So called short run manufacturing environment is now typical for many industrial branches including metallurgy. To
be applicable in such nonstandard conditions classical control charts and capability indices must be modifi ed. In
this paper the design of the methodology for the complex application of the statistical control on the metallurgical
short run processes is presented and verifi ed in conditions of the bars rolling.Web of Science531848

Noskievičová, Darja

Woska, Bogdan

So called short run manufacturing environment is now typical for many industrial branches including metallurgy. To be applicable in such nonstandard conditions classical control charts and capability indices must be modified. In this paper the design of the methodology for the complex application of the statistical control on the metallurgical short run processes is presented and verified in conditions of the bars rolling

D. Noskievičová

B. Woska

Hrčak - Portal of scientific journals of Croatia

Design of methodology for application of statistical control on short run processes in metallurgy

HRČAK - Portal of Croatian Scientific and Professional Journals

81METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ, B. WOSKADESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT RUN PROCESSES IN METALLURGYReceived – Prispjelo: 2012-12-29Accepted – Prihvaćeno: 2013-04-26Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 53(1) 81-84 (2014)UDC – UDK 669.011:621.771:005.642.2=111D. Noskievičová, Faculty of Metallurgy and Materials Engineering, VŠB-TU Ostrava, B. Woska, Viadrus, a.s., Ostrava, Czech RepublicSo called short run manufacturing environment is now typical for many industrial branches including metallurgy. To be applicable in such nonstandard conditions classical control charts and capability indices must be modifi ed. In this paper the design of the methodology for the complex application of the statistical control on the metallurgical short run processes is presented and verifi ed in conditions of the bars rolling.Key words: metallurgy, bars rolling, short run processes, control charts, capability indicesINTRODUCTIONSo called short run (SR) environment is nowadays typical for many industrial branches including metal-lurgy. SR processes are characterized by quite a wide variety of mixed products with relatively smaller lot or batch sizes. These conditions have resulted from the growing product customization, higher and higher pro-duction fl exibility and larger stress on the high quality and low costs. The changing economic and production conditions in metallurgy are discussed in the wider con-text for instance in the papers [1] and [2]. In such condi-tions the conventional methods of statistical process control (SPC) and the capability analysis do not work. Some aspects of the application of SPC and the capabil-ity studies in metallurgy were discussed in the paper [3]. To be able to offer some meaningful information about the process stability and its capability the SPC and the process capability analysis must be modifi ed for the SR processes. The design of the methodology for the complex SPC application in the conditions of the metallurgical SR processes is the main output of this paper. It is based on the critical analysis of the available control charts and the capability indices for the SR proc-esses. This analysis forms the main contents of the ana-lytical part of the research. The proposal of the method-ology is based on the idea that SPC must be applied in a complex way where the capability analysis is an inte-gral part of it. In the experimental part this design was applied in the conditions of the profi le bars rolling. Such combined analysis and application of SPC including the capability study for the SR processes in metallurgy has not yet been found in the professional literature.ANALYTICAL PARTThe analytical part was focused on the following as-pects:SR SPC methods with special stress on the methods • for variables;methods for evaluation of the variation representa-• tiveness;capability indices for SR environment including • confi dence intervals of capability indices.Many proposals for applying the control charts in special conditions of a SR production have been offered up to now by many authors (for instance [4 - 9]). The most exhaustive review of the SPC methods for the SR conditions is offered by P. F. Tang [10]. In the analytical part different control charting methods have been eval-uated using the factors such as the rate of maturity, prac-tical usability, relative simplicity, predominance of the advantages compared with the disadvantages, the rate of the maturity. The result of this analysis is the decision tree (see Figure 1). When selecting suitable SR control charts the as-sumption that the process standard deviation is approxi-mately the same for all the parts must be tested in some cases (the target control charts). In the professional lit-erature several methods for evaluating the process vari-ance homogeneity can be found: the chart for mean ranges (R-bar) [7], the range test, [5], the