Monitoring of Manufacturing Process Conditions with Baseline Changes Using Generalized Regression

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1 Proceedings of the 10th International Conference on Frontiers of Design and Manufacturing June 10~1, 01 Monitoring of Manufacturing Process Conditions with Baseline Changes Using Generalized Regression Saumuy Suriano Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA Hui Wang Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA S. Jack Hu 1, 1 Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI, USA Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI, USA Abstract: Monitoring part-to-part variations in manufacturing processes is important in maintaining product quality. Common monitoring technique use statistical methods to establish a process baseline which is compared with production data to detect abnormal variations. However, the process baseline could change due to process adjustment and maintenance. Reestablishment of the baseline needs a collection of in-control data and could be infeasible or time consuming. Taking advantages of in-plant process history information and parallel manufacturing operations, this paper proposes a selflearning methodology to efficiently monitor process variations with baseline changes. Initial data samples are collected from one machine to understand process normal behaviors via generalized regression that links quality characteristics to both categorical and continuous process variables. This relationship is used to monitor the remaining parallel machines. A case study on an automotive process demonstrates that the methodology accurately monitors the process with no prior process knowledge and a small initial sample size. expected that changing the part type will change the average flatness. To reduce excessive false alarms, the baseline should be updated by collecting in-control data under new conditions. But the reestablishment of process conditions could be infeasible or time-consuming. It is necessary to develop a methodology that incorporates these normal changes (which might have either a cyclical effect or a sudden mean jump) into the process baseline for process monitoring. Avg. Flatness Tool change Avg. Flatness Part type change Keywords: statistical process control, process monitoring, generalized regression Months Months 1 Introduction Monitoring part-to-part variations is critical to product quality. Common methods such as quality control charts use historical data of quality characteristics to build a process baseline which is compared with measurements from production lines to evaluate the process repeatability/consistency. However, manufacturing processes are constantly undergoing changes which affect the process output. For example, in a machining operation changes in dimensional quality can be due to known effects, such as preventive maintenance, tool change, tool wear etc. These changes are part of the day to day operation in the manufacturing floor. In Fig 1, the left panel shows the effect of tool life on average flatness whereby the surface flatness (range of surface height) normally increases as the tool wears. The right panel of Fig. 1 shows an upwards mean shift in the average flatness due to a part type change. Ignoring this process knowledge would result in an out-of-control condition detected, even though this is a normal process change and it Figure 1. Avg. Flatness vs. Time Researchers have proposed various methods to monitor a quality output variable that is affected by external process variables. There are two main approaches to the monitoring of an output variable under the influence of input variables: regression control charts and time series based control charts. A brief discussion of each method is as follows. Regression control charts have been used in a variety of applications in literature. The main premise is that the output variable can be related to the input variable through a linear regression such that Y i ixi, (1) where Y is the output variable, α is a constant, i is the number of input variables, X i is the ith variable, β i is a least squares coefficient attributed to the ith variable, and ε is the residual. The assumptions of this model are that X is normally distributed, and ε is normally and independently distributed 1

2 with mean zero and constant variance. Mandel (1989) used a regression control chart where the control limits are establish at twice the standard deviation of the estimated output value. Skinner et al. (003) and Jearkpaporn et al. (003), amongst others, have expanded on this topic by relaxing the normality assumption of the input and output variables and fitting a generalized linear model for exponential data. One of the most common applications for the use of the regression control chart is to monitor multi-stage manufacturing processes, where the quality at one operation is affected by the upstream operations. Hawkins (1991, 1993) introduced quality control based on multivariate linear regression to monitor multi-stage processes. Further research and examples of the application of the multi-stage monitoring by regression can be found in Rao, et al. (1996), and Hauck et al. (1999), Zantek et al. (00) and Xiang and Tsung (008). While regression approaches are useful, establishing the relationship between the output and input variables can be time consuming and require a large amount of data to establish the normal process baseline. Time series approaches involve the use of previous information to account for autocorrelated data structures. This assumes that the output variable is influenced by time. The most common approaches are the exponentially weighted moving average chart (EWMA) (Johnson and Wichern, 00) and the autoregressive moving average model (ARMA) such as proposed by Jiang et al. (000). These approaches usually only address the difficulty in monitoring data with a correlation structure, but fail to incorporate the engineering knowledge into the process control strategy. In summary, time series and regression charts have been well researched and developed in the past. However, these methods are data