The run sum t control chart for monitoring process mean changes in manufacturing

The $ \overline{X} $ type charts are not robust against estimation errors or changes in process standard deviation. Thus, the t type charts, like the t and exponentially weighted moving average (EWMA) t charts, are introduced to overcome this weakness. In this paper, a run sum t chart is proposed, and its optimal scores and parameters are determined. The Markov chain method is used to characterize the run length distribution of the run sum t chart. The statistical design for minimizing the out-of-control average run length (ARL₁) and the economic statistical design for minimizing the cost function are studied. Numerical results show that the t type charts are more robust than the $ \overline{X} $ type charts for small shifts, in terms of ARL and cost criteria, with respect to changes in the standard deviation. Among the t type charts, the run sum t chart outperforms the EWMA t chart for medium to large shifts by having smaller ARL₁ and lower minimum cost. The run sum t chart surpasses the $ \overline{X} $ type charts by having lower ARL₁ when the charts are optimally designed for large shifts but the run sum $ \overline{X} $ and EWMA $ \overline{X} $ prevail for small shifts. In terms of minimum cost, the $ \overline{X} $ type charts are superior to the t type charts. As occurrence of estimation errors is unpredictable in real process monitoring situations, the run sum t chart is an important and useful tool for practitioners to handle such situations.     

Coercive Force as a Function of Uniaxial Stresses (Part 2)

The relative anisotropy of the coercive force is investigated as a function of the tensile stress. A generalized calculated curve with coefficients averaged over all the low-carbon steels tested is constructed. A mechanism for determining the effective magnetostriction λ ₁₀₀ ^* and λ ₁₁₁ ^* from the field dependence λ(H) is proposed. The magnetoelastic sensitivity ΔH _c coefficients are determined as functions of the magnetostriction λ ₁₀₀ ^* .     

Modeling of surface roughness effect on dry contact friction in metal forming

Interfacial conditions such as friction and roughness substantially affect the process characteristics of metal forming. This study developed a dry friction model that accounted for the adhesion and interference effects of surface roughness. A sliding friction coefficient was suggested to provide fundamental information about the interfacial conditions of the contact surface. The proposed model was easily verified by published experiments and predicted values agreed with experimental results. Accordingly, friction coefficient ?? clearly increased as relative roughness R _m (=?roughness of tool $ R_a^T $ /roughness of workpiece $ R_a^M $ , measured as interference effect) increased. Simulations confirmed that the friction coefficient ?? decreased as dimensionless stress S _m (=?contact pressure p _m /tensile strength $ \sigma_u^0 $ ) increased at small strain hardening exponent n-values. Under the conditions of large n and small R _m values, the friction coefficient ?? initially decreased and then increased. It then slightly decreased as dimensionless stress S _m increased. However, this trend became less apparent as relative roughness R _m increased since friction coefficient ?? simply decreased.     

Experimental Investigation of Viscoelastic Rolling Contacts: A Comparison with Theory

To address the issue of a pin sliding against a boundary film, we calculate the pressure-dependent shear strength of a bilayer of potassium chloride sandwiched between tungsten carbide (WC) slabs using first-principles, density functional theory (DFT) calculations. It has been shown experimentally that the shear strength S of a KCl film on metal substrates varies with pressure P as S = S ₀ + αP, and S ₀ = 65 ± 5 MPa and α = 0.14 ± 0.02. Calculations are performed for KCl in contact with the (1 $ \bar{1} $ 00) and (10 $ \bar{1} $ 0) faces of WC which have almost square surface unit cells. The effect of pressure is mimicked by varying the distance between the outermost layers of the WC slabs. The DFT calculations confirm that the shear strength depends on pressure and yield average values of S ₀ of 70 ± 10 MPa for the WC(1 $ \bar{1} $ 00) and 51 ± 13 MPa for the WC(10 $ \bar{1} $ 0) faces, in reasonable agreement with experiment. Since the calculations were performed for a KCl slab in registry with the WC slabs, the agreement with experiment suggests that the atoms at the interface between the tip and film are also in registry. In addition, the calculated and experimental shear strengths are much lower than the shear modulus of KCl, indicating that shear occurs between the tip and film surface without forming a transfer film, in agreement with previous experimental measurements.     

