An improved control chart structure for process location parameter

The article proposes a Shewhart‐type control chart, namely M_t chart, for an improved monitoring of the mean level of a quality characteristic of interest, say Y, in a process. The proposed control chart uses the information on a single auxiliary characteristic, say X, of the process and is based on product–difference‐type estimator, say M_t (in fact the spirit is to pool different styles of using information on auxiliary variable(s)). Assuming bivariate normality of the characteristic of interest Y and the auxiliary characteristic X, design structure of the proposed M_t chart is developed and its comparisons are made with those of some existing control charts used for the same purposes. The comparisons reveal an improved performance of the proposed M_t chart relative to its existing counterparts due to suggested merger of different approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Conditional Weibull Control Charts Using Multiple Linear Regression

Because in Weibull analysis, the key variable to be monitored is the lower reliability index (R(t)), and because the R(t) index is completely determined by both the lower scale parameter (η) and the lower shape parameter (β), then based on the direct relationships between η and β with the log‐mean (μ_x) and the log‐standard deviation (σ_x) of the analyzed lifetime data, a pair of control charts to monitor a Weibull process is proposed. Moreover, because the fact that in Weibull analysis, right censored data is common, and because it gives uncertainty to the estimated Weibull parameters, then in the proposed charts, μ_x and σ_x are estimated of the conditional expected times of the related Weibull family. After that both, μ_x and σ_x are used to monitor the Weibull process. In particular, μ_x was set as the lower control limit to monitor η, and σ_x was set as the upper control limit to monitor β. Numerical applications are used to show how the charts work. Copyright © 2016 John Wiley & Sons, Ltd.     

Performance evaluation of cryogenic cooling in reaming titanium alloy

Removal of materials in metal cutting operations through drilling and reaming of hard materials is a difficult process. Wear of the tool and high cutting zone temperature have big effect on it. In this study, experiments have been carried out in a reaming operation on titanium alloy material under flood and cryogenic LN₂ cooling separately. Cutting speed, feed rate, and hole depth (constant) are the three input variable parameters. Torque (M_t), thrust force (F_t), cutting temperature (T), quality of the hole, surface roughness (R_a), and chip morphology are the output parameters. In both cooling conditions, each of the nine experiments based on orthogonal array (OA) L₉ were conducted under both cooling conditions. Based on the results obtained, cutting temperature was reduced by 12–21%, thrust force reduction is 17–32%, and torque reduction is 7–30% in cryogenic LN₂ cooling. Surface roughness is increased by 4–15% and hole quality (circularity and cylindricity) parameters are affected in cryogenic LN₂ cooling with respect to flood cooling. Better chip breaking was found in both flood and cryogenic LN₂ cooling. No drastic changes were observed in microstructure under both cooling conditions.     

An improved variable sample size and sampling interval S control chart

The standard deviation chart (S chart) is used to monitor process variability. This paper proposes an upper‐sided improved variable sample size and sampling interval (VSSI_t) S chart by improving the existing upper‐sided variable sample size and sampling interval (VSSI) S chart through the inclusion of an additional sampling interval. The optimal designs of the VSSI_t S chart together with the competing charts under consideration, such as the VSSI S and exponentially weighted moving average (EWMA) S charts, by minimizing the out‐of‐control average time to signal (ATS₁) and expected average time to signal (EATS₁) criteria, are performed using the MATLAB programs. The performances of the standard S, VSSI S, EWMA S, and VSSI_t S charts are compared, in terms of the ATS₁ and EATS₁ criteria, where the results show that the VSSI_t S chart surpasses the other charts in detecting moderate and large shifts, while the EWMA S is the best performing chart in detecting small shifts. An illustrative example is given to explain the implementation of the VSSI_t S chart.     