driven and in practice there are many difficulties to implementing such a chart. The estimation of stable and in-control regression coefficients can be difficult. In some process, the relationship between the quality variable and the inputs is not well documented, and a sample size over the life cycle of the process variable might take a long time to observe. For example, in milling processes for aluminum alloy parts, it takes up to a year to observe the tool wear cycle of the process. Additionally, nowadays manufacturing plants collect multiple process history information on a regular basis but this history has not been well utilized for monitoring. The process information may include categorical process variables such as part flow through machines, part types, and tool types, as well as continuous variables such as tool life. These variables present opportunities for establishing baselines and reducing false alarms. In this paper a self-learning methodology is proposed to monitor output variables affected by process variables in a parallel machining operation. Initial data samples are collected from one machine to understand process normal behaviors via generalized regression that links quality characteristics to both categorical and continuous process variables. This relationship is used to monitor the remaining parallel machines. Section of the paper discusses the proposed selflearning methodology. Section 3 conducts a case study of process monitoring based on real data from a Ford plant, and Section 4 discusses the conclusions and possible extensions of the research. Generalized Regression Based Process Monitoring In this method, it is assumed that process history information is collected automatically by an in-plant computer system and is stored in databases. The methodology has two main steps as seen in Figure : variable selection and model fitting, regression parameter and control limit estimation and monitoring. Step 1. Establishing relationship between process outputs and inputs No Data collection: Find significant variables through regression Select master machine: control limits based on master regression Monitor slave machines Process change? Yes Change regression inputs Figure. Monitoring methodology Step. Process Monitoring Process Relationships established? Use regression to monitor all machine residuals Process change? Change regression inputs In the first step, an initial data sample is collected for all of the parallel machines. A generalized linear regression is used to determine which of the collected input variables are significant. The generalized linear regression was chosen to assess input variable significance since some of the process input variables (such as machine or tool type) may be categorical. In the second step, control limits are established based on the regression. In the ideal scenario, each of the machines could be monitored independently; however a large amount of in-control training data from part measurements are required. To reduce the data collection, one machine is chosen to be the master while the slave machines can be monitored using the control limits from the master. In the third step, the residuals from the generalized linear regression for the slave machines are to be monitored. Further data collection occurs for the master machine and the regression is re-fit to minimize the residual sum of squares (RSS). If one of the machine input parameters

3 changes, all that is necessary is to switch the regression inputs and monitor the resulting residuals. Data collection on the master continues until enough data has been collected to characterize the relationship between the outputs and the inputs. Then, this final generalized regression is used to monitor all machines. The following sections detail each of the steps..1 Variable selection and control limit estimation The selection of the significant variables is critical, as the model has to appropriately reflect process variation. Although many significant correlations may be found linking input variables to output variables, causality is not necessarily implied by having a good regression fit. Therefore, careful model variable selection is necessary, and should be done by engineers with knowledge of the process physics. The proposed steps for variable selection are shown in Figure 1 and are detailed below: Step 0. Identify potential key process input and output variables based on process knowledge. Step 1. Measure and collect initial variables until a sufficient sample is collected from any of all the parallel machines. It is recommended that the sample size for each variable be at least 30, and that the input variable will be observed for at least 0% of the variable s life cycle or operating range. Step. Fit several candidate regression functions (linear, piecewise linear, exponential, quadratic, etc) such that n y, () 0 i x i i1 where y is the critical process output variable, x i, i=1 n are the n input variables that significantly contribute to the variation of y. The input variables can be either continuous or categorical variables. For categorical variables (e.g. machine number) with k levels, the output variable can be coded using k-1 dummy variables which can take on the values of (0,1). Step 3. For each regression model, calculate the residuals such that RSS p i k 1 ( y j f ( x )) n where y j is the actual quality output observation and f(x j ) the predicted regression point. For each regression model, calculate the R value. If the R k is greater than 0.7, the k th regression model will proceed to step 4. Otherwise, the regression model does not explain enough of the output variation. Step 4. Calculate the F-values between the regression points to determine which regression to choose, where j (3) F ( RSS RSS )( DF DF ) j k j k j, k (4) RSS k DFk where DF = n-p, n is the number of observations, p is the number of model parameters to be estimated, and p j < p k ; the F-statistic will follow the distribution F ~ F( p p, n p ) (5) j, k j k k Step 5. Choose model j if F j, k Fp j pk, n pk, After the initial data is collected and the significant variables found, the model