Unbiased estimates of the Weibull parameters by the linear regression method

For sample sizes from 5 to 100, the bias of the scale parameter was investigated for probability estimators, P = (i − a)/(n + b), which yield unbiased estimates of the shape parameter. A class of unbiased estimators for both the shape and scale parameters was developed for each sample size. In addition, the percentage points of the distribution of unbiased estimate of the shape parameter were determined for all sample sizes. The distribution of the scale parameter was found to be normal by using the Anderson-Darling goodness-of-fit test. How the results can be used to establish confidence intervals on both the shape and scale parameters are demonstrated in the paper.     

Steady‐state ARL analysis of ARL‐unbiased EWMA‐RZ control chart monitoring the ratio of two normal variables

Very recently, control charts for monitoring the ratio of 2 normal variables have been investigated in statistical process control. In the two‐sided case, however, these control charts tend to be average run length (ARL) biased, in the sense that some out‐of‐control ARL values are larger than the in‐control ARL. This paper proposes an ARL‐unbiased EWMA control chart for monitoring of this kind of ratio with each subgroup consisting of n?1 sample units. Also, to study the long‐term properties of ARL‐unbiased EWMA‐RZ control chart, we investigate the steady‐state ARL. Several tables and figures are given to show the statistical properties of the proposed control charts. The comparison results show that the proposed ARL‐unbiased chart outperforms other two‐sided control charts in terms of the zero‐state and steady‐state ARL. An example illustrates the use of this chart on a real quality control problem from the food industry.     

Goodness-of-fit testing for accident models with low means

The modeling of relationships between motor vehicle crashes and underlying factors has been investigated for more than three decades. Recently, many highway safety studies have documented the use of negative binomial (NB) regression models. On rare occasions, the Poisson model may be the only alternative especially when crash sample mean is low. Pearson's X² and the scaled deviance (G²) are two common test statistics that have been proposed as measures of goodness-of-fit (GOF) for Poisson or NB models. Unfortunately, transportation safety analysts often deal with crash data that are characterized by low sample mean values. Under such conditions, the traditional test statistics may not perform very well.     

Transferring biological sequence analysis tools to break-point detection for on-line monitoring: A control chart based on the local score

The Lindley process defined for the queuing file domain is equivalent to the cumulative sum (CUSUM) process used for break-point detection in process control. The maximum of the Lindley process, called local score, is used to highlight atypical regions in biological sequences, and its distribution has been established by different manners. I propose here to use the local score and also a partial maximum of the Lindley process over the immediate past to create control charts. Stopping time corresponds to the first time where the statistic achieves a statistical significance less than a given threshold α in ]0,1[, the instantaneous first error rate. The local score p value is computed using existing theoretical results. I establish here the exact distribution of the partial maximum of the Lindley process. Performance of the control charts is evaluated by Monte Carlo estimation of the average run lengths for an in-control process (ARL₀) and for an out-of-control process (ARL₁). I also use the standard deviation of the run length (SdRL) and the extra quadratic loss (EQL). Comparison with the usual and recent control charts present in the literature shows that the local score control chart outperforms the others with a much larger ARL₀ and ARL₁ smaller or of the same order. Many interesting openings exist for the local score chart: not only Gaussian model but also any of them, Markovian dependance of the data, both location and dispersion monitoring at the same time can be considered.     

A methyl parathion electrochemical sensor based on Nano-TiO2, graphene composite film modified electrode

A methyl parathion electrochemical sensor based on nano-TiO₂ and graphene composite film modified glassy carbon electrode has been developed. The electrochemical behavior of MP at the sensor was investigated by cyclic voltammetry and linear sweep voltammetry. Scanning electron microscopy was used to characterize the surface morphology of nano-TiO₂ and graphene composite film. Compared with a bare glassy carbon electrode or a mono-film modified electrode, the redox peak currents of methyl parathion on the composite film modified electrode improved greatly, indicating that the sensor showed good catalytic effects. The optimal experimental condition was obtained. The results indicated that the linear sweep voltammetry responses of methyl parathion, in pH 5.2 acetate buffer solution with open-circuit accumulation for 2 min, were linear with concentrations of methyl parathion in two ranges of 0.002～5 μM and 5～100 μM. The linear equations were i_Pc(μA) = 0.0136 + 4.965c_MP(μM) (R₁² = 0.9911) and i_Pc(μA) = 21.87 + 0.8206c_MP(μM) (R₂² = 0.9914), respectively. The detection limit was 1.0 nM (S/N = 3). The sensor exhibited high sensitivity and good reproducibility as well as certain anti-interference ability. It was applied to the determination of residual MP in fresh apple sample with the recovery of 92%～102%. The result was satisfactory.     