On using peak amplitude and rise time for AE source characterization

Acoustic Emission (AE) signals, which are electrical version of acoustic emissions, are usually analysed using a set of signal parameters. The major objective of signal analysis is to study the characteristics of the sources of emissions. Peak amplitude(P _a ) and rise time(R _t ) are two such parameters used for source characterization. In this paper, we theoretically investigate the efficiency ofP _a andR _t to classify and characterize AE sources by modelling the input stress pulse and transducer. Analytical expressions obtained forP _a andR _t clearly indicate their use and efficiency for source characterization. It is believed that these results may be of use to investigators in areas like control systems and signal processing also     

A t‐chart for Monitoring Multi‐variety and Small Batch Production Run

Statistical process control is an important tool to monitor and control a process. It is used to ensure that the manufacturing process operates in the in‐control state. Multi‐variety and small batch production runs are common in manufacturing environments like flexible manufacturing systems and Just‐in‐Time systems, which are characterized by a wide variety of mixed products with small volume for each kind of production. It is difficult to apply traditional control charts efficiently and effectively in such environments. The method that control charts are plotted for each individual part is not proper, since the successive state of the manufacturing process cannot be reflected. In this paper, a proper t‐chart is proposed for implementation in multi‐variety and small batch production runs to monitor the process mean, and its statistical properties are evaluated. The run length distribution of the proposed t‐chart has been obtained by modelling the multi‐variety process. The ARL performance for various shifts, number of product types, and subgroup sizes has also been obtained. The results show that the t‐chart can be successfully implemented to monitor a multi‐variety production run. Finally, illustrative examples show that the proposed t‐chart is effective in multi‐variety and small batch manufacturing environment. Copyright © 2013 John Wiley & Sons, Ltd.     

The variable sample size variable dimension T2 control chart

In this paper, we describe the development of the variable dimension and variable sample size T² control chart (VSSVDT²), which is an enhancement of the variable dimension T² chart (VDT²). In the VDT² control chart, the number of variables that are measured to compute the T² statistic is made variable. Some of the variables are easy or inexpensive to measure and are always monitored. The variables that are more difficult or expensive to measure are measured only when the T² value from the previous sample exceeds a specified threshold. The VDT² control chart performs well for moderate and large shifts in the mean vector. However, its performance for small shifts is poor. To improve the chart’s performance in detecting such shifts, we propose the application of the variable sample size technique to the VDT² control chart, resulting in the VSSVDT² control chart. To promote the use of the VSSVDT² chart, a user-friendly software has been developed, which the final user can use to find the best parameters of the VSSVDT² chart for a particular process.     

Optimal allocation of testing resources for statistical simulations

Statistical estimates from simulation involve uncertainty caused by the variability in the input random variables due to limited data. Allocating resources to obtain more experimental data of the input variables to better characterize their probability distributions can reduce the variance of statistical estimates. The methodology proposed determines the optimal number of additional experiments required to minimize the variance of the output moments given single or multiple constraints. The method uses multivariate t-distribution and Wishart distribution to generate realizations of the population mean and covariance of the input variables, respectively, given an amount of available data. This method handles independent and correlated random variables. A particle swarm method is used for the optimization. The optimal number of additional experiments per variable depends on the number and variance of the initial data, the influence of the variable in the output function and the cost of each additional experiment. The methodology is demonstrated using a fretting fatigue example.     

Shewhart and EWMA t control charts for short production runs

Short‐run productions are common in manufacturing environments like job shops, which are characterized by a high degree of flexibility and production variety. Owing to the limited number of possible inspections during a short run, often the Phase I control chart cannot be performed and correct estimates for the population mean and standard deviation are not available. Thus, the hypothesis of known in‐control population parameters cannot be assumed and the usual control chart statistics to monitor the sample mean are not applicable. t‐charts have been recently proposed in the literature to protect against errors in population standard deviation estimation due to the limitation of available sampling measures. In this paper the t‐charts are tested for implementation in short production runs to monitor the process mean and their statistical properties are evaluated. Statistical performance measures properly designed to test the chart sensitivity during short runs have been considered to compare the performance of Shewhart and EWMA t‐charts. Two initial setup conditions for the short run fixing the population mean exactly equal to the process target or, alternatively, introducing an initial setup error influencing the statistic distribution have been modelled. The numerical study considers several out‐of‐control process operating conditions including one‐step shifts for the population mean and/or standard deviation. The obtained results show that the t‐charts can be successfully implemented to monitor a short run. Finally, an illustrative example is presented to show the use of the investigated t charts. Copyright © 2010 John Wiley & Sons, Ltd.     

