Integrating SPC and EPC Methods for Quality Improvement. Abstract: This term paper are mainly based on the research paper, which was written by Wei Jiang and John V. Farr. Process variations are classified into common cause and assignable cause variations in the manufacturing and services industries. Firstly, the authors pointed out attention, that Common cause variations are inherent in a process and can be described implicitly or explicitly by stochastic methods. Assignable cause variations are unexpected and unpredictable and can occur before the commencement of any special events.

Statistical process control (SPC) methods has been successfully utilized in discrete parts industry through identification and elimination of the assignable cause of variations, while engineering process control methods (EPC) are widely employed in continuous process industry to reduce common cause variations. This paper provides a review of various control techniques and develops a unified framework to model the relationships among these well-known methods in EPC, SPC, and integrated EPC/SPC, which have been successfully implement in the semiconductor manufacturing.

Keywords: Automatic process control, chemical mechanical planarization, control charts, run-to run control, semiconductor manufacturing. Introduction Two categories of research and applications have been developed independetely to achieve process control. Statistical process control (SPC) uses measurements to monitor the process and look for major changes in order to eliminate the root causes of the changes. Statistical process control has found widespread application in the manufacturing of discrete parts industries for process improvement, process parameter estimation, and process capability determination.

Engineering process control (EPC), on the other hand, uses measurements to adjust the process inputs intended to bring the process outputs closer to targets. By using feedback/feedforward controllers for process regulation, EPS has gained a lot of popularity in continuous process industries. Practitioners of SPC argue that because of the complexity of most manufacturing process, EPC methods can over-control a process and increase process variability before decreasing it. Moreover, important quality events may be masked by frequent adjustments and become ifficult to be detected and removed. Conversely, practitioners of EPC criticize SPC method as being exclusive of the opportunities for reducing the variability in the process output. Traditional SPC methods generate many false alarms and fail to discriminate quality deterioration from the in-control state defined by SPC rules. Recently EPC and SPC has been integrated in the semiconductor manufacturing and resulted in a tremendous improvement of industrial efficiency. Box and Luceno [13] refer to EPC activities as process adjustment and SPC activities as process monitoring.

While the two approaches have been applied independently in different areas for decades, the relationship between them has not been clearly explored yet. Section 2 of this paper reviews various SPC and EPC techniques for industrial process control. Section 3 presents the integrated model of EPC/SPC. Section 4 reviews several cutting-edge statistical process control methods for monitoring auto correlated and EPC processes. Section 5 presents a case study of a chemical mechanical planarization (CMP) process to demonstrate the utility of the EPC/SPC method.

Section 6 presents some concluding remarks. Two Process Control Approaches Engineering Process Control Engineering process control is a popular strategy for process optimization and improvement. It describes the manufacturing or information manipulation process as an input-output system where the input variables (recipes) can be manipulated (or adjusted) to counteract the uncontrollable disturbances to maintain the process target. The output of the process can be measurements of the final product or critical in-process variables that need to be controlled.

In general, without any control actions (adjustment of inputs), the output may shift or drift away from the desired quality target due to disturbances (Box and Luceno). These disturbances are usually not white noise but usually exhibit a dependence on past values. Thus, it is possible to anticipate the process behavior based on past observations and to control the process and outputs by adjusting the input variables. As the name implies, EPC requires a process model. A simple but useful process model that describes a linear relationship between process inputs and outputs is (Vander Wiel et al. , e_t= gx_(t-1)+D_t Where e_t and Xt represent the process output and input (control) deviations from target, Dt represents the process disturbances which pass through part of the system and continue to affect the output, and g is the process gain that measures the impact of input control to process outputs. Another process control strategy widely adopted in industry is feedback control, which uses deviations of the output from the target (set-point) to indicate that a disturbance has upset the process and calculate the amount of adjustment.

Figure 1 presents a typical process with a feedback control scheme. Since deviations or errors are used to compensate for the disturbance, the compensation scheme is essentially two-fold. It is not perfect in maintaining the process on target since any corrective action is taken only when the process deviates from its target first. On the other hand, as soon as the process output deviates from the target, corrective action is initiated regardless of the source and type of disturbances.

