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.     

Plastic deformation depth modeling on grinding of gamma Titanium Aluminides

This work reports on the subsurface plastic deformation depth (PDD) as a result of grinding of γ-TiAl, where the effects of grit size and shape, workpiece speed, and wheel depth of cut were studied. A grinding model based on a stochastic distribution of the chip thickness was used to estimate the expected maximum normal force per grit ( ${F''_{n\:{\rm max}}}$ ), which was correlated to the PDD. It was found that the PDD shows a linear correlation with ${F''_{n\:{\rm max}}}^{0.5}$ . The results suggest that the indentation model is still valid for grinding if ${F''_{n\:{\rm max}}}^{0.5}$ is used as a PDD predictor variable instead of the total grinding force.     

The curved wall jet over a circular cylinder before the interaction of two opposing curved wall jets

A curved wall jet before the interaction of two identical curved wall jets over a circular cylinder was investigated experimentally. Using hot-wire anemometry, the mean velocity, Reynolds stresses, and high order moments of the fluctuating velocity were measured. The turbulent kinetic energy and shear stress budgets were evaluated using the measured data. The correlation coefficient, ${{\overline {uv} } \mathord{\left/ {\vphantom {{\overline {uv} } {u'v'}}} \right. \kern-0em} {u'v'}}$ , the normal stress ratio, ${{\overline {v^2 } } \mathord{\left/ {\vphantom {{\overline {v^2 } } {\overline {u^2 } }}} \right. \kern-0em} {\overline {u^2 } }}$ , and the principal direction of the Reynolds stress are presented. The effects of curvature and adverse pressure gradient on these diistributions are also discurssed. The turbulent kinetic energy and shear stress budgets in two regions before the interaction are analyzed in detail to illuminate the effect of the adverse pressure gradient on the turbulent transport.     

A robust \overline {\hbox{X}} control chart based on M-estimators in presence of outliers

Specifying the control limits is an important step in designing a control chart. The control limits are determined by the estimates of mean and/or standard deviation of the process. In the $ \overline {\hbox{X}} $ control chart, when outliers exist in the data, using the classical estimators to estimate parameters may cause the limits to become wider or to shift in the same direction. Robust estimators which are not affected by outliers are used in this research to determine the control limits for $ \overline {\hbox{X}} $ control chart. The mean and the dispersion estimators which are currently applied to define control limits are evaluated, and their performances in control charting are compared with the proposed method by vast simulation and real data examples. Based on the results, it is revealed that when M-estimators with bisquare ρ functions is used to estimate the mean and the dispersion of the process, the control chart has the best performance among the other robust and classical control charts.     

Deteriorating jobs and learning effects on a single-machine scheduling with past-sequence-dependent setup times

In this paper, we consider the single-machine setup times scheduling with the effects of learning and deterioration. By the effects of learning and deterioration, we mean that the actual processing time of a job depends not only on the processing times of the jobs already processed but also on its scheduled position. The setup times are proportional to the length of the already processed jobs, i.e., the setup times are past-sequence-dependent (p-s-d). We show that the problems to minimize the makespan, the total completion time, and the sum of the $\mathit{\delta}$ th ( ${\mathit{\delta}} \geq 0$ ) power of job completion times are polynomially solvable. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.     

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.     

Stochastic flow-shop scheduling with minimizing the expected number of tardy jobs

In this research, minimizing the expected number of tardy jobs in a dynamic m machine flow-shop scheduling problem, i.e., $ {F_m}\left| {{r_j}\left| {{\text{E}}\left[ {\sum {{U_j}} } \right]} \right.} \right. $ is investigated. It is assumed that the jobs with deterministic processing times and stochastic due dates arrive randomly to the flow-shop cell. The due date of each job is assumed to be normally distributed with known mean and variance. A dynamic method is proposed for this problem by which the m machine stochastic flow-shop problem is decomposed into m stochastic single-machine sub-problems. Then, each sub-problem is solved as an independent stochastic single-machine scheduling problem by a mathematical programming model. Comparison of the proposed method with the most effective rule of thumb for the proposed problem, i.e., shortest processing time first rule shows that the proposed method performs 23.9 % better than the SPT rule on average for industry-size scheduling problems.     