F-test [5], the Bartlett test, the Levene test, the Brown-Forsyth test, the Cochran test, the Hartley test. These methods were analysed considering their complexity, precision, sensi-tivity to particular assumptions and their availability in the common SW products. The advantages and the dis-advantages of the selected methods were then defi ned to offer users a simple methodology for their application in connection with the selection of a suitable SR control chart (see Table 1).82  METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...As compared to the amount of papers and other pro-fessional literature dealing with the various control charts for SR manufacturing there are only several au-thors solving the problem of the capability analysis for the SR conditions in detail (for instance [11, 12]). After analysing the different approaches to the SR capability indices the authors of this paper divided the SR capabil-ity indices into 5 groups:Type A capability indices • Cp, Cpk for the processes with consistent variation for all products computed from the transformed data (deviations from the tar-get value).Type B capability indices • Cp, Cpk for the processes with consistent variation for all products computed from the original measurements.Type C capability indices • Cp, Cpk for the processes with non-consistent variation of all products. These estimations are not often based on the suffi cient data amount. For that reason the capability indices of type C are not very precise.Type D capability indices • Cp, Cpk, using unifi cation of the different tolerances based onthe linear transformation of the measured values. The unifi ed tolerances can lead to the situation when highly capable product will hide the non-capable prod-ucts and vice versa. For that reason the so called dia-grams (ȳ, s) should be added [11].Type E capability indices Cpm and capability run chart [12].Figure 1 Decision tree for selection of the SR charting method [10]Table 1 Methods for evaluation of the variation representativeness [5, 7]Method Advantages DisadvantagesChart for mean ranges (R-bar) Graphical display of all evaluated productsClear and quick answerSimply programmedLess precise measure of variationRange test SimpleClear decision ruleLess preciseF-test More precise than methods aboveSimpleStandard part of the majority of SW productsSuitable for comparison of only 2 samplesSensitive to departures from normalityBartlett test Suitable for k samplesTest with high powerMore complicatedSensitive to departures from normalityLevene test Suitable for k samplesMore robust testmore complicatedless poweredBrown-Forsyth test Suitable for k samplesMost robust testnot standard part of every statistical SW productCochran test Suitable for k subgroupsMore simpleSuitable only for samples of the same sizeSensitive to departures from normalityNot standard part of every statistical SW productHartley test More simple methodFor k samples of the same sizeLess poweredSensitive to departures from normalityNot standard part of every SW product83METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...METHODOLOGY DESIGNBased on the main idea of the authors´ research and on the conclusions of its analytical part, the proposal for a practical complex implementation of SPC including the capability assessment in the conditions of the re-petitive SR processes was proposed (see Figure 2).EXPERIMENTAL PARTThe proposed methodology was verifi ed in the con-ditions of the profi le bars rolling. This production has typical features of a repetitive short run process. The fi rst two steps of the proposed methodology (see Figure 2) can be described as follows:Selected process• : profi le bars rolling;Product family• : hot rolled steel L bars;Products: • 3 products of one type different in di-mensions with tolerances 20 ± 1 mm, 30 ± 1 mm, 40 ± 1 mm;Quality characteristics• : the arm width / mm.The homogeneity of the process variation was veri-fi ed using the control chart for R-bars (see Table 1). It was selected due to its simplicity and its graphical out-put. Based on the results of this analysis and on the defi nition of the sample size n = 4 (randomly selected from the bunch), the SR target x-bar and range control charts were selected (see Figure 1). The control interval was defi ned as every 2nd bunch. The capability indices of type A were applied including the computation of the confi dence intervals.RESULTS AND DISCUSSIONThe quality characteristics was selected on the base of the analysis of rework and the claims in the bar roll-ing process as well as the customer requirements. The product family (hot rolled steel L bars) was created on the base of the analysis of the orders repeatability, the volume of the particular orders and the technological similarity.The applied measurement system analysis MSA led to the suffi cient result: the complex index of the measure-ment system capability GRR = 22,18 % (for more infor-mation about the evaluation of these indicator see [3]).The measurement system then could be considered acceptable for the following statistical