An Elastic–Plastic Model for Single Shot-Peening Impacts

A model was developed for impacts of elastic perfectly plastic spherical particles with impact velocities up to 250 m/s. The model is based on the two master curves, for normalized pressure $\bar{H}$ and projected contact area c ², which both are functions of the representative strain Λ at maximum impact. The model and its parameters were fitted to finite element results for elastic perfectly plastic and strain rate-independent materials. It was applied to a wide range of materials with different ratio between yield stress and elastic properties, different ball sizes and impact velocities. The impact model predicted the results from finite element method for contact radius, maximum impact depth in both target and ball as well as remaining impact depth in target and ball. The remaining impact depth was determined from elastic spring back with Hertzian and quadratic pressure at maximum impact. The rebound velocity was also estimated by following the load-deformation path during spring back. If the strain rate-compensated yield stress was used for the master curve parameters, then the model predicted the impact results also for the investigated strain rate-dependent materials.     

Frequency dependences of higher-order constants of piezoelectric ceramics

The properties of TBC-3 and PZT-23 piezoelectric ceramics have been studied by the method of loaded three-element complex oscillator. Changes in the higher-order (up to fifth) parameters are considered for large mechanical (0–120 MPa) and electric (0–600 kV/m) loads. Results of studying the longitudinal flexibility s ₁₁ ^E , piezoelectric modulus d ₃₁, and dielectric permittivity ε ₃₃ ^σ are presented within a frequency range of 20–200 kHz, where the frequency dispersion of dielectric as well as piezoelectric and elastic parameters is observed.     

Boundary Layer Behaviour in Circular EHL Contacts in the Elastic-Piezoviscous Regime

The solution of elastohydrodynamically lubricated contacts at high loads and/or low speeds can be described as a Hertzian pressure with inlet and outlet boundary layers: zones where significant pressure flow occurs. For the soft lubrication regime (elastic-isoviscous), a self-similar solution exists in the boundary layers satisfying localized equations. In this paper, the boundary layer behaviour in the elastic-piezoviscous regime is investigated. The lengthscale of the boundary layers and the scaling of pressure and film thickness are expressed in non-dimensional parameters. The boundary layer width scales as \(1/\sqrt{M}\) (equivalent to \({\bar{\lambda }}^{3/8}\) ), the maximum pressure difference relative to the Hertzian solution as \(1 / \root 3 \of {M}\) (equivalent to \({\bar{\lambda }}^{1/4}\) ) and the film thickness as \(1/\root 16 \of {M}\) (equivalent to \({\bar{\lambda }}^{3/64}\) ) with \(M\) the Moes non-dimensional load and \({\bar{\lambda }}\) a dimensionless speed parameter. The Moes dimensionless lubricant parameter \(L\) was fixed. These scalings differ from the isoviscous-elastic (soft lubrication) regime. With increasing load (decreasing speed), the solution exhibits an increasing degree of rotational symmetry. The pressure varies less than 10 % over an angle less than 45 degrees from the lubricant entrainment direction. The results provide additional fundamental understanding of the nature of elastohydrodynamic lubrication and give physical rationale to the finding of roughness deformation depending on the “inlet length”. The findings may contribute to more efficient numerical solutions and to improved semi-analytical prediction methods for engineering based on physically correct asymptotic behaviour.     