Refractivity virial coefficients and P, ρ, T data of ethylene

Virial coefficients for gaseous ethylene have been determined in the temperature range 283.15 to 373.15 K by means of a new refractive index P, , T method. Measurements of the pressure and temperature dependence of the refractive index n and the density and temperature dependence of (n — ****- 1) ^–1 were carried out by two coupled grating interferometers. From these interferometric measurements, we determined the refractivity virial coefficients A _R, B _R, and C_R of the Lorentz-Lorenz expansion, P, , T data, and the second and third virial coefficients B(T) and C(T) of the Leiden expansion. The deduced coefficients B(T) and C(T) are in excellent agreement with the accurate literature values.Paper presented at the Tenth Symposium on Thermophysical Properties, June 20–23, 1988, Gaithersburg, Maryland, U.S.A.     

Developing a model‐based sampling plan

Statistical process modeling is widely used in industry for forecasting the production outcomes, for process control and for process optimization. Applying a prediction model in a production process allows the user to calibrate/predict the mean of the distribution of the process outcomes and to partition the overall variation in the distribution of the process outcomes into explained (by the model) and unexplained (residuals) variations; thus, reducing the unexplained variability. The additional information about the process behavior can be used prior to the sampling procedure and may help to reduce the required sample size to classify a lot. This research focuses on the development of a model‐based sampling plan based ontextitCpk (process capability index). It is an extension of a multistage acceptance sampling plan also based on Cpk (Negrin et al., Quality Engineering 2009; 21 :306–318; Quality and Reliability Engineering International 2011; 27 :3–14). The advantage of this sampling plan is that the sample size needed depends directly and quantitatively on the quality of the process (Cpk), whereas other sampling plans such as MIL‐STD‐414 (Sampling Procedures and Tables for Inspection by Variables for Percent Defective, Department of Defense, Washington, DC, 1957.) use only qualitative measures. The objective of this paper is to further refine the needed sample size by using a predictive model for the lot's expectation. We developed model‐based sample size formulae which depend directly on the quality of the prediction model (as measured by R²) and adjust the ‘not model‐based’ multistage sampling plan developed in Negrin et al. (Quality Engineering 2009; 21 :306–318; Quality and Reliability Engineering International 2011; 27 :3–14) accordingly. A simulation study was conducted to compare between the model‐based and the ‘not model‐based’ sampling plans. It is found that when R² = 0, the model‐based and ‘not model‐based’ sampling plans require the same sample sizes in order to classify the lots. However, as R² becomes larger, the sample size required by the model‐based sampling plan becomes smaller than the one required by the ‘not model‐based’ sampling plan. In addition, it is found that the reduction of the sample size achieved by the model‐based sampling plan becomes more significant as Cpk tends to 1 and can be achieved without increasing the proportion of the classification errors. Finally, the suggested sampling plan was applied with areal data set from a chemicals manufacturing process for illustration. Copyright © 2011 John Wiley & Sons, Ltd.     

Densification of (Na,K)NbO<Subscript>3</Subscript> piezoelectric ceramics by two-step mixing process

Lead-free Na_0.5K_0.5NbO₃ (NKN) piezoelectric ceramics were sintered with a new process, “two-step mixing process,” in which a part of alkali source powders was initially preserved and mixed with the rest matrix powders after the calcinations step. As a result, the sintering of NKN ceramics was improved, and the sample sintered at 1082 °C with the initial preservation ratio (R _A) of 5% demonstrated the highest density of ρ = 4.38 g/cm³ (97.1% of the theoretical density), compared with ρ = 4.36 g/cm³ (96.7% of the theoretical density) for the non-preservation specimen (R _A = 0%). The former sample showed the best piezoelectric constant of d ₃₃ = 125 pC/N and electromechanical coupling coefficient of k _p = 0.42, while the latter sample had d ₃₃ = 116 pC/N and k _p = 0.37. These results indicated that the two-step mixing process was effective for the sintering of lead-free NKN ceramics, despite no sintering additive and cold isostatic pressing were used.     