It is important to note that feedback scheme is beneficial only if there is autocorrelations among the outputs. To minimize the variance of the output deviations from the quality target, two types of controllers are popularly used. Minimum Mean Square Error (MMSE) Control. From the time seris transfer function model that represents the relationship between the input x_t and output e_t, Box develop the MMSE controller X_t = (L_1 (B) L_3 (B))/(L_2 (B) L_4 (B)) e_t Where B is backshift operator, L_1 (B),L_2 (B),L_3 (B),L_4 (B) are polynomials in B which are relevant to the process parameters.

Theoretically, if the process can be accurately estimated, the output can be reduces to a white noise by the MMSE controller. Proportional Integral Derivative (PID) Control. It is a special class of the Autoregressive Integrated Moving Average (ARIMA) control model. The three mode PID controller equation is formed by summing three methods of control, proportional (P), integral (I), and derivative (D). The discrete version of the PID controller is x_t=k_0+k_p e_t+k_1 ? _(i=0)^? -e_(t-1) +k_D (e_t-e_(t-1)) , where k_0 is always set to zero.

The MMSE control is optimal in terms of minimizing mean squared residual errors. However, this is only true for the idealized situation in which the model and model parameters are known exactly. Statistical Process Control The basic idea in SPC is a binary view of the state of a process, i. e. , either it is running satisfactorily or not. As developed by Shewhart [51], the two states are classified as common cause of variations and assignable/special cause of variations, respectively. Common Cause Variations.

Common cause of variations is the basic assumption on which the SPC methods are based. It assumes that the sample comes from a known probability distribution, and the process is classified as â€śstatisticallyâ€ť in-control. Special Cause Variations. Based on Shewhartâ€™s classification, Deming [23] argues the special cause of variations as â€śsomething special, not part of the system of common causesâ€ť, should be identified and removed from the root. In many industrial applications, the process mean is often subject to occasional abrupt changes, i. e ? _t=? +? _t where ? s the mean target, and ? _t is zero for t? t_0. When a drift is present, the process mean may follow a linear trend. The goal of SPC charts is to detect the change point t0 as quickly as possible so that corrective actions can be taken before quality deteriorates and defective units are produced. Among many others, the Shewhart chart, the exponentially weighted moving average (EWMA) chart, and the cumulative sum (CUSUM) chart are three important and widely used control charts. Shewhart Chart. Process observations are tested against control limits |e_t |;Lâ€˘? e, where ? _e is the standard deviation of the chart statistic estimated by moving range and sample standard deviation. L is pre-specified to maintain particular probability properties. EWMA Chart. Roberts proposes to monitor the EWMA statistic of the process observation, z_t=? _(i=0)^? -? _i e_(t-1), where z_t=(1-? ) z_(t-1)+? e_t Where z_0 is zero or the process mean. CUSUM Chart. The tabular of a CUSUM chart consists of of two quantities, z_t^+=max[0,e_t+z_(t-1)^+-K],z_t^-=min[0,-e_t+z_(t-1)^â€“K] where z_0^+=z_0^-=0.

Although the purpose of these procedures is to detect process changes, we know that they may signal problems even when the process remains on target due to the randomness of observations. Integtration EPC/SPC Run-to-Run (R2R) Control The relationship between EPC and SPC through prediction has been recently explored in many industrial applications. To make an appropriate selection between the two approaches in practice, it is important to identify disturbance structures and strengths of the two control methods to influence the process.

Here we present four categories of on-going research and application of the two quality control approaches. If a process is not correlated, there is no need to employ EPC schemes and traditional SPC control charts should be used for identifying assignable cause variations; When data are correlated, the possibility of employing EPC techniques should be examined and SPC control charts are called for to monitor autocorrelated processes if no feasible EPC controller exists;

If appropriate controllers are available, EPC control schemes can be employed to compensate for the autocorrelated disturbance. However, no single EPC controller system can compensate for all kinds of potential variations; and To identify and understand the cause of process changes, a unified control framework should be applied to regulate a process using feedback control while using the diagnostic capability of SPC to detect unexpected disturbances to the process. The R2R controller is a model-based process ontrol system in which the controller provides recipes (inputs) based on post-process measurements at the beginning of each run, updates the process model according to the measurements at the end of the run, and provides new recipes for the next run of the process. It generally does not modify recipes during a run because obtaining real-time information is usually very expensive in a semiconductor process and frequent changes of inputs to the process may increase the variability of the processâ€™s outputs and even make the process unstable. A block diagram of such a R2R controller is shown in Figure 2.