analysis. In spite of this result it was decided to improve the capability of this measurement system by implementing the working instruction for the data collection and record.The chart for the R-bar (see Table 1) showed that the variation of the rolling process can be considered ho-mogenous for all the analysed products.The target range control chart, where the range R for every sample was depicted, confi rmed the results of the previous process homogeneity analysis. The SR target x-bar control chart, where the difference (x̄ –T) between the average and the target value for every sample was Figure 2 Steps of the designed methodologydepicted, showed that the stability with regard to the process level is infl uenced by the same cause irrespec-tive of the particular products. It was revealed that it was an infl uence of tampering the process by the operators.The data normality and the data independence for every product were verifi ed using suitable statistical tests (the Shapiro – Wilk test, the test for the sample 84  METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...skewness and kurtosis, the test for randomness) and graphical tools. The results of this analysis showed that the data could be considered normally distributed and independent.The capability analysis was done using the capabil-ity indices of type A with the confi dence intervals as the best solution with regard to the applied control charting method. The values of the indices and the confi dence intervals are the same for all products due to the fact that all three analysed products had the same width (see Table 2).tion in the conditions of the SR processes. It was based on the critical analysis of the available control charting methods and the capability indices for the SR processes conditions. In the end, this proposal has been applied in the real conditions of the profi le bars rolling. The gained results showed that the proposal was applicable and led to the reduction of the process variability and to the sig-nifi cant scrap reduction.AcknowledgementThe work was realized within the solution of the ESF project InterDV Z.1.07/2.2.00/15.0132 and the specifi c research project SP2013/49, solved at the Fac-ulty of Metallurgy and Materials Engineering, VŠB-TU Ostrava with the support of Ministry of Education, Youth and Sports, Czech Republic.Legend of symbolsR range / mmR-bar mean range / mmx-bar mean / mmCp process capability index / -Cpk critical process capability index / -Cpm Taguchi´s capability index / -x̄ –T  difference between the mean and target value / mmn sample size GRR index of gage reproducibility and repeatability / %REFERENCES[1] B. Gajdzik, Metalurgija, 52 (2013) 1, 131-134.[2] W. Sroka, Metalurgija 52 (2013) 1, 127-130.[3] D. Noskievičová, R. Kucharczyk, Metalurgija, 51 (2012) 1, 137-140.[4] T. Pyzdek, Quality Progress, 26 (1993), 51-60.[5] G. K. Griffi th, Statistical Process Control Methods For Long and Short Runs, ASQC Quality Press, Milwaukee, Wisconsin, 1996.pp. 39-58 and 121-145.[6] D. C. Montgomery, Introduction to Statistical Quality Control, J.Wiley & Sons, New York, 2009, pp. 435-438.[7] D. Wheeler, Short Run SPC, SPC Press Inc., Knoxville, Tennessee, 1991, pp. 1-32 and 9-10.[8] S. A. Wise, C. F. Douglas, Innovative Control Charting. Practical SPC Solutions for Today´s Manufacturing Envi-ronment, ASQ Quality Press, Milwaukee, Wisconsin, 1998, pp. 7-273 and 91-163.[9] C. P. Quesenberry, Journal of Quality Technology, 27 (1995) 3, 204-213.[10] P. F. Tang, Statistical Process Control with Special Refe-rence to Multivariable Processes and Short Runs, PhD the-sis, Victoria University of Technology, Melbourne, 1996, pp. 4-5 and 9-40.[11] M. Deleryd, Enhancing the Industrial Use of Process Ca-pability Studies, Doctoral thesis, University of Technolo-gy, Lulea, 1998, pp. 15-49 and 134-197.[12] F. Spiring, Determining and Assessing Process Capability for Engineers and Manufacturing, Nova Science Publi-shers, Inc., New York, 2010, pp. 159-173.Note:  The responsible for English language is: Otilia Drottnerová, Department of Foreign Languages, VŠB-TU Ostrava, Czech RepublicTable 2 Capability indicesCp / -1,2,3Cpk / -1,2,3Confi dence interval limits for Cp / -Confi dence interval limits for Cpk / -Lower Upper Lower Upper1,46 1,45 1,2775 1,6425 1,276 1,624It was clear that the process had to be improved to reduce the risk of the true value of Cpk being less than the obvious target value of 1,33.During two months after the fi rst analysis, SPC was applied on a regular basis and the operators started to decide about the process adjustment according to the information from the control charts. It led to the reduc-tion of the process variation (see Figures 3 and 4) and to the reduction of the scrap by 14,2 t per these two months.Figure 3  Process variation at the beginning of the SPC implementation (Target x-bar control chart)Figure 4  Reduction of the process variability after two months (Target x-bar control chart)CONCLUSIONSThe main output of this paper was the original de-sign of the methodology for the complex SPC applica-