Books Received

Regression models of the forms proposed by Scheffé and by Becker have been widely and usefully applied to describe the response surfaces of mixture systems. These models do not contain a constant term. It has been common practice to test the statistical significance of these mixture models by the same statistical procedures used for other regression models whose constant term is absent (e.g., because the regression must pass through the origin). In this paper we show that the common practice produces misleading reslllts for mixtures. The mixture models require a different set of F, R ², and R _A ² statistics. The correct mixture statistics correspond to a physically consistent null hypothesis and are also consistent with the expression of the mixture model in the older “slack-variable” form. An illustrative example is included.     

The characteristics of granular-bright facet in hydrogen pre-charged and uncharged high strength steels in the very high cycle fatigue regime

In this study, the effect of hydrogen on fatigue strength of high strength steels in the very high cycle fatigue regime was further discussed. It is found that the calculated results of fatigue strength by modified Murakami’s expression are in good accordance with the experimental results in ±15% error band. The relationship between fatigue life (N _f) and the ratio of granular-bright facet (GBF) to inclusion size (\frac?{A_\textGBF } ?{A_\textinc } ) \left({\frac{{\sqrt {A_{\text{GBF}} } }}{{\sqrt {A_{\text{inc}} } }}}\right) for quenching and tempering (QT) specimens and pre-charged specimens by soaking (SK) and cathodic (CD) charging can be approximately expressed by \frac?{A_\textGBF } ?{A_\textinc } = \fracR_\textGBF R_\textinc = 0. 2 5N_\textf ^{0. 1 2 5} {\frac{{\sqrt {A_{\text{GBF}} } }}{{\sqrt {A_{\text{inc}} } }}} = {\frac{{R_{\text{GBF}} }}{{R_{\text{inc}} }}} = 0. 2 5N_{\text{f}}^{ 0. 1 2 5} ; however, the value of \frac?{A_\textGBF } ?{A_\textinc } {\frac{{\sqrt {A_{\text{GBF}} } }}{{\sqrt {A_{\text{inc}} } }}} for specimens pre-charged by high-pressure thermal hydrogen charging is obviously greater than that for QT specimens and pre-charged specimens by SK and CD charging at an identical N _f. The stress intensity factor range at the periphery of the GBF, ΔK _GBF, was calculated in this work. It is found that the value of ΔK _GBF is not a constant but approximately proportional to (?{A_\textGBF } ) ^{1/ 3} (\sqrt {A_{\text{GBF}} } )^{ 1/ 3} . Besides it is also found that ΔK _GBF decreases with the increase of hydrogen content.     

Compression fatigue performance of a fire resistant syntactic foam

Compression–compression fatigue test study of a fire resistant Eco-Core was conducted at two values of stress ratios (R = 10 and 5). Tests were conducted at S_min/S_o values of 0.9–0.6 for R = 10 and 0.95–0.8 for R = 5. Here S_min is the maximum compression stress and S_o is the compression strength. The study showed that Eco-Core has well defined failure modes and associated fatigue lives. The failure modes are: damage on-set; damage progression, and final failure. The damage on-set, propagation and final failure were characterized by 2%, 5% and 7% changes in compliance. The three failure modes were found to be same for both static and fatigue loadings. The endurance limit was found to be 0.72S_o, 0.75S_o and 0.76S_o, respectively for three failure modes for R = 10 and 0.81S_o, 0.82S_o and 0.82S_o, respectively for R = 5. The fatigue life is defined by a power law equation, S_min/S_o = A_oN^α. Constants of the equation were established for all three modes of failures and the two stress ratios. Finally, fatigue life was found to be less sensitive to R ratio when expressed in terms of stress range versus number of load cycles, which is similar to that of metallic materials.     