A good R2R controller should be able to compensate for various disturbances, such as process drifts, process shifts due to maintenance or other factors, model or sensor errors, etc. Diagnostic module. It is generalized SPC to distinguish between slow drifts and rapid shifts and decide if the process is running in accordance with the current process model. Gradual model. This module uses historical data lo linearly update process models by giving less weight to old data. Rapid module. This module quickly updates the process model based on changes detected by te diagnostic module.

Significant research on the design of adaptive and robust controllers for the gradual control module exists. Double exponential forecasting method (Bulter and Stefani; Castillo) has been proposed using a Predictor Corrector Controller (PCC) to eliminate the impact of machine and process drift. Other control methods include Optimized Adaptive Quality Control (Castillo and Yeh), Kalman filter (Palmer et al. ), set-value methods (Baras and Patel), and machine learning methods such as Artificial Neural Network (Smith and Boning). SPC Methods for EPC/SPC Systems

To develop efficient tools for monitoring EPC/SPC systems, it is important to understand the impact of autocorrelation on the performance of control charts. Many authors have found that the presence of autocorrelation has a substantial and detrimental effect on the statistical properties of control charts developed under the i. i. d. assumption. One common SPC strategy for monitoring autocorrelated processes is to modify the control limits of traditional charts and then to apply the modified charts to the original autocorrelated data.

Vasilopoulos and Stamboulis provide an adjustment of control limits for Shewhart charts when monitoring autocorrelated processes. Johnson and Bagshaw and Bagshaw and Johnson provide the factor to adjust the critical boundary of CUSUM charts to correct the test procedure in the presence of correlation. 4. 1. Forecast-Based Monitoring Methods A natural idea of monitoring an autocorrelated sequence is to transform the sequence into an i. i. d. or near i. i. d. sequence so that the â€śinnovationsâ€ť can be monitored by the traditional control charts developed for i. i. d. observations.

This family of control chart is called the forecast-based residual chart. Alwan and Roberts [2] first propose to use Special Cause Chart (SCC) to monitor MMSE prediction errors. For simplicity, assume the underlying process {Xt} follows an ARMA(1,1) process, i. e. , x_t-uX_(t-1)=? _t-v? _(t-1) Where u and v are scalar constant and ? _t is white noise. The EWMA predictor is another alternative proposed by Montgomery and Mastrangelo (M-M chart). Jiang et al. further generalize the use of proportional-integrated-derivative (PID) predictors with subsequent monitoring of the prediction errors. . 2. Generalized Likelihood Ratio Test (GLRT) Metods Forecast-based residual methods involve only a single testing statistic and often suffers from the problem of a narrow â€świndow of opportunityâ€ť when the underlying process is positively correlated (Vander Wiel). For example, for monitoring an AR(1) process with ? 1=0. 9, a shift with size =1 will reduce to ? = 0. 1 from the second run after the shift occurrence due to forecast recovery. If an SCC missed the detection in the first place, it will become very difficult to signal since the mean deviation shrinks to only 10% of the original size.

If the shift occurrence time was known, the â€świndow of opportunityâ€ť problem is expected to be alleviated by including more historical observations/residuals in the statistical hypothesis test. 4. 3. Monitoring EPC/SPC Systems Control charts developed for monitoring autocorrelated observations shed lights to monitoring integrated EPC/SPC control systems. Forecast-based methods, assignable causes have an effect that is always contaminated by the EPC control action and result in a small â€świndow of opportunityâ€ť for detection (Vander Wiel).

As an alternative, some authors suggest that monitoring the EPC control action may improve the chance of detection (Box and Kramer; Capilla et al. ). Kourti et al. propose a method of monitoring process outputs conditional on the inputs or other changing process parameters. Jiang and Tsui and Tsung and Tsui demonstrate that monitoring the control action may be more efficient than monitoring the output of the EPC/SPC system for some autocorrelated processes and vice versa for others. To integrate the information provided by process inputs and outputs, Tsung et al. evelop multivariate techniques based on Hotellingâ€™s T^2 chart and Bonferroni approach. A Chemical-Mechanical Planarization Example Chemical-Mechanical Planarization (CMP) of dielectric films is basically a surface planarization method in which a wafer is affixed to a carrier and pressed face-down on a rotating platen holding a polishing pad (Zantye et al. ). This enabling technology is used for the manufacturing of integrated circuits with interconnect geometries of less than 0. 18 micron. Silica-based alkaline slurry is applied during polishing thus providing a chemical and mechanical component to the polishing process.

