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.     

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.     

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.     

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.     

Modeling cutting machining process using symbolic regression \alpha -\beta

An analysis of a cutting machining process is made by manipulating equations generated by means of symbolic regression $\alpha $ - $\beta $ . This regression approach can generate mathematical models of any process considering only measured data. Usually a mathematical model is preferred over other approaches like linear regression or neural networks. As a practical case, a cutting machining process of Titanium 6Al-4V is modeled considering the absence and existence of cooling. An analysis of the surface of response is made to visualize the effects of the machining parameters on roughness. These plots could be useful to establish the machining parameters when a desirable roughness is expected. On the other hand, the mathematical models can be useful for prediction, simulation and optimization.     

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.     

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.     

Experimental milling moment model in orthogonal cutting condition: to an accurate energy balance

The control of cutting energy parameters is essential to optimize the cutting condition during the milling process. Our previous works (Cahuc et al., Int J Adv Manuf Technol 18(9):648?C656, 2001; Darnis et?al. 2000) have shown the existence of the six components of the cutting mechanical actions. Thus, the influence of geometric and kinematic parameters on the six components must be quantified. Based on the experimental approach explained in our last works (Albert et al., 2008a, b), this study proposes an energetic criterion characterizing the cutting moment in orthogonal cutting condition. Then, the energy balance has to take into account the cutting moment, highlighting the utility of this criterion. Therefore, the cutting moment model proposed allows an accurate evaluation of the energy balance and the mechanical actions (forces and moments) applied to the workpiece. Consequently, the cutting parameters can be chosen in order to optimize the cutting power consumption.     

Performance evaluation of control chart for multiple assignable causes using genetic algorithm

With a view to monitoring and controlling manufacturing processes in industries, control charts are widely used and needed to be designed economically to achieve minimum quality costs. Many authors have studied the economic design of the $ \overline{X} $ control chart after Duncan (J Am Stat Assoc 51(274):228–242, 1956) first proposed the economic model of the $ \overline{X} $ control chart for a single assignable cause. But, in practice, multiple assignable causes are more logical and realistic. Moreover, the economic design does not consider statistical properties like bound on type I and type II error, and average time to signal (ATS). This paper focuses on evaluating the performance of genetic algorithm (GA) in pure economic and economic statistical design of the $ \overline{X} $ control chart for multiple assignable causes. The performances of GA are demonstrated by comparing its result with the previously proposed grid search technique for a numerical example. The Duncan model of multiple assignable causes is adopted to formulate objective function, and the computation is achieved by approximation through a numerical method named Simpson's 1/3 rule. Comparison distinctly shows the superiority of GA over grid search results for economic statistical design.     

Using genetic algorithm and response surface methodology for statistically constrained optimization of VSI X-bar control charts under multiple assignable causes and non-normality

Variable sampling interval (VSI) control charts have been introduced with the aim of improving performance of traditional control charts. Usually, in the economic–statistical design of the VSI $ \overline{X} $ control charts, it is assumed that observations are normally distributed and process is subjected to only one assignable cause. However, in practice these assumptions could easily fail to hold, and results no longer could be realistic. This paper considers non-normal observations for the case of multiple assignable causes to develop a cost model for the economic design of VSI $ \overline{X} $ control chart. Being more applicable for all types of distributions, Burr distribution is employed for representing the distribution of non-normal process data. Since the proposed design consists of a complex nonlinear cost function that cannot be solved using a classical optimization method, genetic algorithm (GA) searching method as an efficient famous metaheuristic is employed to find the optimal values for the design parameters. Moreover, to improve the performances, response surface methodology is employed to calibrate GA parameters. The effectiveness of the proposed scheme is evaluated through a numerical example. Sensitivity analysis is also carried out to show the effects of cost and process parameters on the outputs of the model. Results show that in all cases, presented VSI model has better economical and statistical performances than its corresponding fixed sampling interval scheme.     

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 note on “Selection of cutting parameters in side milling operation using graph theory and matrix approach”

Determination of optimal cutting parameters is one of the vital modules in process planning of parts since economy of machining operations plays an important role in increasing productivity and competitiveness. Recently, Gadakh and Shinde (Int J Adv Manuf Technol 2011) presented a graph theory and matrix approach (GTMA) and few other multiple attribute decision making (MADM) methods for selection of cutting parameters in side milling operation in their paper “Selection of cutting parameters in side milling operation using graph theory and matrix approach” Gadakh and Shinde (Int J Adv Manuf Technol DOI 10.1007/S00170-011-3256-Z, 2011). The authors had presented the experimental results of Chiang-Kao and Lu (Int J Adv Manuf Technol 34:440–447, 2007) to demonstrate the proposed methods. However, the systematic procedures of GTMA and the other MADM methods were already reported exhaustively by Rao (2007), and Gadakh and Shinde (Int J Adv Manuf Technol 2011) had reproduced the related contents. Many computational and fundamental mistakes were also present in their work. Furthermore, the authors had presented the incorrect values of metal removal rate (MRR) and these values were different from the values presented by Chiang-Kao and Lu (Int J Adv Manuf Technol 34:440–447, 2007). This note discusses these mistakes and presents the correct approaches and the results.     