Increasing the signal-to-noise ratio during joint use of the spectrum extrapolation and splitting methods

The possibility of increasing the signal-to-noise ratio by the method of echo-signal spectrum splitting jointly with spectrum extrapolation is considered. The essence of the method proposed is that the echo-signal spectrum known within a given frequency range (f _min, f _max) is divided into several subranges (f _min ⁱ , f _max ⁱ ). The construction of the AR model of the echo-signal spectrum allows the spectrum extrapolation from each subrange by an interval (f _min ^e , f _max ^e that far exceeds the initial interval. This means that, with the use of one echo signal, a set of signals can be obtained, the adding together of which increases the signal-to-noise ratio and ensures an ultrafine beam resolution for flaw images. The presented results of processing echo signals, which were obtained in numerical and model experiments, confirm the efficiency of the proposed technique for processing echo signals.     

Parameterization of prismatic shapes and reconstruction of free-form shapes in reverse engineering

This article proposes an adaptive loss function (AL) control chart for statistical process control (SPC). This chart is able to monitor process shifts in the mean and variance simultaneously. It is appealing for its effectiveness in detecting process shifts and simplicity in operation under a computerized SPC environment. By using a fixed sample size and a fixed sampling interval, the AL chart can be operated as easily as the conventional ${\bar X}$ and S charts from the stand of the operators. Nevertheless, via the computer-aided adaption of some charting parameters, the AL chart is not only significantly more effective than the ${\bar X}$ and S charts, but it also outperforms the cumulative sum (CUSUM) charts for most of the combinations of mean and increasing variance shifts.     

Improved feature-based test statistic for assessing suitability of the preliminary samples for constructing control limits of \bar{X} chart

In spite of using a large number of subgroups (m) of small samples (n), the estimated control limits of $ \bar{X} $ chart in phase I can be erroneous unless the preliminary samples are drawn from a stable process. As a result, the performance of the chart in phase II can be significantly affected. The pattern in the $ \bar{X} $ chart, exhibited by the plots of the subgroup averages of the preliminary samples, will be different depending on stability and instability of the process while the preliminary samples were collected. Based on this concept, a new feature-based test statistic (FTS) is proposed for evaluating suitability of the preliminary samples for the designing of the $ \bar{X} $ chart. The FTS, for given m, approximately follows $ N[1,{\text{ SD(}}m{)]} $ , where SD(m) is a function of m. The goodness of the approximation and effectiveness of the test are evaluated using simulated data. The results show that both are satisfactory for m?>?=48. The proposed statistic is also quite effective in detecting unstable process condition resulting in a cyclic pattern. The computation of FTS involves some complexities. However, now-a-days computers are widely available and so computation difficulty may not be a problem.     

Prediction of fatigue strength in HSS-Co, S55C and the friction welded materials based on statistical evaluation of inclusion size

In this paper, the effects of nonmetallic inclusions on the fatigue strength of medium and high strength steels are quantitatively investigated by considering the relationship between the Vickers hardness, Hv and the maximum size of nonmetallic inclusion, $\sqrt {(area)_{\max } } $ . The maximum size of nonmetallic inclusion defined by the square root of the projected area in an inclusion can be estimated by the statistics of extreme values with a definite number of specimens or structural components. While most of other studies using the parameter $\sqrt {(area)_{\max } } $ have performed the experiments with the specimens with small artificial defects or notches, this study investigates the possibility of prediction on fotigue strength in the unnotched smooth specimens. The results show that strength of the friction welded joints of HSS-Co to S55C carbon steel is almost equal to that of the weaker material in the optimum welding conditions. Under the limiting condition for the nonpropagating cracks emanating from defects or inclusions, the threshold stress intensity factor range °K_th and the lower limit of fatigue strength σ_w1 were successfully estimated from the largest inclusion size $\sqrt {(area)_{\max } } $ . From the analysis of SEM fractographs, it can be concluded that the fatigue fractures of the specimens are associated primarily with the inclusions located at the outer periphery of the specimens.     

