The paper deals with the statistical analysis of the selected parameter of the blast furnace process. It was proved that analyzed measurements have been autocorrelated. ARIMA control chart was selected for their analysis as a very useful statistical process control (SPC) method. At first the methodology for control limits setting in ARIMA control charts considering the time series outlier analysis as an integral part of the ARIMA model building was designed. Then this proposal was applied to the statistical analysis of the selected blast furnace process output parameter with the aim to compare two production methods.Rad prikazuje statističku analizu nekih parametara procesa u visokoj peći. Dokazana je autokorelacija analiziranih mjernih vrijednosti. Kao vrlo prikladna metoda statističke kontrole procesa (SKP) za analizu parametara odabran je ARIMA – kontrolni dijagram. U prvom koraku integralnog modeliranja ARIMA postupkom, definirana je metodologija uspostave kontrolnih limita u ARIMA – dijagramu obzirom na izlazne vrijednosti vremenske sekvence. Ova pretpostavka primijenjena je na statističku analizu odabranih izlaznih parametara procesa visoke peći radi usporedbe dvaju proizvodnih metoda

D. Noskievičová

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D. NOSKIEVI^OVÁSTATISTICAL ANALYSIS OF THE BLAST FURNACE PROCESSOUTPUT PARAMETER USING ARIMA CONTROL CHART WITHPROPOSED METHODOLOGY OF CONTROL LIMITS SETTINGReceived – Prispjelo: 2008-03-18Accepted – Prihva}eno: 2009-02-20Review Paper – Pregledni radINTRODUCTIONStatistical process control (SPC) can be defined as amethod of monitoring, controlling and, ideally, improv-ing a process using statistical analysis. It is used to iden-tify and remove undesirable variation that exceeds thenatural (common) variation with the aim of reaching sta-tistical stability of a process.Correct setting of control limits in control charts isone of the main conditions for the successful applicationof statistical process control and for meeting its basicgoal, i.e. verifying statistical stability of the analyzedprocess.The control limits setting has been solved in manypublications (for instance 1-3). But no publications dis-tinguish between autocorrelated and nonautocorrelateddata from the point of view of this problem.The standard methodology for the control limits set-ting can be summarized into the following steps:1. Data collection.2. Computation of control limits using appropriateformulae.3. Control chart construction.4. Control chart analysis.5. Process regulation.6. Control limits recalculation.Steps 5 and 6 are realized only when the analysis instep 4 has revealed the process nonstability (there weresome points out of the limits or some nonrandom pat-terns in the control chart). Process regulation (step 5)consists of specifying the assignable causes of the pro-cess nonstability and acceptance and realization of ade-quate corrective actions. Without this step it is not rec-ommended to go to the next step. Step 6 is obviouslyworked out via excluding out-of control points and con-trol limits recomputation using the remaining points 4.These steps are repeated until the control chart starts tosignalize the statistical stability of the analyzed process.Standard way of the control limits recomputation(excluding them from the data set) is not suitable forautocorrelated data and when ARIMA modeling is ap-plied.Autoregressive integrated moving average (ARIMA)models represent very useful class of linear models thatform the heart of the stochastic model-based Box-Jenkinsmethodology for the time series analysis 4.In practice time series are often influenced by uncon-trolled or unexpected events that can lead to occurrenceMETALURGIJA 48 (2009) 4, 281-284 281The paper deals with the statistical analysis of the selected parameter of the blast furnace process. It was pro-ved that analyzed measurements have been autocorrelated. ARIMA control chart was selected for their anal-ysis as a very useful statistical process control (SPC) method. At first the methodology for control limits settingin ARIMA control charts considering the time series outlier analysis as an integral part of the ARIMA model buil-ding was designed. Then this proposal was