures. The observation of hysteresis is taken as an evidence for field trapping in the grains. We show that the hysteresis in ρ(H) occurs for applied fields much lower than that at whichdρ(H)/dH exhibits a discontinuity. In addition, we find that when the applied magnetic field (H _a) is lowered from a maximum field, the effective intergranular field,H _eff, becomes zero forH _c>0, which gives rise to a minimum in ρ(H).     

On the Nature of Spontaneous Rectangular and Square Hysteresis Loops in Ferrites

The conditions necessary for producing rectangular- and square-loop ferrites are inferred from analysis of new and earlier reported experimental data. The effect of microinhomogeneities on the properties of such ferrites is investigated. It is shown that -Fe₂O₃ inclusions, local tetragonal distortions, and linear microinhomogeneities have an adverse effect on their magnetic properties and that the high values of H _t/H _c in all rectangular-loop ferrites are due to aggregated microinhomogeneities containing increased concentrations of cation vacancies compared to the host material. The origin of such inhomogeneities is discussed.     

Fluctuation-induced diamagnetism in type II superconductors above H c2

The fluctuation-induced diamagnetism in strong magnetic fields in type II superconductors is studied theoretically. It is shown that the fluctuation-induced diamagnetism at low temperatures (i.e., TT _c0) is described in terms of a universal function of [B \s- H _c2(T)]/H_s(T) for both dirty and pure superconductors, where H _s(T), the scaling field, is proportional to (T/T _c0)H_c2(0).Work supported by the National Science Foundation under Grant DMR 76-21032.     

Fuel ignition and flame front stabilization in supersonic flow using electric discharge

Recent achievements in the field of stabilization of the front of high speed combustion using electric discharge are presented. Near-surface discharge at the plane wall between electrodes installed in the plane of the wall is applied in this study. Hydrogen and ethylene directly injected from the wall to the flow with a Mach number M = 2 and an air total temperature T ₀ = 300–760 K are used as fuel. The excess fuel coefficient calculated by the total air flow rate in the channel does not exceed ER = 0.1. The value of electric power input into the discharge is W _pl/H _tot < 2% of the total flow enthalpy, while the thermal power due to combustion exceeds W _com/H _tot > 100% at a low initial gas temperature. Electric discharge is first applied to stabilize combustion under conditions of a fixed separated zone and on the plane wall of the combustion chamber. A two-stage combustion regime is demonstrated. It is shown that the application of electric discharge makes it possible to achieve complete fuel combustion η > 0.9 in a wide range of experimental parameters.     

Control of Carrier Distribution for Tailoring Superconducting Properties of Layered Cuprates

A general view has been developed to correlate spatial inhomogeneity in the carrier density over different dimensions in crystals of high-T _c cuprate superconductors to basic superconducting properties such as T _c , H _irr and peak effect. Employing the BVS concept, it is shown that there are three different routes for doping the CuO ₂ plane with holes, and that the more confined holes are in the middle of the CuO ₂ -plane stack, the higher is T _c . With the Cu(Ba,Sr) ₂ (Yb,Ca)Cu ₂ O _6+z system it is shown that the distribution of holes is different when holes are generated with different doping routes, and further that the more homogeneous the hole distribution along the c axis is, the better is the H _irr characteristics. This agrees with observations made for Hg-1223 and Cu-1223 that the more overdoped these phases are, the more improved is the H _irr characteristics. Studies on peak effect in various high-T _c superconductors indicate that some mesoscopical inhomogeneity in oxygen content or hole density causes the peak. Thus control of hole density over dimensions from atomic bonds to tens of nanometers is essential in tailoring the fundamental superconducting properties.     

Influence of magnetic breakdown on low-frequency conductivity and weak damping electromagnetic waves in metals

Low-frequency electroconductivity under magnetic breakdown conditions is investigated in the two qualitatively different situations: (a) coherent and (b) stochastic. In the former situation (a) the consideration is fulfilled in terms of the incidental magnetic breakdown spectrum of electrons. In the latter situation (b) it is fulfilled in terms of discrete random walking of classical electron. In these cases the general expressions of the conductivity tensor under conditions of both strong and weak spatial dispersion are derived. It is shown that magnetic breakdown does not violate the conditions of compensation of the volumes of electrons and holes in the case of closed trajectories. In the coherent situation the magnetic breakdown has the most essential influence upon Landau adsorption which is determined by a macroscopic layer of valuesP _z (projection of the momentum of the electrons on the direction of the magnetic field). In the stochastic case it is shown that magnetic breakdown results in the appearance of peculiar ergodic states in which an electron is spread on all bands (which take part in the breakdown) with equal probability. Together with it the probability of breakdown disappears from the low-frequency conductivity in a wide interval of magnetic fields and the conductivity is expressed in terms of the classical motion along an united compound orbit. The results of both coherent and stochastic calculations are used to investigate the weak damping electromagnetic waves. It is shown that the magnetic breakdown essentially changes only the dependence of the helicon damping on the magnetic fieldH. In many situations the dependence is represented by nonmonotonic functions ofH. In the coherent and stochastic cases these functions are qualitatively different.     

Estimating a transformation and its effect on Box-CoxT-ratio

This article concernsi) the stochastic behavior of the Box-Cox transformation estimator andii) the effect of estimating a transformation on the Box-CoxT-ratio used for the post-transformation analysis. It is shown that the transformation estimator depends on three factors: the model structure, the mean-spread and the error standard deviation σ₀. In general, a structured model is able to estimate the transformation very well; an unstructured model can do well also unless the mean-spread and σ₀ are both small; and a one-mean mode can give a poor-estimate if σ₀ is small. When the sample is not large, it is shown that the unconditional effect of estimating a transformation on the Box-CoxT-ratio is generally small, and the “conditional” effect is also negligible in most of the situations except the case of one-way ANOVA with small σ₀. Extensive Monte Carlo simulations are performed to support the theoretical findings.     

Cationic conduction and diffusion and the compensation law

It is shown that measurements of ionic conductivity or diffusion made in the region intermediate between the intrinsic and extrinsic ranges closely obey the compensation law logD ₀ =a + bH _d, whereD ₀ is the pre-exponential term in the equation for the diffusion coefficient, H _d is the experimentally determined activation enthalpy, anda andb are constants. It is further shown that such measurements can allow determination of defect formation energies. A procedure for analysing results in the intermediate region is proposed and tested for ion conduction by Li⁺ in LiF. Data for oxides are presented to show semi-quantitative agreement with the procedure.