Internal energy minimization in biarc interpolation

The problem of scheduling n multioperation jobs on a single machine such as the flexible manufacturing system is considered. Each job comprises up to F operations, which belong to several distinct families, and a sequence-independent setup time is incurred whenever an operation is to be processed following an operation of a different family. A job completes when all of its operations have been processed. Two variants with maximum lateness and total completion time as optimality criterion are considered. The problems are denoted as $1\left| {s_f ,{\text{assembly}},GT} \right|L_{\max } $ and $1\left| {s_f = 1,{\text{assembly}},GT,p_{ij} = 0\,{\text{or}}\,1} \right|\sum {C_j } $ . The decision is to sequence all the families in order to minimize the predefined criterion. This environment has a variety of real world applications such as flexible manufacturing systems scheduling and food industry scheduling. A heuristic is presented and a branch and bound is developed for benchmarking. Experimental results show that the heuristic provides good results and the branch and bound procedure is efficient. These results may narrow down the gap between easy and hard cases of the general problem.     

Studies of chipping mechanisms for dicing silicon wafers

The purpose of this study was to investigate the chipping modes produced in the die edges of dicing silicon wafer using the thin diamond blades. The effects of dicing directions and different wafer types on the chipping size were studied. Furthermore, scratching tests were also used to assist the analysis of studying chipping conditions of the silicon wafer. The experimental results showed that the trace behaviors produced by the diamond indenter in the scratching test of silicon wafer can be divided into the three stages: rubbing, plastic deformation, cracking. The plastic pile up and crack of the scratching traces on the wafer mainly propagate along the development of the easiest slip direction family <110>. The chipping modes produced in dicing silicon wafer can be broadly classified as four types: (1) 30° chipping; (2) 60° chipping; (3) 90° chipping; (4) irregular chipping, which causes these mechanisms of chipping modes due to the meeting between the radial cracks of 30°, 60°, and 90° along the easiest slip direction family <110> and the lateral cracks along the easiest cleavage plane family {111}. When using the thin diamond blade diced on the (111) silicon wafer along the $ {\left[ {\overline{1} 10} \right]} $ direction, the size of top chipping produced was smaller than that of along the $ {\left[ {11\overline{2} } \right]} $ direction. Besides, for the (100) plane of silicon wafer, the size and the distribution of the chipping modes produced along the $ {\left[ {\overline{1} 10} \right]} $ and $ {\left[ {\overline{1} \overline{1} 0} \right]} $ directions were similar.     

On the Fractal Dimension of Rough Surfaces

Most natural surfaces and surfaces of engineering interest, e.g., polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension $D_{\mathrm{f}} = 2.15\pm 0.15$ . We give several examples illustrating this and a simple argument, based on surface fragility, for why the fractal dimension usually is <2.3. A kinetic model of sandblasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments.     

Energy, Adhesion, and the Elastic Foundation

A theory for elastic contact adhesion between a rigid sphere and an elastic foundation is developed. The theory derives relationships between the contact deformation and the externally applied force. The derivation is based on elastic contact between a sphere and a thin linear-elastic foundation in which the strain energies are balanced by the work of indentation and the change in surface energy. Contacting regimes where there is either compressive strain energy or only tensile strain energy (pull-off regime) are both treated. The model is non-dimensionalized and an order of magnitude analysis is performed in order to develop simplified closed form solutions; the simplified model is then evaluated and compared to the full solution. This theory finds that the adhesion force is significantly larger for an elastic foundation in which the surface elements act independently as compared to more traditional solutions for elastic solids. The theory gives an adhesion force of $ F_{\text{adh}} \cong 7\pi R\Updelta \gamma . $      

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.     

Bicriteria scheduling of a two-machine flowshop with sequence-dependent setup times

A two-machine flowshop scheduling problem is addressed to minimize setups and makespan where each job is characterized by a pair of attributes that entail setups on each machine. The setup times are sequence-dependent on both machines. It is shown that these objectives conflict, so the Pareto optimization approach is considered. The scheduling problems considering either of these objectives are $ \mathcal{N}{\wp } - {\text{hard}} $ , so exact optimization techniques are impractical for large-sized problems. We propose two multi-objective metaheurisctics based on genetic algorithms (MOGA) and simulated annealing (MOSA) to find approximations of Pareto-optimal sets. The performances of these approaches are compared with lower bounds for small problems. In larger problems, performance of the proposed algorithms are compared with each other. Experimentations revealed that both algorithms perform very similar on small problems. Moreover, it was observed that MOGA outperforms MOSA in terms of the quality of solutions on larger problems.     