parameters are estimated. To estimate the parameters, sufficient data should be collected to determine the normal state of the process. Unfortunately in some processes it is difficult to collect enough data in order to correctly characterize the impact of the different input variables on the output. Thus, in this methodology we adopt the idea of a master machine and the parallel slave machines. It is assumed that one of the CNC machines has a higher number of cycles than the others, and this machine is chosen as the master. The other machines will be slaves which will follow the control limits that are set by the master machine. This allows for the reduction in observation time and the amount of data that needs to be collected to establish the normal baseline before process monitoring can take place. It is also important to note that there is the assumption that the machines are the same and have similar characteristics and outputs. In the event that the machines have different outputs, the methodology still applies with some modifications as noted below. The parameter estimates obtained by the steps below will be used to monitor all of the CNC machines. Step 0. Select master machine. Step 1. Take new output variable measurement Step. If the input variable is at 75%, 50% or 5% of its life cycle or operating range, then go to Step 3. If the input variable is at 0% of its remaining life, proceed to Step 10. Step 3. Go to the procedure in Section.1 and find the best regression based on all of the collected data from the master. Step 4. Use the least squares estimate for the regression coefficients using all of the data collected from the master. Step 5. Using the in-control points as found in Step 5, recalculate the regression parameters. Step 6. Calculate the model residuals. Step 7. Calculate the residual control limits using either X-bar and R charts, CUSUM or EWMA charts. Step 8. Use the control limits calculated in Step 8 to monitor the slave machines while the remaining life cycle data is collected. 3

4 Step 9. If the input variable is at 0%, use the regression limits calculated in Step 6 for monitoring production data.. Monitoring and baseline updates Once the regression parameters are established using the procedures in section.1, a control chart of the regression residuals can be used to monitor the process. Establishing the normal baseline based on the relationship between the output variable and the input variables account for some of the normal process changes as mentioned in the introduction. However there might be instances when a new variable is introduced to the process (such as a new part type) which can change the baseline of the process. Thus, if the control chart exhibits trending behavior, this could be an indication of (1) mean shift or change in common cause variation () trending indicates a special cause that was not addressed in the process input and output relationship. Before the model is refit, engineers have to ascertain that the normal process baseline has changed and that there is no special cause present. 3 Case Study The methodology was applied data from an automotive engine head milling operation. The operation consists of 4 parallel CNC machines, each operating with independent controllers and capable of machining 4 different part types. The characteristic that reflects the operation quality is the overall surface flatness, and it is calculated from measurements obtained from a Coordinate Measurement Machine (CMM) or a profilometer. The overall flatness is the difference between the maximum surface height reading and the minimum, and its specification is 80 microns. Each machine can use one of two different tool types, and each tool type has a different tool life depending on how many surfaces it has milled. The remaining tool life for each machine usually ranges from 40%-100% and it has a cyclical effect on the flatness, as seen in Figure 3. Another variable of interest that is collected by the plant is the cutter path. Due to clearance restrictions, one classification of part types has a curved entry path, and the other part type has a straight path entry. The relationship between the tool life, part type and tool type with flatness can be seen in Figure 3. The process was observed for four months, during which all of the input and output variables were measured and recorded for all 800 parts that were inspected. The generalized linear regression model used for each stage of the case study is y flatness 0 x 41 m1 x 51 p1 1 life 4 5 m p type m3 p3 3 path, (6) 3.1 Master selection and initial regression Process data was collected for each of the machines for a period of one month. Table 1 shows the coefficients for the model in (6). The results show that all of the variables in the model are significant. In addition, machine 4 is different than the other machines, so this should be taken into consideration for monitoring purposes. Flatness Scatterplot of Flatness vs Tool Life Tool Life Fig 3. Flatness vs. Tool Life stratified by Tool Type and Part Type Since the relationship between the flatness and the tool life has a long renewal cycle time, the normal baseline can be established for one machine (master), and that regression used to monitor the other machines (slaves). Table 1. Regression coefficients and p-values Part Type where y flatness is the surface flatness, x life is the percent of the remaining tool life, x path is an indicator variable with values 1 for curved cutter path and 0 for straight path, x mi, (i = 1-3) are indicator variables for the four machines, and x pi, (i = 1-3) are indicator variables for the four part types. 4