The primary function of CMP is to smooth a nominally macroscopically flat wafer at the feature (or micro-level), i. e. , planarize features. The post-polish nonuniformity (NU), measured by the ratio of the standard deviation of the post-polish wafer thickness to the average post-polish wafer thickness, is usually required to be less than 5% variation in film thickness across wafer. Therefore, to evenly planarize features across the whole wafer it is crucial to have a uniform material removal rate (RR) across the wafer.

This removal rate uniformity, measured by the within wafer non uniformity, ensures that the entire wafer is uniformly reduced in height. Figure 4 presents an experiment of material removal rate under a R2R control system. Due to the nonuniformity of incoming dielectric, the output wafer nonuniformity may drift away from target if without EPC/SPC control. In addition, a wear problem starts from the 51st run on the polish pad. Now a EWMA (I) controller is employed to adjust the polish rate and the CMP nonuniformity of material removal rate is found closer to target, 1. %, before the wear problem occurs but more than 2% afterwards. Note that, although the EWMA controller is designed to reduce incoming dielectric variations, the severity of the polish pad deterioration is also weakened (the drift has been reduced to a step shift). If a Shewhart chart is applied to monitor the EPC-CMP process, a signal will be triggered at the 54th run and the polish rate model can be updated to take into consideration the polish pad deterioration. The nonuniformity can be always maintained at 1. % whatever the pad wear problem happens or not, showing the effectiveness of SPC methods in improving product quality. Concluding Remarks The paper provides a review of current EPC and SPC techniques and their applications in parts and process industries for quality improvement. The two classes of methods can be linked and integrated in a unified quality control framework. The case study demonstrates the effectiveness of the EPC/SPC integration. Authors also paid our attention about the crucial task of monitoring autocorrelated processes and EPC systems.

Integrating SPC and EPC Methods for Quality Improvement. Abstract: This term paper are mainly based on the research paper, which was written by Wei Jiang and John V. Farr. Process variations are classified into common cause and assignable cause variations in the manufacturing and services industries. Firstly, the authors pointed out attention, that Common cause variations are inherent in a process and can be described implicitly or explicitly by stochastic methods. Assignable cause variations are unexpected and unpredictable and can occur before the commencement of any special events.

Statistical process control (SPC) methods has been successfully utilized in discrete parts industry through identification and elimination of the assignable cause of variations, while engineering process control methods (EPC) are widely employed in continuous process industry to reduce common cause variations. This paper provides a review of various control techniques and develops a unified framework to model the relationships among these well-known methods in EPC, SPC, and integrated EPC/SPC, which have been successfully implement in the semiconductor manufacturing.

Keywords: Automatic process control, chemical mechanical planarization, control charts, run-to run control, semiconductor manufacturing. Introduction Two categories of research and applications have been developed independetely to achieve process control. Statistical process control (SPC) uses measurements to monitor the process and look for major changes in order to eliminate the root causes of the changes. Statistical process control has found widespread application in the manufacturing of discrete parts industries for process improvement, process parameter estimation, and process capability determination.

Engineering process control (EPC), on the other hand, uses measurements to adjust the process inputs intended to bring the process outputs closer to targets. By using feedback/feedforward controllers for process regulation, EPS has gained a lot of popularity in continuous process industries. Practitioners of SPC argue that because of the complexity of most manufacturing process, EPC methods can over-control a process and increase process variability before decreasing it. Moreover, important quality events may be masked by frequent adjustments and become difficult to be detected and removed.

Conversely, practitioners of EPC criticize SPC method as being exclusive of the opportunities for reducing the variability in the process output. Traditional SPC methods generate many false alarms and fail to discriminate quality deterioration from the in-control state defined by SPC rules. Recently EPC and SPC has been integrated in the semiconductor manufacturing and resulted in a tremendous improvement of industrial efficiency. Box and Luceno [13] refer to EPC activities as process adjustment and SPC activities as process monitoring.