Design and implementation of qth quantile‐unbiased tr‐chart for monitoring times between events

The times between events control charts have been proposed in literature for statistical monitoring of high‐yield processes by observing the waiting times up to r ^th (r ≥ 1  ) non‐conforming items or defects. The average run length (ARL) is the most widely used performance measure to evaluate the chart's performance, but in recent years, it has been subjected to criticisms. Because the run length distribution is highly skewed and hence, the ARL is not necessarily a typical value of the run length. Thus, evaluation of the control chart based on ARL alone could be misleading. In this paper, the quantiles of run length distribution are considered, instead of ARL, to design the t_r ‐chart. Further, we eliminate the bias in q ^th quantile function of the t_r ‐chart for both the known and unknown parameter case. In particular, the MRL‐unbiased t_r ‐chart is discussed in detail and compared with the ARL‐unbiased t_r ‐chart. It is found that the MRL‐unbiased t_r ‐chart outperforms than the corresponding ARL‐unbiased chart in unknown parameter case. It is also found that the proposed chart requires less phase I observations than that of the earlier studies has been suggested.     

A Synthesis of Feedback and Feedforward Control for Process Improvement Under Stationary and Nonstationary Time Series Disturbance Models

Process adjustment strategy is an important part of the process improvement methods. The feedback control technique is used to compensate for the deviation of the output, and it has been intensively investigated. For continuous improvement and proactive strategies, feedback control has a delay and thus is not the ideal solution. In this article, motivated by a realistic manufacturing example, we propose the periodic shift disturbance models and investigate the feedforward control application from a new disturbance decomposition framework. We combine feedforward control with feedback control for maintaining the stability of the process and delivering products at target values. Then, we evaluate the performance of different control strategies for various disturbance models by using the output mean square error criterion. Sensitivity analysis of these control methods is made on different model parameter spaces, and robustness analysis for both model parameter and model structure misspecifications is presented. Two simulated examples show that the proposed control strategies can significantly reduce the variation of an evolving disturbance process. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

Estimating three-dimensional vehicle motion in an outdoor scene using stereo image sequences

We propose a motion estimation system that uses stereo image pairs as the input data. To perform experimental work, we also obtain a sequence of outdoor stereo images taken by two metric cameras. The system consists of four main stages, which are (1) determination of point correspondences on the stereo images, (2) correction of distortions in image coordinates, (3) derivation of 3D point coordinates from 2D correspondences, and (4) estimation of motion parameters based on 3D point correspondences. For the first stage of the system, we use a four-way matching algorithm to obtain matched point on two stereo image pairs at two consecutive time instants (t_i and t_{i + 1}). Since the input data are stereo images taken by cameras, it has two types of distortions, which are (i) film distortion and (ii) lens distortion. These two distortions must be corrected before any process can be applied on the matched points. To accomplish this goal, we use (i) bilinear transform for film distortion correction and (ii) lens formulas for lens distortion correction. After correcting the distortions, the results are 2D coordinates of each matched point that can be used to derive 3D coordinates. However, due to data noise, the calculated 3D coordinates to not usually represent a consistent rigid structure that is suitable for motion estimation; therefore, we suggest a procedure to select good 3D point sets as the input for motion estimation. The procedure exploits two constraints, rigidity between different time instants and uniform point distribution across the object on the image. For the last stage, we use an algorithm to estimate the motion parameters. We also wish to know what is the effect of quantization error on the estimated results; therefore an error analysis based on quantization error is performed on the estimated motion parameters. In order to test our system, eight sets of stereo image pairs are extracted from an outdoor stereo image sequence and used as the input data. The experimental results indicate that the proposed system does provide reasonable estimated motion parameters.     