applied to the statistical analysis of the selected blast furnace pro-cess output parameter with the aim to compare two production methods.Key words:ARIMA control chart, blast furnace process, environmental aspects, time series outliers analysisStatisti~ka analiza izlaznih parametara procesa u visokoj pe}i pomo}u ARIMA – kontrolnog dijagra-ma uz prijedlog metodologije odre|ivanja kontrolnih granica.Rad prikazuje statisti~ku analizu nekih pa-rametara procesa u visokoj pe}i. Dokazana je autokorelacija analiziranih mjernih vrijednosti. Kao vrlo prikladnametoda statisti~ke kontrole procesa (SKP) za analizu parametara odabran je ARIMA – kontrolni dijagram. Uprvom koraku integralnog modeliranja ARIMA postupkom, definirana je metodologija uspostave kontrolnih limi-ta u ARIMA – dijagramu obzirom na izlazne vrijednosti vremenske sekvence. Ova pretpostavka primijenjena je nastatisti~ku analizu odabranih izlaznih parametara procesa visoke pe}i radi usporedbe dvaju proizvodnih metoda.Klju~ne rije~i: ARIMA kontrolni dijagram, visokope}ni procesi, ekolo{ki aspekti, izlazne vrijednosti vremenskesekvenceISSN 0543-5846METABK 48(4) 281-284 (2009)UDC - UDK 005.642.2:519.246: 621.745.57=111D. Noskievi~ová, Faculty of Metallurgy and Materials Engineering,V[B-TU Ostrava, Czech Republicof large unusual observations calledoutliers. Outliers can largely affect se-lection of a suitable model, estimationof model parameters, forecasting, prop-erties of the model residuals including(more detailed information concerningreasons for the outlier detection and ad-justment can be found for instance in5, 6). For that reason outlier analysismust be an integral part of the modelbuilding phase. The algorithm of theoutlier detection and adjustment is dis-cussed in 6 and it is also mentioned in4.In the frame of statistical processcontrol (SPC) an approach based ontime series modeling using ARIMAmodels has proved to be useful in deal-ing with autocorrelated data (see for in-stance 3, 7, 8). Some criticism of theresidual control charts has appeared inthe paper by MacGregor 9. He re-minds that the residual charts are ineffi-cient at detecting shifts in the mean, es-pecially when the autocorrelation islarge and positive. But he does not con-sider that the absence of the time seriesoutlier analysis can be one of the main insufficiencies ofSPC using the control charts based on the residuals fromARIMA models. Wright, Booth and Hu in 10 suggestusing the joint estimation outlier detection method as anSPC method. But they deal especially with short-runautocorrelated data and they do not solve the problem ofcontrol limits setting in the ARIMA residuals controlchart.This paper deals with the proposal of the methodol-ogy for the control limits setting in ARIMA controlcharts which considers the time series outlier analysis asan integral part of the model building and which con-tains the outlier analysis as a step before the control lim-its setting.USED METHODOLOGYDemonstration of applicability of the SPC methodsto comparison of the iron ore production variants fromthe point of view of the selected output parameter wasthe main goal of these research activities. It was provedthat analyzed measurements are autocorrelated. For thatreason it was decided to use ARIMA control chart. Butbefore applying it to the statistical analysis of the se-lected blast furnace output parameters control limits set-ting had to be solved because the standard way (recom-putation without out-of control points) is not suitableand the SPC literature does not offer solution of thisproblem. For that reason the procedure for control limitssetting in ARIMA control chart was proposed and then itwas applied to the statistical analysis of the selected pa-rameter.The proposal of the procedureProposed algorithm for control limits setting whenusing ARIMA modeling is described using the flowchart (see Figure 1).As it can be seen on the figure after identification ofthe initial ARIMA model and estimation of its parame-ters (assuming that there are no outliers in the analyzedtime series) the outliers´ identification and assessmenthave to be realized. When some outlier is identified itscause must be searched for and adequate corrective ac-tion must be realized.When