While the two approaches have been applied independently in different areas for decades, the relationship between them has not been clearly explored yet. Section 2 of this paper reviews various SPC and EPC techniques for industrial process control. Section 3 presents the integrated model of EPC/SPC. Section 4 reviews several cutting-edge statistical process control methods for monitoring auto correlated and EPC processes. Section 5 presents a case study of a chemical mechanical planarization (CMP) process to demonstrate the utility of the EPC/SPC method.

Section 6 presents some concluding remarks. Two Process Control Approaches Engineering Process Control Engineering process control is a popular strategy for process optimization and improvement. It describes the manufacturing or information manipulation process as an input-output system where the input variables (recipes) can be manipulated (or adjusted) to counteract the uncontrollable disturbances to maintain the process target. The output of the process can be measurements of the final product or critical in-process variables that need to be controlled.

In general, without any control actions (adjustment of inputs), the output may shift or drift away from the desired quality target due to disturbances (Box and Luceno). These disturbances are usually not white noise but usually exhibit a dependence on past values. Thus, it is possible to anticipate the process behavior based on past observations and to control the process and outputs by adjusting the input variables. As the name implies, EPC requires a process model. A simple but useful process model that describes a linear relationship between process inputs and outputs is (Vander Wiel et al. , e_t= gx_(t-1)+D_t Where e_t and Xt represent the process output and input (control) deviations from target, Dt represents the process disturbances which pass through part of the system and continue to affect the output, and g is the process gain that measures the impact of input control to process outputs. Another process control strategy widely adopted in industry is feedback control, which uses deviations of the output from the target (set-point) to indicate that a disturbance has upset the process and calculate the amount of adjustment.

Figure 1 presents a typical process with a feedback control scheme. Since deviations or errors are used to compensate for the disturbance, the compensation scheme is essentially two-fold. It is not perfect in maintaining the process on target since any corrective action is taken only when the process deviates from its target first. On the other hand, as soon as the process output deviates from the target, corrective action is initiated regardless of the source and type of disturbances. It is important to note that feedback scheme is beneficial only if there is autocorrelations among the outputs.

To minimize the variance of the output deviations from the quality target, two types of controllers are popularly used. Minimum Mean Square Error (MMSE) Control. From the time seris transfer function model that represents the relationship between the input x_t and output e_t, Box develop the MMSE controller X_t = (L_1 (B) L_3 (B))/(L_2 (B) L_4 (B)) e_t Where B is backshift operator, L_1 (B),L_2 (B),L_3 (B),L_4 (B) are polynomials in B which are relevant to the process parameters. Theoretically, if the process can be accurately estimated, the output can be reduces to a white noise by the MMSE controller.

Proportional Integral Derivative (PID) Control. It is a special class of the Autoregressive Integrated Moving Average (ARIMA) control model. The three mode PID controller equation is formed by summing three methods of control, proportional (P), integral (I), and derivative (D). The discrete version of the PID controller is x_t=k_0+k_p e_t+k_1 ? _(i=0)^? -e_(t-1) +k_D (e_t-e_(t-1)) , where k_0 is always set to zero. The MMSE control is optimal in terms of minimizing mean squared residual errors. However, this is only true for the idealized situation in which the model and model parameters are known exactly.

Statistical Process Control The basic idea in SPC is a binary view of the state of a process, i. e. , either it is running satisfactorily or not. As developed by Shewhart [51], the two states are classified as common cause of variations and assignable/special cause of variations, respectively. Common Cause Variations. Common cause of variations is the basic assumption on which the SPC methods are based. It assumes that the sample comes from a known probability distribution, and the process is classified as â€śstatisticallyâ€ť in-control. Special Cause Variations.

Based on Shewhartâ€™s classification, Deming [23] argues the special cause of variations as â€śsomething special, not part of the system of common causesâ€ť, should be identified and removed from the root. In many industrial applications, the process mean is often subject to occasional abrupt changes, i. e ? _t=? +? _t where ? is the mean target, and ? _t is zero for t? t_0. When a drift is present, the process mean may follow a linear trend. The goal of SPC charts is to detect the change point t0 as quickly as possible so that corrective actions can be taken before quality deteriorates and defective units are produced.