Pulse chemical vapour deposition and infiltration of pyrocarbon in model pores with rectangular cross-sections

Model straight pores with rectangular cross-section (size ranging from 60 to 320 m) have been infiltrated with pyrocarbon resulting from the cracking of C₃H₈ or CH₄ under pulse chemical vapour infiltration (P-CVI) conditions. Three main parameters control the quality of the pore infiltration: temperature and pressure, as previously known for regular CVI under isothermal/isobaric conditions (I-CVI) and, additionally, the residence time t _R, which appears to be the key parameter in P-CVI. There is a direct correlation between t _R, on the one hand, and both the PyC thickness gradient and anisotropy along the pores, on the other hand. The experimental results are explained on the basis of a qualitative model assuming two competing deposition mechanisms, depending on whether PyC is formed from small and H-rich molecules (akin to C₃H₈) (low t _R values) or from large aromatic H-poor intermediates resulting from the maturation of the gas phase (high t _R values). The use of CH₄ (more stable thermally than C₃H₈) slows down the maturation process and favours in-depth infiltration. The best infiltrations, similar to and even better than those reported for I-CVI, are achieved under low t _R, T, P conditions but require a very large number of pulses. P-CVI is an efficient way to control the microstructure of the deposit.     

Long-term oxidation kinetics of aluminide coatings on alloy steels by low temperature pack cementation process

The long-term oxidation kinetics of the P92 steel and iron aluminide diffusion coating formed on its surface by the pack cementation process have been investigated at 650 °C over a period of more than 7000 h both in 100% steam and in air under normal one atmospheric pressure by intermittent weight measurement at room temperature. X-ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) techniques were used to analyse the oxidised surfaces. For the P92 steel substrate, the scale formed by oxidation is largely magnetite (Fe₃O₄) in steam and haematite (Fe₂O₃) in air. Despite this difference in the type of oxide scales formed, it was found that the long-term oxidation kinetics of the P92 steel substrate in both steam and air can be described by a logarithmic time relationship: Δm _t = k _lln(t/t° + 1); the constants k _l and t° were subsequently determined using a closest fit process for oxidations in steam and air. For the coating, the oxide scale formed in both steam and air was Al₂O₃, which provided the long-term oxidation resistance. It was observed that the long-term oxidation kinetics of the coating in both steam and air can be best described by Δm _t = Δm ₀ + k _c t ^1/3; the rate constant k _c of oxidation in steam and air was then determined by the least squares method. For both the P92 steel substrate and coating, the rate of oxidation is faster in steam than in air at 650 °C particularly in the case of the P92 steel substrate.     

Optimal PID controller parameters for first order and second order systems with time delay using a connectionist approach

This article focuses on developing a neural controller based on a proportional integral derivative (PID) law. The main objective is to show that using neural networks represents a better alternative compared with other conventional models that were used in the past to express the tuning parameters as a function of process parameters such as process gain (K _P ), process time constants (τ₁, τ₂, etc.,) and process time delay (θ). A Levenberg-Marquardt backward propagation algorithm is used to get the required PID parameters corresponding to different types of processes. In the present study, the PID parameters for the first order plus time delay (FOPTD) and the second order plus time delay (SOPTD) are obtained. It was observed that very high R ² values between the actual PID parameters and the parameters obtained from the NN were achieved. Furthermore, the performance of PID control systems with FOPTD and SOPTD processes are applied on a number of case studies and compared with the conventional Zeigler-Nichols (Z-N) method of tuning PID controllers. Using the proposed NN controller was found to be efficient and the current method could be of potential use in control systems with gain scheduling also where the controller parameters are tuned according to a continuous gain schedule variable that changes based on different levels of process parameters.     