English

DSpace at VSB Technical University of Ostrava

81METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ, B. WOSKADESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT RUN PROCESSES IN METALLURGYReceived – Prispjelo: 2012-12-29Accepted – Prihvaćeno: 2013-04-26Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 53(1) 81-84 (2014)UDC – UDK 669.011:621.771:005.642.2=111D. Noskievičová, Faculty of Metallurgy and Materials Engineering, VŠB-TU Ostrava, B. Woska, Viadrus, a.s., Ostrava, Czech RepublicSo called short run manufacturing environment is now typical for many industrial branches including metallurgy. To be applicable in such nonstandard conditions classical control charts and capability indices must be modifi ed. In this paper the design of the methodology for the complex application of the statistical control on the metallurgical short run processes is presented and verifi ed in conditions of the bars rolling.Key words: metallurgy, bars rolling, short run processes, control charts, capability indicesINTRODUCTIONSo called short run (SR) environment is nowadays typical for many industrial branches including metal-lurgy. SR processes are characterized by quite a wide variety of mixed products with relatively smaller lot or batch sizes. These conditions have resulted from the growing product customization, higher and higher pro-duction ﬂ exibility and larger stress on the high quality and low costs. The changing economic and production conditions in metallurgy are discussed in the wider con-text for instance in the papers [1] and [2]. In such condi-tions the conventional methods of statistical process control (SPC) and the capability analysis do not work. Some aspects of the application of SPC and the capabil-ity studies in metallurgy were discussed in the paper [3]. To be able to offer some meaningful information about the process stability and its capability the SPC and the process capability analysis must be modiﬁ ed for the SR processes. The design of the methodology for the complex SPC application in the conditions of the metallurgical SR processes is the main output of this paper. It is based on the critical analysis of the available control charts and the capability indices for the SR proc-esses. This analysis forms the main contents of the ana-lytical part of the research. The proposal of the method-ology is based on the idea that SPC must be applied in a complex way where the capability analysis is an inte-gral part of it. In the experimental part this design was applied in the conditions of the proﬁ le bars rolling. Such combined analysis and application of SPC including the capability study for the SR processes in metallurgy has not yet been found in the professional literature.ANALYTICAL PARTThe analytical part was focused on the following as-pects:SR SPC methods with special stress on the methods • for variables;methods for evaluation of the variation representa-• tiveness;capability indices for SR environment including • conﬁ dence intervals of capability indices.Many proposals for applying the control charts in special conditions of a SR production have been offered up to now by many authors (for instance [4 - 9]). The most exhaustive review of the SPC methods for the SR conditions is offered by P. F. Tang [10]. In the analytical part different control charting methods have been eval-uated using the factors such as the rate of maturity, prac-tical usability, relative simplicity, predominance of the advantages compared with the disadvantages, the rate of the maturity. The result of this analysis is the decision tree (see Figure 1). When selecting suitable SR control charts the as-sumption that the process standard deviation is approxi-mately the same for all the parts must be tested in some cases (the target control charts). In the professional lit-erature several methods for evaluating the process vari-ance homogeneity can be found: the chart for mean ranges (R-bar) [7], the range test, [5], the F-test [5], the Bartlett test, the Levene test, the Brown-Forsyth test, the Cochran test, the Hartley test. These methods were analysed considering their complexity, precision, sensi-tivity to particular assumptions and their availability in the common SW products. The advantages and the dis-advantages of the selected methods were then deﬁ ned to offer users a simple methodology for their application in connection with the selection of a suitable SR control chart (see Table 1).82  METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...As compared to the amount of papers and other pro-fessional literature dealing with the various control charts for SR manufacturing there are only several au-thors solving the problem of the capability analysis for the SR conditions in detail (for instance [11, 12]). After analysing the different approaches to the SR capability indices the authors of this paper divided the SR capabil-ity indices into 5 groups:Type A capability indices • Cp, Cpk for the processes with consistent variation for all products computed from the transformed data (deviations from the tar-get value).Type B capability indices • Cp, Cpk for the processes with consistent variation for all products computed from the original measurements.Type C capability indices • Cp, Cpk for the processes with non-consistent variation of all products. These estimations are not often based on the sufﬁ cient data amount. For that reason the capability indices of type C are not very precise.Type D capability indices • Cp, Cpk, using uniﬁ cation of the different tolerances based onthe linear transformation of the measured values. The uniﬁ ed tolerances can lead to the situation when highly capable product will hide the non-capable prod-ucts and vice versa. For that reason the so called dia-grams (yˉ, s) should be added [11].Type E capability indices Cpm and capability run chart [12].Figure 1 Decision tree for selection of the SR charting method [10]Table 1 Methods for evaluation of the variation representativeness [5, 7]Method Advantages DisadvantagesChart for mean ranges (R-bar) Graphical display of all evaluated productsClear and quick answerSimply programmedLess precise measure of variationRange test SimpleClear decision ruleLess preciseF-test More precise than methods aboveSimpleStandard part of the majority of SW productsSuitable for comparison of only 2 samplesSensitive to departures from normalityBartlett test Suitable for k samplesTest with high powerMore complicatedSensitive to departures from normalityLevene test Suitable for k samplesMore robust testmore complicatedless poweredBrown-Forsyth test Suitable for k samplesMost robust testnot standard part of every statistical SW productCochran test Suitable for k subgroupsMore simpleSuitable only for samples of the same sizeSensitive to departures from normalityNot standard part of every statistical SW productHartley test More simple methodFor k samples of the same sizeLess poweredSensitive to departures from normalityNot standard part of every SW product83METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...METHODOLOGY