Among many others, the Shewhart chart, the exponentially weighted moving average (EWMA) chart, and the cumulative sum (CUSUM) chart are three important and widely used control charts. Shewhart Chart. Process observations are tested against control limits |e_t |>Lâ€˘? _e, where ? _e is the standard deviation of the chart statistic estimated by moving range and sample standard deviation. L is pre-specified to maintain particular probability properties. EWMA Chart. Roberts proposes to monitor the EWMA statistic of the process observation, z_t=? _(i=0)^? -? _i e_(t-1), where z_t=(1-? z_(t-1)+? e_t Where z_0 is zero or the process mean. CUSUM Chart. The tabular of a CUSUM chart consists of of two quantities, z_t^+=max[0,e_t+z_(t-1)^+-K],z_t^-=min[0,-e_t+z_(t-1)^â€“K] where z_0^+=z_0^-=0. Although the purpose of these procedures is to detect process changes, we know that they may signal problems even when the process remains on target due to the randomness of observations. Integtration EPC/SPC Run-to-Run (R2R) Control The relationship between EPC and SPC through prediction has been recently explored in many industrial applications. To make an appropriate selection etween the two approaches in practice, it is important to identify disturbance structures and strengths of the two control methods to influence the process. Here we present four categories of on-going research and application of the two quality control approaches. If a process is not correlated, there is no need to employ EPC schemes and traditional SPC control charts should be used for identifying assignable cause variations; When data are correlated, the possibility of employing EPC techniques should be examined and SPC control charts are called for to monitor autocorrelated processes if no feasible EPC controller exists;

If appropriate controllers are available, EPC control schemes can be employed to compensate for the autocorrelated disturbance. However, no single EPC controller system can compensate for all kinds of potential variations; and To identify and understand the cause of process changes, a unified control framework should be applied to regulate a process using feedback control while using the diagnostic capability of SPC to detect unexpected disturbances to the process.

The R2R controller is a model-based process control system in which the controller provides recipes (inputs) based on post-process measurements at the beginning of each run, updates the process model according to the measurements at the end of the run, and provides new recipes for the next run of the process. It generally does not modify recipes during a run because obtaining real-time information is usually very expensive in a semiconductor process and frequent changes of inputs to the process may increase the variability of the processâ€™s outputs and even make the process unstable.

A block diagram of such a R2R controller is shown in Figure 2. A good R2R controller should be able to compensate for various disturbances, such as process drifts, process shifts due to maintenance or other factors, model or sensor errors, etc. Diagnostic module. It is generalized SPC to distinguish between slow drifts and rapid shifts and decide if the process is running in accordance with the current process model. Gradual model. This module uses historical data lo linearly update process models by giving less weight to old data. Rapid module.

This module quickly updates the process model based on changes detected by te diagnostic module. Significant research on the design of adaptive and robust controllers for the gradual control module exists. Double exponential forecasting method (Bulter and Stefani; Castillo) has been proposed using a Predictor Corrector Controller (PCC) to eliminate the impact of machine and process drift. Other control methods include Optimized Adaptive Quality Control (Castillo and Yeh), Kalman filter (Palmer et al. ), set-value methods (Baras and Patel), and machine learning methods such as Artificial Neural Network (Smith and Boning).

SPC Methods for EPC/SPC Systems To develop efficient tools for monitoring EPC/SPC systems, it is important to understand the impact of autocorrelation on the performance of control charts. Many authors have found that the presence of autocorrelation has a substantial and detrimental effect on the statistical properties of control charts developed under the i. i. d. assumption. One common SPC strategy for monitoring autocorrelated processes is to modify the control limits of traditional charts and then to apply the modified charts to the original autocorrelated data.

Vasilopoulos and Stamboulis provide an adjustment of control limits for Shewhart charts when monitoring autocorrelated processes. Johnson and Bagshaw and Bagshaw and Johnson provide the factor to adjust the critical boundary of CUSUM charts to correct the test procedure in the presence of correlation. 4. 1. Forecast-Based Monitoring Methods A natural idea of monitoring an autocorrelated sequence is to transform the sequence into an i. i. d. or near i. i. d. sequence so that the â€śinnovationsâ€ť can be monitored by the traditional control charts developed for i. i. d. observations.