A simple theory for the dependence of the electrical resistance of the magnetic superconductors TmRh4B4 and ErRh4B4 on temperature and field

The warmup rate of the¹⁶⁵Ho-enhanced nuclear spins in a HoVO₄ single crystal in contact with dilute³He is shown to be dominated by the Kapitza resistanceR _K at low bath temperature (T _b <100 mK). This result is obtained from an analysis of the NMR signal during the warmup, following a demagnetization which cools the sample to a temperature of about 5 mK. The temperature variation ofR _K (T _b< ^/–3 ) is consistent with the acoustic mismatch model, but the magnitude is 40 times smaller than the theoretical predictions for a solid-liquid interface. The spin-lattice relaxation is also estimated, and found to be in agreement with the results of other authors.     

Spectroscopy of Disordered Laser Crystals

The nonuniform broadening of optical spectra is analyzed for two types of rare-earth-activated disordered laser crystals: substituted garnets and yttria-stabilized zirconia (ZrO₂–Y₂O₃). By decomposing nonuniformly broadened, composite R³⁺ absorption and luminescence bands, several principal centers (K and L for Eu³⁺ andA, B, C, and D for Nd³⁺) are identified and correlated with particular configurations of the near-neighbor environment of the activator ions (optical centers). It is shown that the formation of activator associates has a weaker effect on the optical spectra than the nearest neighbor coordination of the activator.     

A detection system for energetic light heavy ions

A light heavy ion detection system which consists of a gas-filled ionization chamber (IC) connected to a scattering chamber via a time-of-flight (TOF) system has been constructed. The entrance window of the IC has an area of 14 × 40 cm², the active depth is 115 cm. Filled with CF₄ at a pressure of 350 Torr, the energy range for ¹²C and ⁴⁰Ar is 5–20 MeV/A and 6–30 MeV/A, respectively. The TOF system consists of two parallel plate avalanche counters with a flightpath of 70 cm in between. The IC has been tested with ¹²C ions at an energy of 39 MeV. The energy resolution of the IC (1.1%) is mainly determined by the energy straggling in the foils of the TOF system and the ionization chamber. The energy-loss resolution is 3.5%, the horizontal position resolution varies between 6 and 20 mm and the vertical position resolution is 2 mm. The time resolution of the TOF system ranges from 800 ps for ⁴He at 5.0 MeV, to 280 ps for ²⁸Si at 55 MeV.     

Internal symmetry groups for perfect elastoplasticity under axial‐torsional loadings

Abstract

In the material modeling of experimental axial‐torsional strain control tests, the hoop and radial strains are always unknown, a priori, and hence can not be viewed as inputs. This greatly complicates constitutive model analyses because the resulting differential equations become highly nonlinear. To tackle this problem, we demonstrate two new formulations. By using the two‐integrating factors idea we derive two Lie type systems in the product space M ¹⁺¹?M ¹⁺¹. The Lie algebra is the direct sum so(1, 1)?so(1, 1), and correspondingly the symmetry group is the direct product SO_o (1, 1) ?SO_o (1, 1). Then, by using the one‐integrating factor idea we convert the nonlinear constitutive equations to a Lie type system X=A(X, t)X with A?sl(2, 1, R), a Lie algebra of the special orthochronous pseudo‐linear group SL(2, 1, R). The underlying space is a cone in the pseudo‐Riemann manifold. Consistent numerical methods are also developed according to these Lie symmetries.     

Formation of zirconia fibres on unidirectional freezing of a gel

A zirconia hydrogel prepared by dialysing ZrOCI₂ aqueous solution against water buffer was unidirectionally frozen in a cylindrical polyethylene cell which was immersed in a -78° C cold bath at various rates. Freezing rate,R, and temperature gradient,G, at the frozen gel front were continuously measured during freezing. It was found that zirconia fibres longer than 20 mm are formed whenG/R = 2 to 8° C h cm^–2. Either lower or higherG/R values gave only fragmental zirconia. The diameter,d, of the long zirconia fibres was changed from 25 to 55 m with the temperature gradient and the freezing rate according to the equationd ^– A/(GR) +B, whereA andB are constants. It was concluded that long fibres of the desired diameter are obtained by controlling both the freezing rate and the temperature gradient. These results were interpreted in terms of cellular growth of ice crystals.     