DESIGNBased on the main idea of the authors´ research and on the conclusions of its analytical part, the proposal for a practical complex implementation of SPC including the capability assessment in the conditions of the re-petitive SR processes was proposed (see Figure 2).EXPERIMENTAL PARTThe proposed methodology was veriﬁ ed in the con-ditions of the proﬁ le bars rolling. This production has typical features of a repetitive short run process. The ﬁ rst two steps of the proposed methodology (see Figure 2) can be described as follows:Selected process• : proﬁ le bars rolling;Product family• : hot rolled steel L bars;Products: • 3 products of one type different in di-mensions with tolerances 20 ± 1 mm, 30 ± 1 mm, 40 ± 1 mm;Quality characteristics• : the arm width / mm.The homogeneity of the process variation was veri-ﬁ ed using the control chart for R-bars (see Table 1). It was selected due to its simplicity and its graphical out-put. Based on the results of this analysis and on the deﬁ nition of the sample size n = 4 (randomly selected from the bunch), the SR target x-bar and range control charts were selected (see Figure 1). The control interval was deﬁ ned as every 2nd bunch. The capability indices of type A were applied including the computation of the conﬁ dence intervals.RESULTS AND DISCUSSIONThe quality characteristics was selected on the base of the analysis of rework and the claims in the bar roll-ing process as well as the customer requirements. The product family (hot rolled steel L bars) was created on the base of the analysis of the orders repeatability, the volume of the particular orders and the technological similarity.The applied measurement system analysis MSA led to the sufﬁ cient result: the complex index of the measure-ment system capability GRR = 22,18 % (for more infor-mation about the evaluation of these indicator see [3]).The measurement system then could be considered acceptable for the following statistical analysis. In spite of this result it was decided to improve the capability of this measurement system by implementing the working instruction for the data collection and record.The chart for the R-bar (see Table 1) showed that the variation of the rolling process can be considered ho-mogenous for all the analysed products.The target range control chart, where the range R for every sample was depicted, conﬁ rmed the results of the previous process homogeneity analysis. The SR target x-bar control chart, where the difference (xˉ –T) between the average and the target value for every sample was Figure 2 Steps of the designed methodologydepicted, showed that the stability with regard to the process level is inﬂ uenced by the same cause irrespec-tive of the particular products. It was revealed that it was an inﬂ uence of tampering the process by the operators.The data normality and the data independence for every product were veriﬁ ed using suitable statistical tests (the Shapiro – Wilk test, the test for the sample 84  METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...skewness and kurtosis, the test for randomness) and graphical tools. The results of this analysis showed that the data could be considered normally distributed and independent.The capability analysis was done using the capabil-ity indices of type A with the conﬁ dence intervals as the best solution with regard to the applied control charting method. The values of the indices and the conﬁ dence intervals are the same for all products due to the fact that all three analysed products had the same width (see Table 2).tion in the conditions of the SR processes. It was based on the critical analysis of the available control charting methods and the capability indices for the SR processes conditions. In the end, this proposal has been applied in the real conditions of the proﬁ le bars rolling. The gained results showed that the proposal was applicable and led to the reduction of the process variability and to the sig-niﬁ cant scrap reduction.AcknowledgementThe work was realized within the solution of the ESF project InterDV Z.1.07/2.2.00/15.0132 and the speciﬁ c research project SP2013/49, solved at the Fac-ulty of Metallurgy and Materials Engineering, VŠB-TU Ostrava with the support of Ministry of Education, Youth and Sports, Czech Republic.Legend of symbolsR range / mmR-bar mean range / mmx-bar mean / mmCp process capability index / -Cpk critical process capability index / -Cpm Taguchi´s capability index / -xˉ –T  difference between the mean and target value / mmn sample size GRR index of gage reproducibility and repeatability / %REFERENCES[1] B. Gajdzik, Metalurgija, 52 (2013) 1, 131-134.[2] W. Sroka, Metalurgija 52 (2013) 1, 127-130.[3] D. Noskievičová, R. Kucharczyk, Metalurgija, 51 (2012) 1, 137-140.[4] T. Pyzdek, Quality Progress, 26 (1993), 51-60.[5] G. K. Grifﬁ th, Statistical Process Control Methods For Long and Short Runs, ASQC Quality Press, Milwaukee, Wisconsin, 1996.pp. 39-58 and 121-145.[6] D. C. Montgomery, Introduction to Statistical Quality Control, J.Wiley & Sons, New York, 2009, pp. 435-438.[7] D. Wheeler, Short Run SPC, SPC Press Inc., Knoxville, Tennessee, 1991, pp. 1-32 and 9-10.[8] S. A. Wise, C. F. Douglas, Innovative Control Charting. Practical SPC Solutions for Today´s Manufacturing Envi-ronment, ASQ Quality Press, Milwaukee, Wisconsin, 1998, pp. 7-273 and 91-163.[9] C. P. Quesenberry, Journal of Quality Technology, 27 (1995) 3, 204-213.[10] P. F. Tang, Statistical Process Control with Special Refe-rence to Multivariable Processes and Short Runs, PhD the-sis, Victoria University of Technology, Melbourne, 1996, pp. 4-5 and 9-40.[11] M. Deleryd, Enhancing the Industrial Use of Process Ca-pability Studies, Doctoral thesis, University of Technolo-gy, Lulea, 1998, pp. 15-49 and 134-197.[12] F. Spiring, Determining and Assessing Process Capability for Engineers and Manufacturing, Nova Science Publi-shers, Inc., New York, 2010, pp. 159-173.Note:  The responsible for English language is: Otilia Drottnerová, Department of Foreign Languages, VŠB-TU Ostrava, Czech RepublicTable 2 Capability indicesCp / -1,2,3Cpk / -1,2,3Confi dence interval limits for Cp / -Confi dence interval limits for Cpk / -Lower Upper Lower Upper1,46 1,45 1,2775 1,6425 1,276 1,624It was clear that the process had to be improved to reduce the risk of the true value of Cpk being less than the obvious target value of 1,33.During two months after the ﬁ rst analysis, SPC was applied on a regular basis and the operators started to decide about the process adjustment according to the information from the control charts. It led to the reduc-tion of the process variation (see Figures 3 and 4) and to the reduction of the scrap by 14,2 t per these two months.Figure 3  Process variation at the beginning of the SPC implementation (Target x-bar control chart)Figure 4  Reduction of the process variability after two months (Target x-bar control chart)CONCLUSIONSThe main output of this paper was the original de-sign of the methodology for the complex SPC applica-