A control scheme for monitoring the frequency and magnitude of an event

While many control charts have been developed for monitoring the time interval (t) between the occurrences of an event, many other charts are employed to examine the magnitude (x) of the event. These two types of control charts have usually been investigated and applied separately with limited syntheses in conventional statistical process control (SPC) methods. This article presents an SPC method for simultaneously monitoring the time interval t and magnitude x. It, essentially, combines a t chart and an x chart, and is therefore referred to as a t&x chart. The new chart is more effective than an individual t chart or individual x chart for detecting the out-of-control status of the event, in particular for detecting downward shifts (sparse occurrence and/or small magnitude). More profound is that, compared with an individual t or x chart, the detection effectiveness of the t&x chart is more invariable against different types of shifts, i.e. t shift, x shift and joint shift in t and x. The t&x chart has demonstrated its potential not only for manufacturing systems, but also for non-manufacturing sectors such as supply chain management, office administration and health care industry.     

Control of the freezing interface morphology in solidification processes in the presence of natural convection

This paper presents a methodology for the solution of an inverse solidification design problem in the presence of natural convection. In particular, the boundary heat flux q₀ in the fixed mold wall, δΩ₀, is calculated such that a desired freezing front velocity and shape are obtained. As the front velocity together with the flux history q_ms on the solid side of the freezing front play a determinant role in the obtained cast structure, the potential applications of the proposed methods to the control of casting processes are enormous. The proposed technique consists of first solving a direct natural convection problem of the liquid phase in an a priori known shrinking cavity, Ω_L(t), before solving an ill-posed inverse design conduction problem in the solid phase in an a priori known growing region, Ω_S(t). The direct convection problem is used to evaluate the flux q_ml in the liquid side of the freezing front. A front tracking deforming finite element technique is employed. The flux q_ml can be used together with the Stefan condition to provide the freezing interface flux q_ms in the solid side of the front. As such, two boundary conditions (flux q_ms and freezing temperature θ_m) are especified along the (known) freezing interface δΩ_I(t). The developed design technique uses the adjoint method to calculate in L₂ the derivative of the cost functional, ∥θ_m – θ( x , t; q₀)∥, that expresses the square error between the calculated temperature θ( x , t; q₀) in the solid phase along δΩ_I(t) and the given melting temperature. The minimization of this cost functional is performed by the conjugate gradient method via the solutions of the direct, sensitivity and adjoint problems. A front tracking finite element technique is employed in this inverse analysis. Finally, an example is presented for the solidification of a superheated incompressible liquid aluminium, where the effects of natural convection in the moving interface shape are controlled with a proper adjustment of the cooling boundary conditions.     

Efficient bivariate EWMA charts for monitoring process dispersion

To ensure high quality standards of a process, the application of control charts to monitor process performance has become a regular routine. Multivariate charts are a preferred choice in the presence of more than one process variable. In this article, we proposed a set of bivariate exponentially weighted moving average (EWMA) charts for monitoring the process dispersion. These charts are formulated based on a variety of dispersion statistics considering normal and non-normal bivariate parent distributions. The performance of the different bivariate EWMA dispersion charts is evaluated and compared using the average run length and extra quadratic loss criteria. For the bivariate normal process, the comparisons revealed that the EWMA chart based on the maximum standard deviation (SMAX_E) was the most efficient chart when the shift occurred in one quality variable. It also performed well when the sample size is small and the shift occurred in both quality variables. The EWMA chart based on the maximum average absolute deviation from median (MDMAX_E) performed better than the other charts in most situations when the shift occurred in the covariance matrix for the bivariate non-normal processes. An illustrative example is also presented to show the working of the charts.     

On the reverse short‐channel effect and threshold voltage roll‐off controls for 90 nm node MOSFETs

Abstract

In order to let device designers tune the short channel behavior of MOSFETs, a method is proposed in this work to demonstrate how to use LDD (lightly doped drain) and pocket implants to control RSCE (reverse short channel effect) and threshold voltage (V_t ) roll‐off. The method is based on the process parameters and silicon data of the 90 nm node technology of UMC (United Microelectronics Corporation). With the help of computers, 17 different process conditions of 8 different gate lengths were simulated using ISE TCAD to collect V_t variation data. Four characteristics representing the short channel behaviors of the MOSFETs were designed and extracted from the simulated data. Their empirical equations were also established subsequently. After verification, those mathematical models were demonstrated to help device designers in choosing the most suitable LDD and pocket implant parameters to generate required V_t characteristics.