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題名 以主成分分析法建立製程共變異數矩陣管制圖之研究
The Study of Covariance Matrix Control Chart Based on the Principal Component Analysis Method作者 簡廷安
Chien, Ting-An貢獻者 楊素芬
Yang, Su-Fen
簡廷安
Chien, Ting-An關鍵詞 多維度管制圖
主成分分析方法
符號管制圖
平均連串長度
維度變動
調整後的管制圖偵測出異常訊息的平均時間
Adjusted average time to signal
Average run length
Multivariate control chart
Principal component analysis
Sign chart
Variable dimension日期 2021 上傳時間 4-Aug-2021 14:41:58 (UTC+8) 摘要 在監測製造過程中，管制圖是經常使用的手法，現今蒐集到的資料多是高維度且來自未知的分配，使得多維度且無分配假設的管制圖之研究變得更加重要。本文提出一個監控製程共變異數矩陣的管制圖，在母體分配未知或是來自非常態時，使用主成分分析方法 (PCA) 結合符號管制圖 (sign chart) 建立多元製程共變異數矩陣管制圖，並且以平均連串長度 (ARL) 做為衡量此管制圖在製程失控時的偵測能力的指標。此外，本文進一步考慮變動維度 (VD) 的想法，以減少在監測失控製程中的所需偵測時間及抽樣成本，本文採調整後的管制圖偵測出異常訊息的平均時間 (AATS) 來評估管制圖表現。本文與文獻上存在的管制圖偵測能力比較，結果發現提出的管制圖在抽樣樣本數為5且製程的共變異數或相關係數發生小幅度偏移時有較好的偵測能力，最後以半導體製程資料及礫石資料說明所提出的管制圖的應用。
The control chart is a widely used approach to monitor manufacturing processes. In the era big data, most of the collected data are high dimensional from an unknown distribution. In statistical process control (SPC), the effectiveness of univariate Shewhart control charts is challenged by monitoring highly correlated quality variables simultaneously. The development of nonparametric multivariate statistical process control (MSPC) is critically important these days.In this article, we propose a new Phase II nonparametric multivariate expone-ntially weighted moving average (EWMA) control chart for monitoring the process covariance matrix, which is based on the principal component analysis (PCA) and sign statistics. We use the average run length (ARL) to measure the detection performance of the proposed control chart. The proposed control chart surpasses the existing nonparametric control charts in some out-of-control scenarios, especially with sample size 5 and small shifts in the covariance or the correlation coefficients. The application of the proposed control is demonstrated by gravel and semiconductor process data.Further, we extend the proposed control chart by considering of variable dimension (VD) to diminish the detection time and the sampling cost under an out-of-control process. We use the adjusted average time to signal (AATS) to measure the detection efficiency of the VD control chart for various sampling plans.參考文獻 [1] Alt, F. B. (1985). Multivariate Quality Control, in Encyclopedia of Statistical Sciences, Vol. 6, 110-122.[2] Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.[3] Aparisi, F., Epprecht, E. K., & Ruiz, O. (2012). T2 control charts with variable dimension. Journal of quality technology, 44(4), 375-393.[4] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.[5] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.[6] Bell, R. C., Jones-Farmer, L. A., & Billor, N. (2014). A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics, 56(4), 528-538.[7] Capizzi, G., & Masarotto, G. (2017). Phase I distribution-free analysis of multivariate data. Technometrics, 59(4), 484-495.[8] Chakraborti, S., & Eryilmaz, S. (2007). A nonparametric Shewhart-type signed-rank control chart based on runs. Communications in Statistics—Simulation and Computation®, 36(2), 335-356.[9] Chakraborti, S., & Van de Wiel, M. A. (2008). A nonparametric control chart based on the Mann-Whitney statistic (pp. 156-172). Institute of Mathematical Statistics.[10] Cheng, C. R., & Shiau, J. J. H. (2015). A distribution‐free multivariate control chart for phase I applications. Quality and Reliability Engineering International, 31(1), 97-111.[11] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[12] Chou, Y. M., Polansky, A. M., & Mason, R. L. (1998). Transforming non-normal data to normality in statistical process control. Journal of Quality Technology, 30(2), 133-141.[13] Costa, A. F., & Machado, M. A. (2008). A new chart for monitoring the covariance matrix of bivariate processes. Communications in Statistics—Simulation and Computation®, 37(7), 1453-1465.[14] Costa, A. F. B., & Machado, M. A. G. (2009). A new chart based on sample variances for monitoring the covariance matrix of multivariate processes. The International Journal of Advanced Manufacturing Technology, 41(7-8), 770-779.[15] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[16] Das, N. (2008). Non-parametric control chart for controlling variability based on rank test.[17] Doornik, J. A., & Hansen, H. (2008). An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics, 70, 927-939.[18] Douglas M. Hawkins & Edgard M. Maboudou-Tchao (2008) Multivariate Exponentially Weighted Moving Covariance Matrix, Technometrics, 50:2, 155-166.[19] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), 268-282.[20] Farokhnia, M., & Niaki, S. T. A. (2020). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 49(7), 1815-1838.