This family of control chart is called the forecast-based residual chart. Alwan and Roberts [2] first propose to use Special Cause Chart (SCC) to monitor MMSE prediction errors. For simplicity, assume the underlying process {Xt} follows an ARMA(1,1) process, i. e. , x_t-uX_(t-1)=? _t-v? _(t-1) Where u and v are scalar constant and ? _t is white noise. The EWMA predictor is another alternative proposed by Montgomery and Mastrangelo (M-M chart). Jiang et al. further generalize the use of proportional-integrated-derivative (PID) predictors with subsequent monitoring of the prediction errors. 4. . Generalized Likelihood Ratio Test (GLRT) Metods Forecast-based residual methods involve only a single testing statistic and often suffers from the problem of a narrow â€świndow of opportunityâ€ť when the underlying process is positively correlated (Vander Wiel). For example, for monitoring an AR(1) process with ? 1=0. 9, a shift with size =1 will reduce to ? = 0. 1 from the second run after the shift occurrence due to forecast recovery. If an SCC missed the detection in the first place, it will become very difficult to signal since the mean deviation shrinks to only 10% of the original size.

If the shift occurrence time was known, the â€świndow of opportunityâ€ť problem is expected to be alleviated by including more historical observations/residuals in the statistical hypothesis test. 4. 3. Monitoring EPC/SPC Systems Control charts developed for monitoring autocorrelated observations shed lights to monitoring integrated EPC/SPC control systems. Forecast-based methods, assignable causes have an effect that is always contaminated by the EPC control action and result in a small â€świndow of opportunityâ€ť for detection (Vander Wiel).

As an alternative, some authors suggest that monitoring the EPC control action may improve the chance of detection (Box and Kramer; Capilla et al. ). Kourti et al. propose a method of monitoring process outputs conditional on the inputs or other changing process parameters. Jiang and Tsui and Tsung and Tsui demonstrate that monitoring the control action may be more efficient than monitoring the output of the EPC/SPC system for some autocorrelated processes and vice versa for others. To integrate the information provided by process inputs and outputs, Tsung et al. evelop multivariate techniques based on Hotellingâ€™s T^2 chart and Bonferroni approach. A Chemical-Mechanical Planarization Example Chemical-Mechanical Planarization (CMP) of dielectric films is basically a surface planarization method in which a wafer is affixed to a carrier and pressed face-down on a rotating platen holding a polishing pad (Zantye et al. ). This enabling technology is used for the manufacturing of integrated circuits with interconnect geometries of less than 0. 18 micron. Silica-based alkaline slurry is applied during polishing thus providing a chemical and mechanical component to the polishing process.

The primary function of CMP is to smooth a nominally macroscopically flat wafer at the feature (or micro-level), i. e. , planarize features. The post-polish nonuniformity (NU), measured by the ratio of the standard deviation of the post-polish wafer thickness to the average post-polish wafer thickness, is usually required to be less than 5% variation in film thickness across wafer. Therefore, to evenly planarize features across the whole wafer it is crucial to have a uniform material removal rate (RR) across the wafer.

This removal rate uniformity, measured by the within wafer non uniformity, ensures that the entire wafer is uniformly reduced in height. Figure 4 presents an experiment of material removal rate under a R2R control system. Due to the nonuniformity of incoming dielectric, the output wafer nonuniformity may drift away from target if without EPC/SPC control. In addition, a wear problem starts from the 51st run on the polish pad. Now a EWMA (I) controller is employed to adjust the polish rate and the CMP nonuniformity of material removal rate is found closer to target, 1. %, before the wear problem occurs but more than 2% afterwards. Note that, although the EWMA controller is designed to reduce incoming dielectric variations, the severity of the polish pad deterioration is also weakened (the drift has been reduced to a step shift). If a Shewhart chart is applied to monitor the EPC-CMP process, a signal will be triggered at the 54th run and the polish rate model can be updated to take into consideration the polish pad deterioration. The nonuniformity can be always maintained at 1. % whatever the pad wear problem happens or not, showing the effectiveness of SPC methods in improving product quality. Concluding Remarks The paper provides a review of current EPC and SPC techniques and their applications in parts and process industries for quality improvement. The two classes of methods can be linked and integrated in a unified quality control framework. The case study demonstrates the effectiveness of the EPC/SPC integration. Authors also paid our attention about the crucial task of monitoring autocorrelated processes and EPC systems.