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.     

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.     

Optimal inventory policy involving back-order discounts and variable lead time demand

This paper allows the backorder rate as a control variable to widen applications of the Wu and Tsai’s 2001 model. Moreover, we also consider the backorder rate that proposed by combining the work of Ouyang and Chuang 2001 (also see Lee 2005) with the work of Pan and Hsiao 2001, 2005) (also see Pan et al. 2004) to present a new general form. Thus, the backorder rate is dependent on the amount of shortages and backorder price discounts. In addition, we also develop an algorithmic procedure to find the optimal inventory policy. Finally, a numerical example is also given to illustrate the results.     

A new adaptive control chart for monitoring process mean and variability

Traditionally, an $\bar{X}$ chart is used to control the process mean, and an R chart is used to control the variance. However, these charts are not sensitive to the small shifts in the processes. The adaptive charts might be considered if the aim is to detect process changes quickly. In this paper, we propose a new adaptive single control chart which integrates the exponentially weighted moving average procedure with the generalized likelihood ratio test statistics for jointly monitoring both the process mean and variability. This new chart is effective in detecting the disturbances that shift the process mean, increase or decrease the process variance, or lead to a combination of both effects.     

New systematic and time-saving procedure to design cup grinding wheels for the application of ultrasonic-assisted grinding

Since glass and ceramic materials have beneficial properties, they have gained more importance in numerous technical applications during the last 30 years. For example, nowadays, ceramics are used as artificial hip joints or as mechanical seals for highest relative speeds. Glass components are used for multitude of optical applications like cameras and reflectors. But besides a lot of advantages, the processing of these materials is very difficult. In particular, this contains the manufacturing of small components like microreactor plates or glass wafers with hundreds of small holes, too. Using ultrasonic-assisted grinding, the treatment can significantly be optimized and higher removal rates can be realized. For the generation of ultrasonic waves, often piezoactors are used that excite the grinding tools with vibrations of 20 kHz and amplitudes of a few microns (Markov 1966; Kuttruff 1988). Using an ultrasonic wave, the tool geometry is strongly restricted to guarantee the hybrid functionality (Siegert 2002; Dawe Instruments Ltd. 1967; Derks 1984). The paper describes a new way to calculate the design of tools suitable for their use in ultrasonic-assisted grinding. As a machining process, the manufacturing of spherical optics with cup-grinding wheels is selected.     

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.     

Effect of gate dimension on micro injection molded weld line strength with polypropylene (PP) and high-density polyethylene (HDPE)

As a defect of micro injection molding parts, weld line is unfavorable since it will influence the surface quality and mechanical properties of micro parts. Therefore, the investigation on the developing process of weld line would be a significant issue for improving the quality of micro injection molded parts. In this study, one injection mold with four micro tensile sample cavities was designed and constructed. Every cavity responses to various gate dimensions, which is marked as Gate $ {\text{Nr}}.1\left( {1.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.2\left( {1.0 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , $ {\text{Nr}}.3\left( {1.0 \times 0.05 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ , and $ {\text{Nr}}.4\left( {0.5 \times 0.1 \times 0.{\text{5mm}},{\text{width}} \times {\text{depth}} \times {\text{length}}} \right) $ . The effects of gate dimension of the mold on mechanical properties of weld line have been studied by experiments in different processing parameters. The tensile test was used to characterize the micro injection molded weld line strength. The results for polypropylene show that with the changing of injection pressure and mold temperature, Gate Nr.3 is corresponding to the strongest weld strength; the next is Gate Nr.2; Gates Nr.4 and Nr.1 are in the end. The difference between them is not obvious. For high-density polyethylene, Gate Nr.1 is not able to be completely filled, which is due to the blocking of stick materials and dirt based on the simulation analysis. The investigation was only carried out for the other three gate sizes; results present that Gate Nr.3 always gives the best weld line strength whatever the processing parameters are, Gate Nr.4 is next and then Gate Nr.2. There are always middle optimal values for processing parameters leading to strongest weld line strength, when injection pressure is 80 MPa, injection speed is 90 cm³/s, melt temperature is 200°C, and mold temperature is 130°C. Higher and lower processing parameters result in reduced weld line strength.