final overall outlier model is identified residu-als from this model should be verified. When they arenormally distributed and independent with constantvariance central line (CTR) and control limits (uppercontrol limit UCL and lower control limit LCL) for theselected control chart (classical Shewhart control charts,exponentially weighted moving average (EWMA) orcumulative sum (CUSUM) control charts for individualmeasurements) can be computed from these residualsand ongoing statistical process control can start.When using the classical Shewhart control chart forindividual observations formulae for computation ofCTR, UCL and LCL are as follows:CTR e ( ),0 (1)UCL e R 31128,,kl (2)LCL e R 31128,,kl (3)282 METALURGIJA 48 (2009) 4, 281-284D. NOSKIEVI^OVÁ: STATISTICAL ANALYSIS OF THE BLAST FURNACE PROCESS OUTPUT PARAMETER USING...Figure 1. Flow chart of the proposed procedure for control limits setting inARIMA control chartwhere:e - mean of residuals,Rkl - average moving range.When residuals do not meet all assumptions somedifferent time series model than ARIMA (for instanceTAR model, linear or nonlinear volatility model) orsome nonparametric method can be applied.Application of suggested algorithmSuggested algorithm will be shown on the analysis ofthe selected output parameter of the blast furnace process,i.e. the amount of H2 in the output blast furnace gas in %(daily measurements). During the analyzed period (2004and 2005) there were applied two production methodsdifferent in additional fuel (let us mark these differentmethods I (using the tar) and II (using the oil)). The com-parison of stability of these two production methods fromthe point of view of this selected output parameter hasbeen set as a goal of this analysis. For the both methodsthe fitting ARIMA model was identified (it was selectedfrom several acceptable models based on the residualsverification and the value of criteria AIC and BIC for theselection of the best one) and estimated using data fromthe 2004 year. After residuals verification control limitsfor the classical Shewhart control chart for individualmeasurements were computed using residuals of thismodel. These control limits were used for the ongoingprocess control in 2005.The time series outlier analysis was realized usingsoftware SPSS 15 and all the rest of statistical analysiscontrol charts including was made in STATGRAPHICSPlus, Version 5.0.RESULTS AND DISCUSSIONAutocorrelation of H2 / % for the production methodI was confirmed by tests for randomness. As the bestmodel for this time series there was identified ARIMA(1, 0, 0). More information about this model can befound in Table 1.Table 1. Final model parameters for H2 / % in 2004 –production method IParametersestimationOutliers Outlier estimationConstant =2,8071 =0,80548 Additive70 Additive79 TransientMagnitudeDecay factor97 Innovational109 Additive0,9040,7510,9810,7260,7380,735Causes of outliers were discussed and possible cor-rective actions were considered.In the next step residuals from this final overall out-lier model were verified. Tests confirmed that residualsare normally distributed, independent and with constantvariance (see Table 2).Table 2. Results of the residuals verificationVerifiedassumptionTest P-valueNormality X2 0,49Kolmogorov 0,65Kolmogorov-Smirnov > 0,1Anderson-Darling 0,55Skewness 0,89Kurtosis 0,22Autocorrelation Runs above and below median 0,34Box-Pierce 0,78Constant variance Bartlett 0,78Results of the residuals verification of the finalARIMA model enabled to use these residuals for settingof control limits and verifying the process stability.Shewhart control chart for individuals was applied tothese residuals (see Figure 2). It can be seen that processin 2004 can be considered to be statistical stable (in con-trol) and that control limits were set correctly and theycan be applied to the process in a future (see Figure 3).As it can be seen on Figure 3 in 2005 process couldnot be considered to be in control. It reflects that someMETALURGIJA 48 (2009) 4, 281-284 283D. NOSKIEVI^OVÁ: STATISTICAL ANALYSIS OF THE BLAST FURNACE PROCESS OUTPUT PARAMETER USING...Figure 2. Shewhart control chart for residuals of ARIMAmodel for H2 / % (production method I) in2004Figure 3. Shewhart