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81 METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ, B. WOSKADESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT RUN PROCESSES IN METALLURGYReceived – Prispjelo: 2012-12-29Accepted – Prihvaćeno: 2013-04-26Preliminary Note – Prethodno priopćenjeISSN 0543-5846METABK 53(1) 81-84 (2014)UDC – UDK 669.011:621.771:005.642.2=111D. Noskievičová, Faculty of Metallurgy and Materials Engineering, VŠB-TU Ostrava, B. Woska, Viadrus, a.s., Ostrava, Czech RepublicSo called short run manufacturing environment is now typical for many industrial branches including metallurgy. To be applicable in such nonstandard conditions classical control charts and capability indices must be modifi  ed. In this paper the design of the methodology for the complex application of the statistical control on the metallurgical short run processes is presented and verifi  ed in conditions of the bars rolling.Key words: metallurgy, bars rolling, short run processes, control charts, capability indicesINTRODUCTIONSo called short run (SR) environment is nowadays typical for many industrial branches including metal-lurgy. SR processes are characterized by quite a wide variety of mixed products with relatively smaller lot or batch sizes. These conditions have resulted from the growing product customization, higher and higher pro-duction ﬂ  exibility and larger stress on the high quality and low costs. The changing economic and production conditions in metallurgy are discussed in the wider con-text for instance in the papers [1] and [2]. In such condi-tions the conventional methods of statistical process control (SPC) and the capability analysis do not work. Some aspects of the application of SPC and the capabil-ity studies in metallurgy were discussed in the paper [3]. To be able to offer some meaningful information about the process stability and its capability the SPC and the process capability analysis must be modiﬁ  ed for the SR processes. The design of the methodology for the complex SPC application in the conditions of the metallurgical SR processes is the main output of this paper. It is based on the critical analysis of the available control charts and the capability indices for the SR proc-esses. This analysis forms the main contents of the ana-lytical part of the research. The proposal of the method-ology is based on the idea that SPC must be applied in a complex way where the capability analysis is an inte-gral part of it. In the experimental part this design was applied in the conditions of the proﬁ  le bars rolling. Such combined analysis and application of SPC including the capability study for the SR processes in metallurgy has not yet been found in the professional literature.ANALYTICAL PARTThe analytical part was focused on the following as-pects:SR SPC methods with special stress on the methods  • for variables;methods for evaluation of the variation representa- • tiveness;capability indices for SR environment including  • conﬁ  dence intervals of capability indices.Many proposals for applying the control charts in special conditions of a SR production have been offered up to now by many authors (for instance [4 - 9]). The most exhaustive review of the SPC methods for the SR conditions is offered by P. F. Tang [10]. In the analytical part different control charting methods have been eval-uated using the factors such as the rate of maturity, prac-tical usability, relative simplicity, predominance of the advantages compared with the disadvantages, the rate of the maturity. The result of this analysis is the decision tree (see Figure 1). When selecting suitable SR control charts the as-sumption that the process standard deviation is approxi-mately the same for all the parts must be tested in some cases (the target control charts). In the professional lit-erature several methods for evaluating the process vari-ance homogeneity can be found: the chart for mean ranges (R-bar) [7], the range test, [5], the F-test [5], the Bartlett test, the Levene test, the Brown-Forsyth test, the Cochran test, the Hartley test. These methods were analysed considering their complexity, precision, sensi-tivity to particular assumptions and their availability in the common SW products. The advantages and the dis-advantages of the selected methods were then deﬁ  ned to offer users a simple methodology for their application in connection with the selection of a suitable SR control chart (see Table 1).82   METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...As compared to the amount of papers and other pro-fessional literature dealing with the various control charts for SR manufacturing there are only several au-thors solving the problem of the capability analysis for the SR conditions in detail (for instance [11, 12]). After