5 Using engineering knowledge, machine 1 was chosen as the master, as it was the leading machine that usually had a higher a throughput and therefore would have the most data available. Figure 4 shows the flatness plot versus the tool life for the master machine so that the effect of tool life can be visualized. Again, a regression was run with Machine 1 data, and the results shown in Table 4. The regression explained 87.4% of the process variation. Although the regression explains a large amount of the variation, a scatterplot (Fig 5) shows that a linear relationship might not be the best fit regression, as the relationship seems to be asymptotical from a remaining tool life of 50%-80%. Table 4. Final Regression model Figure 4. Flatness vs. Remaining tool life for Master machine Since the master machine was chosen to establish the control limits for the other machines, a regression analysis for machine 1 was done. This regression was used to find predictions the slave machines for the observations when their remaining tool life is between 75% and 100% is shown in Table 3. The residuals for the predictions for the slave machines were also calculated, and monitored using an I-MR chart with 4-sigma control limits. These limits were chosen by engineers because the manufacturing process is well within the specification limits, and the process variation is low compared to the limit range. Because machine 4 is different than the other machines, the regression in Table 3 was still used with an additional constant added in to account for the difference. Table 3. Regression for Machine 1 with RTL from 100%-75% A piecewise linear generalized regression was fit to the models to see if it resulted in a better data fit. The critical F-value comparing the regressions was calculated as1.3; therefore, the piecewise linear regression should be used as it provides the best fit. Thus, the residuals for machine and 3 using the piecewise linear model were fit and the control charts in Figure 6 calculated. Flatness = Tool Life Flatness = Tool Life Figure 5. Flatness vs. Remaining Tool Life (50-100) 3.. Regression Parameters and Control Limit estimation While machines through 4 were being monitored, more data was collected from machine 1 to complete the observation of the relationship between the overall flatness and the tool life. Both figures show out of control MR points. After more analysis, it was found that these points corresponded to different calendar days. Due to the nature of the manufacturing routing and inspection process, some part types and machine 5

6 combinations were measured more often, and there were large gaps in the collection data time frame. It was decided that these fluctuations were normal in the context of the process and the data collection procedure, and that the regression in place explained a sufficient amount of the process variation Monitoring and baseline updates The final regression model that was used to calculate the residuals for monitoring for machines 1-3 is shown in Table 4, and the resulting control charts for machines 1 and are shown in Figure 3. Part type change Figure 6. I-MR Control Charts for Machines 1 and For machine 3, there was a change in the part type produced as indicated in the figure, but this change was reflected in the generalized regression, thus there was no out of control condition in the individual chart. The study was concluded before the tool life decreased from 50%, however, a similar approach can be used until the end of the tool life cycle. 4. Conclusions The proposed methodology is an effective way of monitoring processes where baseline condition could be changed by utilizing in-plant process history information and generalized regression. Compared with quality control charts based on data-driven methods, the developed methodology has the following improvements: (1) incorporates the process knowledge into the data monitoring such that expected process changes do not result in false alarms () establishes the monitoring baseline by using the established process knowledge through generalized regression so that additional measurements on product quality characteristics to reestablish the baseline are not needed and (3) develops algorithms of updating baselines when the established process knowledge is subject to permanent changes. The next steps are to extend the methodology in dealing with high-dimensional quality characteristics such as surface variation monitoring. Another extension of the methodology would be to allow for the non-linearity of the relationships between the critical output variable and the process variables. Acknowledgement This research was supported by a NIST-Advanced Technology Program grant with the Powertrain Engineering and Manufacturing Alliance (PEMA). Mr. Tom Rothermel from Ford Motor Company, Jeffrey Trumble from Trumble Inc., and Richard Wineland from PEMA made indispensable contributions to this research. References 1. Hauck, D. R. (1999). Multivariate statistical process monitoring and diagnosis with grouped regression-adjusted variables. Communications in Statistics - Simulation and Computation, 8, Hawkins, D. (1993). Multivariate quality control based on regression-adjusted variables. Technometrics, 5, Jearkpaporn, D. M. (003). Process-monitoring for correlated gamma-distributed data using generalized linear model based control charts. Quality and Reliability Engineering International, 19, Jiang, W., Tsui, K-L, Woodall, W. (000). A new SPC monitoring method: The ARMA chart. Technometrics, 4(4), Johnson, R.A. and Wichern, D.W., Applied Multivariate Statistical Analysis, 5 th Edn, Prentice Hall, NJ., Mandel, B. (1969). The regression Control chart. Journal of Quality Technology, 1, Rao, S. S. (1996). Monitoring multistage integrated circuit fabrication processes. IEEE Transactions on Semiconductor Manufacturing, 9, Shu, L. T.-L. (008). Shu, L., Tsui, K-L. and Tsung, F (008). Regression Control charts, Encylopedia of Statistics in Quality and Reliability. 9. Skinner, K. M. (003). Process monitoring for multiple count data using generalized linear model-based control charts. International Journal of Production Research, 41, Woodall, W. S. (004). Using control charts to monitor process and product profiles. Journal of Quality Technology, 36, Xiang, L. &. (008). Statistical monitoring of multistage processes based on engineering models. IIE Transactions, 40, Zantek, P. W. (00). Process and Product Improvement in manucturing systems with correlated stages. Management Science, 48, Zantek, P. W. (00). Process and product improvement in manufacturing systems with correlated stages. Management Science, 48,