control chart for residuals of ARIMAmodel for H2 / % (production method I) in 2005discussed corrective actions have not been actually real-ized.Analysis of the portion of H2 in the blast furnace gasby the production method II was done in the same wayas the previous one. As the best final model for the timeseries of data from 2004 year there was identifiedARIMA (0, 1, 2). There were no outliers identified.Shewhart control chart for individual measurementsfrom the residuals of this model has been constructed(see Figure 4). Figure 4 shows that the process (produc-tion method II) in 2004 can be considered to be statisti-cal stable (in control) and that control limits were cor-rectly set and they can be applied to the process in a fu-ture (see Figure 5).As it can be seen on Figure 5 in 2005 process couldnot be considered to be in control. It reflects the same asthe technology I, i.e. some mentioned corrective actionshave not been actually realized.Comparing Figure 3 and Figure 5 it can be seen thattechnology II is less stable than technology I (4 pointsout of limits as compared to 2 points out of limits). In ad-dition expressed with standard deviation of the originalH2 measurements variation of technology II is largerthen variation of technology I.CONCLUSIONComparison of two iron production methods differ-ent in the used additional fuel from the point of view ofthe selected output parameter of the blast furnace pro-cess was the goal of the statistical analysis demonstratedin this paper. As the main instrument for this compari-son ARIMA control chart was selected. By the applica-tion of ARIMA control chart the problem with correctcontrol limits setting had appeared. As a result the algo-rithm for control limits setting in ARIMA control chartwas proposed and applied to the selected parameter. Themain ideas of this algorithm can be formulated as fol-lows:– Time series outliers´ analysis must be realized asan integral part of the ARIMA model building.– Outliers´ analysis must precede control limits set-ting.– Causes of the identified outliers must be searchedfor and adequate correct actions must be realized.Then control limits of the final ARIMA model canserve as criteria for the process statistical stability evalu-ation and for comparison of the analyzed productionmethods.The work was realized within the frame of solution ofthe Czech national research project CEZ MSM6198910019 Reduction of CO2 Production - DECOxProcesses.REFERENCES1 H. M. Wadsworth et al., Modern Methods for Quality Con-trol and Improvement, Wiley, New York, 1986.2 A. Mitra, Fundamentals of Quality Control and Improve-ment, Macmillan Publishing Company, New York, 1993.3 D.C. Montgomery, Introduction to Statistical Quality Con-trol, Wiley, New York, 2001.4 G.E.P. Box, G. M. Jenkins, G. L. Reinsel, Time Series Anal-ysis. Forecasting and Control. Prentice Hall, EnglewoodCliffs, New Jersey, 1994.5 A.J. Fox, Journal of Royal Statistical Society, B34 (1972),350-363.6 I. Chang I, G.C. Tiao, C. Chen, Technometrics, 30 (1988) 2,193-204.7 D.C. Montgomery, D.J. Friedman, Statistical process con-trol in a computer-integrated manufacturing environment,Statistical Process Control in Automated Manufacturing,M. Dekker, New York, 1989, 67-89.8 D.G. Wardel, H. Moskovitz, R.D. Plante, ManagementScience 38 (1992), 1084-1105.9 J.F. MacGregor, Journal of Quality Technology, 23 (1991)3, 198-199.10 C.M. Wright, D.E. Booth, M.Y. Hu, Journal of Quality Tec-hnology, 33 (2001) 3, 365 – 378.Note: The responsible for English language is D. Noskievi~ová, CzechRepublic.284 METALURGIJA 48 (2009) 4, 281-284D. NOSKIEVI^OVÁ: STATISTICAL ANALYSIS OF THE BLAST FURNACE PROCESS OUTPUT PARAMETER USING...Figure 4. Shewhart control chart for residuals of ARIMAmodel for H2 / % (method II) in 2004Figure 5. Shewhart control chart for residuals of ARIMAmodel for H2/% (method II) in 2005

Statistička analiza izlaznih parametara procesa u visokoj peći pomoću ARIMA – kontrolnog dijagrama uz prijedlog metodologije određivanja kontrolnih granica

Statistička analiza izlaznih parametara procesa u visokoj peći pomoću ARIMA – kontrolnog dijagrama uz prijedlog metodologije određivanja kontrolnih granica

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