analysing the different approaches to the SR capability indices the authors of this paper divided the SR capabil-ity indices into 5 groups:Type A capability indices  •  Cp, Cpk for the processes with consistent variation for all products computed from the transformed data (deviations from the tar-get value).Type B capability indices  •  Cp, Cpk for the processes with consistent variation for all products computed from the original measurements.Type C capability indices  •  Cp, Cpk for the processes with non-consistent variation of all products. These estimations are not often based on the sufﬁ  cient data amount. For that reason the capability indices of type C are not very precise.Type D capability indices  •  Cp, Cpk, using uniﬁ  cation of the different tolerances based onthe linear transformation of the measured values. The uniﬁ  ed tolerances can lead to the situation when highly capable product will hide the non-capable prod-ucts and vice versa. For that reason the so called dia-grams (y ˉ, s) should be added [11].Type E capability indices Cpm and capability run chart [12].Figure 1 Decision tree for selection of the SR charting method [10]Table 1 Methods for evaluation of the variation representativeness [5, 7]Method Advantages DisadvantagesChart for mean ranges (R-bar)  Graphical display of all evaluated productsClear and quick answerSimply programmedLess precise measure of variationRange test  SimpleClear decision ruleLess preciseF-test  More precise than methods aboveSimpleStandard part of the majority of SW productsSuitable for comparison of only 2 samplesSensitive to departures from normalityBartlett test  Suitable for k samplesTest with high powerMore complicatedSensitive to departures from normalityLevene test  Suitable for k samplesMore robust testmore complicatedless poweredBrown-Forsyth test  Suitable for k samplesMost robust testnot standard part of every statistical SW productCochran test  Suitable for k subgroupsMore simpleSuitable only for samples of the same sizeSensitive to departures from normalityNot standard part of every statistical SW productHartley test  More simple methodFor k samples of the same sizeLess poweredSensitive to departures from normalityNot standard part of every SW product83 METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...METHODOLOGY DESIGNBased on the main idea of the authors´ research and on the conclusions of its analytical part, the proposal for a practical complex implementation of SPC including the capability assessment in the conditions of the re-petitive SR processes was proposed (see Figure 2).EXPERIMENTAL PARTThe proposed methodology was veriﬁ  ed in the con-ditions of the proﬁ  le bars rolling. This production has typical features of a repetitive short run process. The ﬁ  rst two steps of the proposed methodology (see Figure 2) can be described as follows:Selected process •  : proﬁ  le bars rolling;Product family •  : hot rolled steel L bars;Products:  •  3 products of one type different in di-mensions with tolerances 20 ± 1 mm, 30 ± 1 mm, 40 ± 1 mm;Quality characteristics •  : the arm width / mm.The homogeneity of the process variation was veri-ﬁ  ed using the control chart for R-bars (see Table 1). It was selected due to its simplicity and its graphical out-put. Based on the results of this analysis and on the deﬁ  nition of the sample size n = 4 (randomly selected from the bunch), the SR target x-bar and range control charts were selected (see Figure 1). The control interval was deﬁ  ned as every 2nd bunch. The capability indices of type A were applied including the computation of the conﬁ  dence intervals.RESULTS AND DISCUSSIONThe quality characteristics was selected on the base of the analysis of rework and the claims in the bar roll-ing process as well as the customer requirements. The product family (hot rolled steel L bars) was created on the base of the analysis of the orders repeatability, the volume of the particular orders and the technological similarity.The applied measurement system analysis MSA led to the sufﬁ  cient result: the complex index of the measure-ment system capability GRR = 22,18 % (for more infor-mation about the evaluation of these indicator see [3]).The measurement system then could be considered acceptable for the following statistical analysis. In spite of this result it was decided to improve the capability of this measurement system by implementing the working instruction for the data collection and record.The chart for the R-bar (see Table 1) showed that the variation of the rolling process can be considered ho-mogenous for all the analysed products.The target range control chart, where the range R for every sample was depicted, conﬁ  rmed the results of the previous process homogeneity analysis. The SR target x-bar control chart, where the