Tire–Road Contact Stiffness

When a rubber block is squeezed against a nominal flat but rough surface, the rubber bottom surface will penetrate into the substrate roughness profile. The relation between penetration depth \(w\) (or the average interfacial separation \(\bar{u}\) ) and the applied squeezing pressure \(p\) determines the (perpendicular) contact stiffness \(K=\hbox {d}p/\hbox {d}w=-\hbox {d}p/\hbox {d}\bar{u}\) , which is important for many applications. We have measured the relation between \(p\) and \(\bar{u}\) for a rubber block squeezed against 28 different concrete and asphalt road surfaces. We find a linear relation between \({\mathrm{log}}p\) and \(\bar{u}\) , in agreement with theory predictions. The measured stiffness values correlate rather well with the theory prediction.     

A hybrid cuckoo search and variable neighborhood descent for single and multiobjective scheduling problems

Cuckoo search (CS) is a relatively new meta-heuristic that has proven its strength in solving continuous optimization problems. This papers applies cuckoo search to the class of sequencing problems by hybridizing it with a variable neighborhood descent local search for enhancing the quality of the obtained solutions. The Lévy flight operator proposed in the original CS is modified to address the discrete nature of scheduling problems. Two well-known problems are used to demonstrate the effectiveness of the proposed hybrid CS approach. The first is the NP-hard single objective problem of minimizing the weighted total tardiness time ( \(1|| \sum {T_{w}}\) ) and the second is the multiobjective problem of minimizing the flowtime \(\overline {C}\) and the maximum tardiness T _{m a x} for single machine ( \(1|| (\frac {1}{n}\sum {C}, T_{max})\) ). For the first problem, computational results show that the hybrid CS is able to find the optimal solutions for all benchmark test instances with 40, 50, and 100 jobs and for most instances with 150, 200, 250, and 300 jobs. For the second problem, the hybrid CS generated solutions on and very close to the exact Pareto fronts of test instances with 10, 20, 30, and 40 jobs. In general, the results reveal that the hybrid CS is an adequate and robust method for tackling single and multiobjective scheduling problems.     

Optimal design of \overline {\text{X}} -control chart with Pareto in-control times

Economic control chart models usually assume that the time to occurrence of an assignable cause follows an exponential or Weibull distribution. This paper extends that to the Pareto distribution in order to investigate, in general, the effect on the economic control chart parameters like sample size, time between two successive samples, and the cost per unit time of the distributional assumption. The Pareto distribution arises as a limiting distribution of the waiting time for the number of new observations needed to obtain a value exceeding the greatest among “n” observations. It was found that the economic design of $ \overline {\text{X}} $ chart is greatly influenced by the distributional assumption. Using the cost model, the sensitivity analysis of the statistical economic design of the $ \overline {\text{X}} $ chart with respect to the parameters and costs is studied.     

Similarity and approximate solutions of laminar film condensation on a flat plate

Laminar film condensation of a saturated pure vapor in forced flow over a flat plate is analyzed as boundary layer solutions. Similarity solutions for some real fluids are presented as a function of modified Jakob number (C _pl ΔT/Prh _fg ) with property ratio ( $\sqrt {\sigma _l \mu _l /\rho _v \mu _v } $ ) andPr as parameters and compared with approximate solutions which were obtained from energy and momentum equations without convection and inertia terms in liquid flow. Approximate solutions agree well with the similarity solutions when the values of modified Jakob number are less then 0.1 near 1 atmospheric pressure.     

Atomic structure of extended defects in boron-implanted silicon layers

The structure of extended defects introduced into Si by means of boron implantation followed by thermal annealing at T = 900 °C is studied by the method of high-resolution transmission electron microscopy and computer modeling for different values of the implantation dosage (D) and concentration of boron atoms in substitutional positions B₀ \((C_{B_0 } )\) injected into the Si lattice before implantation. It is shown that the Frank dislocation loops of both interstitial (I) and vacancy (V) type at a ratio of 4: 1 are observed in Si samples with D = 10¹⁶ cm^?2 up to \(C_{B_0 } \) = 0.8·10²⁰ cm^?3. The atomic structure of the I-type Frank dislocation loops is heavily deformed, which suggests segregation of finely dispersed boron in the defect plane. At the same time, the structure of the V-type Frank dislocation loops tends to be reconstructed due to interaction with self-interstitials. At \(C_{B_0 } \) = 2.5·10²⁰ cm^?3, the I-type Frank dislocation loops are found to transform to perfect dislocation loops, and boron precipitates with a high density appear in Si. Based on the results obtained, probable reasons for vacancy deficit formation in boron-implanted Si are discussed.     