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.     

An investigation on multistage bending of blank sheet into cylindrical tube by experiment and numerical simulation

In this paper, one pair of punch and die was employed to experimentally investigate the pure bending of blank sheet into cylindrical tube by multistage process. The investigated material was hot-rolled HSLA370 with the thickness of 2?mm. Numerical simulation was conducted on bending and springback with LS-DYNA solver. Results showed that multistage bending technique was an alternative way to produce cylindrical tubes. The sequence is described as $ {\text{Blank}}\,{\text{sheet}}\xrightarrow{{{\text{Multistage}}\,{\text{bending}}}}{\text{C - tube}}\xrightarrow[{{\text{Welding}}}]{{{\text{Squeezing}}}}{\text{O - tube}} $ . Gap width and roundness of C-tube (configuration like letter ??C??) were two dominant parameters to evaluate the bending performance. The effects of blank positioning on both of them were investigated by means of numerical simulation. Laser-welded tubes meeting roundness and the tolerance limit of diameter were produced. Simulation revealed that effective plastic strain along circumferential direction was much low, mostly ranging between 0.03 and 0.05. Severe thinning and shape defects were not observed in the finished tubes. A numerical model was developed and its effectiveness was verified by a comparison between the predicted results and the corresponding experiments.     

Preparation of KTiOPO4 thin films on different substrates by pulsed laser deposition

Pulsed laser deposition (PLD) technique is applied in fabrication of thin films of KTiOPO₄ (KTP) material, which possesses electro-optic and nonlinear optical properties. Thin film fabrication of optically functional KTP on fused silica and different sapphire substrates by changing an ambient oxygen pressure and a substrate temperature during PLD is investigated. Highly oriented KTP thin films could be grown on sapphire $ {\left( {11\overline{2} 0} \right)} $ in an oxygen atmosphere by PLD using a composite target whose stoichiometry is nearly same as KTP. Although the film contained polycrystalline crystallites, predominant crystallites seemed to be epitaxially grown.     

Double sampling \overline{X} control chart for a first-order autoregressive moving average process model

In this paper, we consider the double sampling (DS) $\overline{X} $ control chart for monitoring processes in which the observations can be represented as a first-order autoregressive moving average (ARMA(1, 1)) model. The properties of the DS $\overline{X} $ control chart with the sampling intervals driven by the rational subgroup concept are studied and compared with the Shewhart chart and the variable sample size (VSS) chart, both properly modified to account for the serial correlation. Numerical results show that the correlation within subgroups has a significant impact on the properties of the charts. For processes with low to moderate correlation levels, the DS $\overline{X} $ chart is substantially more efficient in detecting process mean shifts.     

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.     

Three half-axis tool orientation optimization for spiral machining of blades

A regular three-axis computer numerical control (CNC) machine combined with an automatic indexing rotary table (AIRT) is always used to produce four-axis machining for blades in many medium-sized and small industries. Generally, AIRT has the characteristic of low precision, which often leads to obvious tool marks like overcut on the machined blade surface. To overcome this problem, a machining technique, named as $ 3\frac{1}{2} $ -axis spiral machining method that uses the simplicity of three-axis tool positioning and the flexibility of four-axis tool orientation, is developed and implemented. Key issues are focused on transformations of tool orientations from four-axis to $ 3\frac{1}{2} $ -axis and concrete contributions are twofold. First, universal principles are proposed to transfer tool orientations for general convex and concave surfaces. Second, with respect to the pressure and suction surfaces of blades in $ 3\frac{1}{2} $ -axis spiral machining, a unified transformation method is also addressed in detail. A cutting test shows that overcut marks that easily occur in four-axis spiral machining can be effectively controlled by using the proposed $ 3\frac{1}{2} $ -axis machining technique.