Resonant fatigue test bench for shaft testing

Shaft fatigue testing involves long test times (~3 months), high energy consumption and high test equipment maintenance costs owing to the high bending and twisting moments required (~1600 Nm), high number of cycles (~10⁷) and large sample sizes (~30). To reduce testing time, we designed, manufactured and evaluated a resonant plate test bench. Using finite element analysis and topological optimization, we redesigned the traditional resonant flat plates for higher resonant frequency and lower deflection at the plate free ends. We found that the optimal topology is an I‐beam; it doubles the frequency of flexion tests, up to 100 Hz, and exhibits 2 mm of deflection under a load of 1 kN. To measure the moments induced on the shaft sample during testing, we measured the surface deflection of the resonant plates. Tests on a calibration axle showed that the induced shaft moment has very high linear correlation (R² > 0.99) with the plate's surface deformation. We used our test bench to evaluate fatigue resistance for a type of crankshaft manufactured by a local company. We found that their fatigue resistance limit was 1250 Nm at 10⁷ cycles and that their mean useful life was 10⁴ cycles when they are subjected to a 1400 Nm moment. These results agree with previous results on this type of crankshaft using other methods.     

Effects of creep properties of materials on unified creep constraint parameter Ac for cracked pipes

Extensive finite element analyses of cracked pipes with different crack sizes and orientations have been conducted to investigate effects of creep properties of materials on the unified creep constraint parameter A_c. The results show that the constraint parameter A_c is independent on Norton’s coefficient A, and it is only affected by the creep exponent n of materials. For a given crack size, with increasing n, A_c decreases and constraint level increases. The A_c of lower constraint cracks is more sensitive to n. The unified correlation equations between A_c and n have been obtained for cracked pipes with a wide range of crack sizes and constraint levels. They may be used to estimate the constraint parameter A_c at different positions along the crack fronts in cracked pipes made of materials with different n values. The two-parameter C*-A_c approach for assessing creep life of cracked pipes has also been discussed.     

Joint ―X and R Charts with Two‐stage Samplings

When joint ―X and R charts are in use, samples of fixed size are regularly taken from the process, and their means and ranges are plotted on the ―X and R charts, respectively. In this article, joint ―X and R charts have been used for monitoring continuous production processes. The sampling is performed, in two stages. During the first stage, one item of the sample is inspected and, depending on the result, the sampling is interrupted if the process is found to be in control; otherwise, it goes on to the second stage, where the remaining sample items are inspected. The two‐stage sampling procedure speeds up the detection of process disturbances. The proposed joint ―X and R charts are easier to administer and are more efficient than the joint ―X and R charts with variable sample size where the quality characteristic of interest can be evaluated either by attribute or variable. Copyright © 2004 John Wiley & Sons, Ltd.     

Solid rectangular and T-shaped conductors in semi-closed slots

Summary Previous methods of calculating the internal impedance of rectangular and T-shaped conductors have made arbitrary assumptions about the form of the magnetic field. These have led to inconsistencies. A method is developed which necessitates less restrictive assumptions, thereby removing the inconsistencies. Results are compared for typical conductor sizes.List of symbols a, b, c, d dimensions of conductor or slot - J current density - E electric field strength - V scalar potential - I current (r.m.s.) in conductor - B flux density - H magnetic field strength with componentsH _x,H _y in thex, y coordinate directions respectively - L inductance/unit length - R resistance/unit length - A vector potential - A modified vector potential - A ^*,A ^** single and double cosine transforms ofA - conductivity of conductor - relative permeability of conductor - angular frequency - ² j ₀ - m, n transform parameters - C _m {(m/c)²+ ₁ ² }^1/2 - D _n {(n/d)²+ ₂ ² }^1/2 - P _m,Q _n coefficients - K constant of integration - Re, Im real imaginary parts of complex function respectively