Effects of structure and defect on fatigue limit in high strength ductile irons

In this paper, the influence of several factors such as hardness, internal defect and non-propagating crack on fatigue limits was investigated with three kinds of ductile iron specimens. From the experimental results the fatigue limits were examined in relation with hardness and tensile strength in case of high strength specimens under austempering treatment; in consequence the marked improvement of fatigue limits were not showed. The maximum defect size was an important factor to predict and to evaluate the fatigue limits of ductile irons. And, the quantitative relationship between the fatigue limits (σ _w ) and the maximum defect sizes ( $\sqrt {area} _{\max } $ ) was expressed as $\sigma _w ^n \cdot \sqrt {area} _{\max } = C_2 $ . Also, it was possible to explain the difference for the fatigue limits in three ductile irons by introduction of the non-propagating crack rates.     

Effect of mechanical and fractographic properties on hole expandability of various automobile steels during hole expansion test

Hole expandability is a vital formability parameter for automobile body parts that are subjected to deep drawing conditions. In this paper, the influence of mechanical and fractographic properties on hole expansion ratio has been studied and reported. The hole expansion test has been carried out for seven different automotive steel sheets of varying thicknesses. Hole expansion ratio expressed in terms of hole expansion percentage is strongly influenced by the microstructure of the sheet metal. Hole expansion test experiments were performed on flat circular plates with a hole in the center to investigate the fracture behaviors of various automobile steels such as microalloyed, C–Mn, high-strength I.F. (SPRC-35) of three grades, extra galvannealed I.F., and HSLA (E-36) steel sheets. In the hole expansion test, deformation by lip is caused when the punch expands the hole. Fracture by petalling occurs when the holes in the sheets are completely pierced by the punch. Large circumferential strains are accommodated in the deforming sheet material. The mechanical properties, namely, strain hardening exponent (n), normal anisotropy ( $ \overline{r} $ ), formability parameter (n $ \overline{r} $ ), and other properties, namely, Mohr's circle shear strains (γ ₃₁ and γ ₁₂), strain triaxiality factor (T), and stress triaxiality factor (T _o), affected the hole expansion ratio of different steels tested. Similarly, the fractographic factors, such as void size in micrometers, void area fraction, and d-factor, affect the hole expansion ratio. Among the steel sheets tested, extra galvannealed I.F. steel possesses the highest hole expansion ratio.     

The effect of the plastic tension of steels on the dependences of the coercive force on elastic compressive stresses

The effect of compressive stresses σ^? on the coercive force H _c of annealed isotropic low-carbon steels, which were preliminarily subjected to plastic tension ? _pl ⁺ of different values, has been studied. It was shown that the shape of hysteresis loops H _c (σ^?) and their changes with increasing ? _pl ⁺ are related to induced residual compressive and tensile stresses, which result from plastic tension, and also to the occurrence of plastic compressive deformations ? _pl ^? because of the Bauschinger effect. The causes of the openness of the first cycle of the H _c (σ^?) dependence and also for the occurrence of maximum of the H _c (σ^?) function in the ascending branch of this cycle are considered. A procedure for determining the residual tensile stresses, which result from the preliminary plastic tension, has been suggested and achieved experimentally. It was shown that the magnetoelastic change of magnetization, which is observed in the plastic compression, can serve as an indicator of these deformations σ _pl ^? .