difference (x ˉ–T) between the average and the target value for every sample was Figure 2 Steps of the designed methodologydepicted, showed that the stability with regard to the process level is inﬂ  uenced by the same cause irrespec-tive of the particular products. It was revealed that it was an inﬂ  uence of tampering the process by the operators.The data normality and the data independence for every product were veriﬁ  ed using suitable statistical tests (the Shapiro – Wilk test, the test for the sample 84   METALURGIJA 53 (2014) 1, 81-84D. NOSKIEVIČOVÁ et al.: DESIGN OF METHODOLOGY FOR APPLICATION OF STATISTICAL CONTROL ON SHORT...skewness and kurtosis, the test for randomness) and graphical tools. The results of this analysis showed that the data could be considered normally distributed and independent.The capability analysis was done using the capabil-ity indices of type A with the conﬁ  dence intervals as the best solution with regard to the applied control charting method. The values of the indices and the conﬁ  dence intervals are the same for all products due to the fact that all three analysed products had the same width (see Table 2).tion in the conditions of the SR processes. It was based on the critical analysis of the available control charting methods and the capability indices for the SR processes conditions. In the end, this proposal has been applied in the real conditions of the proﬁ  le bars rolling. The gained results showed that the proposal was applicable and led to the reduction of the process variability and to the sig-niﬁ  cant scrap reduction.AcknowledgementThe work was realized within the solution of the ESF project InterDV Z.1.07/2.2.00/15.0132 and the speciﬁ  c research project SP2013/49, solved at the Fac-ulty of Metallurgy and Materials Engineering, VŠB-TU Ostrava with the support of Ministry of Education, Youth and Sports, Czech Republic.Legend of symbolsR  range / mmR-bar  mean range / mmx-bar  mean / mmCp  process capability index / -Cpk  critical process capability index / -Cpm  Taguchi´s capability index / -x ˉ– T    difference between the mean and target value / mmn  sample size GRR  index of gage reproducibility and repeatability / %REFERENCES[1]  B. Gajdzik, Metalurgija, 52 (2013) 1, 131-134.[2]  W. Sroka, Metalurgija 52 (2013) 1, 127-130.[3]  D. Noskievičová, R. Kucharczyk, Metalurgija, 51 (2012) 1, 137-140.[4]  T. Pyzdek, Quality Progress, 26 (1993), 51-60.[5]  G. K. Grifﬁ  th, Statistical Process Control Methods For Long and Short Runs, ASQC Quality Press, Milwaukee, Wisconsin, 1996.pp. 39-58 and 121-145.[6]  D. C. Montgomery, Introduction to Statistical Quality Control, J.Wiley & Sons, New York, 2009, pp. 435-438.[7]  D. Wheeler, Short Run SPC, SPC Press Inc., Knoxville, Tennessee, 1991, pp. 1-32 and 9-10.[8]  S. A. Wise, C. F. Douglas, Innovative Control Charting. Practical SPC Solutions for Today´s Manufacturing Envi-ronment, ASQ Quality Press, Milwaukee, Wisconsin, 1998, pp. 7-273 and 91-163.[9]  C. P. Quesenberry, Journal of Quality Technology, 27 (1995) 3, 204-213.[10]  P. F. Tang, Statistical Process Control with Special Refe-rence to Multivariable Processes and Short Runs, PhD the-sis, Victoria University of Technology, Melbourne, 1996, pp. 4-5 and 9-40.[11]  M. Deleryd, Enhancing the Industrial Use of Process Ca-pability Studies, Doctoral thesis, University of Technolo-gy, Lulea, 1998, pp. 15-49 and 134-197.[12]  F. Spiring, Determining and Assessing Process Capability for Engineers and Manufacturing, Nova Science Publi-shers, Inc., New York, 2010, pp. 159-173.Note:   The responsible for English language is: Otilia Drottnerová, Department of Foreign Languages, VŠB-TU Ostrava, Czech RepublicTable 2 Capability indicesCp / -1,2,3Cpk / -1,2,3Confi  dence interval limits for Cp / -Confi  dence interval limits for Cpk / -Lower Upper Lower Upper1,46 1,45 1,2775 1,6425 1,276 1,624It was clear that the process had to be improved to reduce the risk of the true value of Cpk being less than the obvious target value of 1,33.During two months after the ﬁ  rst analysis, SPC was applied on a regular basis and the operators started to decide about the process adjustment according to the information from the control charts. It led to the reduc-tion of the process variation (see Figures 3 and 4) and to the reduction of the scrap by 14,2 t per these two months.Figure 3   Process variation at the beginning of the SPC implementation (Target x-bar control chart)Figure 4   Reduction of the process variability after two months (Target x-bar control chart)CONCLUSIONSThe main output of this paper was the original de-sign of the methodology for the complex SPC applica-

Design of methodology for application of statistical control on short run processes in metallurgy

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