[21] Ghute, V. B., & Shirke, D. T. (2008). A multivariate synthetic control chart for process dispersion. Quality Technology & Quantitative Management, 5(3), 271-288.[22] Haq, A., & Sohrab, K. (2021). Directionally sensitive MCUSUM mean charts. Quality and Reliability Engineering International.[23] Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.[24] Holmes, D. S., & Mergen, A. E. (1993). Improving the performance of the T2 control chart. Quality Engineering, 5(4), 619-625.[25] Hotelling, H. (1947) Multivariate quality control-illustrated by the air testing of sample bombsights, Techniques of Statistical Analysis, Eisenhart, C., Hastay, M.W. and Wallis, W.A. (eds), McGraw-Hill, New York, NY, pp. 111–184.[26] Huwang, L., Lin, P. C., Chang, C. H., Lin, L. W., & Tee, Y. S. (2017). An EWMA chart for monitoring the covariance matrix of a multivariate process based on dissimilarity index. Quality and Reliability Engineering International, 33(8), 2089-2104.[27] Huwang, L., Lin, L. W., & Yu, C. T. (2019). A spatial rank–based multivariate EWMA chart for monitoring process shape matrices. Quality and Reliability Engineering International, 35(6), 1716-1734.[28] Jackson, J. E. (1959). Quality Control Methods for Several Related Variables, Technometrics,Vol. 1(4),pp. 359–377.[29] Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and psychological measurement, 20(1), 141-151.[30] Khilare, S. K., & Shirke, D. T. (2012). Nonparametric synthetic control charts for process variation. Quality and Reliability Engineering International, 28(2), 193-202.[31] Krupskii, P., Harrou, F., Hering, A. S., & Sun, Y. (2020). Copula-based monitoring schemes for non-Gaussian multivariate processes. Journal of Quality Technology, 52(3), 219-234.[32] Li, B., Wang, K., & Yeh, A. B. (2013). Monitoring the covariance matrix via penalized likelihood estimation. IIE Transactions, 45(2), 132-146.[33] Li, C., & Mukherjee, A. (2021). Two economically optimized nonparametric schemes for monitoring process variability. Quality and Reliability Engineering International.[34] Li, Z., Zou, C., Wang, Z., & Huwang, L. (2013). A multivariate sign chart for monitoring process shape parameters. Journal of Quality Technology, 45(2), 149-165.[35] Li, Z., Xie, M., & Zhou, M. (2018). Rank-based EWMA procedure for sequentially detecting changes of process location and variability. Quality Technology & Quantitative Management, 15(3), 354-373.[36] Liang, W., Xiang, D., Pu, X., Li, Y., & Jin, L. (2019). A robust multivariate sign control chart for detecting shifts in covariance matrix under the elliptical directions distributions. Quality Technology & Quantitative Management, 16(1), 113-127.[37] Lowry, C. A., Woodall, W. H., Champ, C. W., & Rigdon, S. E. (1992). A multivariate exponentially weighted moving average control chart. Technometrics, 34(1), 46-53.[38] Lowry, C. A., & Montgomery, D. C. (1995). A review of multivariate control charts. IIE transactions, 27(6), 800-810.[39] Malela-Majika, J. C. (2021). New distribution-free memory-type control charts based on the Wilcoxon rank-sum statistic. Quality Technology & Quantitative Management, 18(2), 135-155.[40] Malela-Majika, J. C., Chakraborti, S., & Graham, M. A. (2016). Distribution-free Phase II Mann–Whitney control charts with runs-rules. The International Journal of Advanced Manufacturing Technology, 86(1), 723-735.[41] Michael, M. C., & Johnston, A. (2008). Secom Data Sets of UCI Machine Learning Repository.[42] Montgomery, D. C., & Wadsworth, H. M. (1972, May). Some techniques for multivariate quality control applications. In ASQC Technical Conference Transactions (Vol. 26, pp. 427-435).[43] Montgomery, D. C. (2020). Introduction to statistical quality control. John Wiley & Sons.[44] Pearson, K. (1901). LIII. On lines and planes of closest fit to systems of points in space. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 2(11), 559-572.[45] Perry, M. B., & Wang, Z. (2020). A distribution-free joint monitoring scheme for location and scale using individual observations. Journal of Quality Technology, 1-18.[46] Pignatiello Jr, J. J., & Runger, G. C. (1990). Comparisons of multivariate CUSUM charts. Journal of quality technology, 22(3), 173-186.[47] Qiu, P. (2018). Some perspectives on nonparametric statistical process control. Journal of Quality Technology, 50(1), 49-65.[48] Reynolds, M. R., Amin, R. W., Arnold, J. C., & Nachlas, J. A. (1988). Charts with variable sampling intervals. Technometrics, 30(2), 181-192.[49] Royston, P. (1992). Approximating the Shapiro-Wilk W-test for non-normality. Statistics and computing, 2(3), 117-119.[50] Shewhart, W. A. (1931). Economic control of quality of manufactured product. Macmillan And Co Ltd, London.[51] Scrucca, L. (2013). GA: a package for genetic algorithms in R. Journal of Statistical Software, 53(4), 1-37.[52] Stoumbos, Z. G., Reynolds Jr, M. R., Ryan, T. P., & Woodall, W. H. (2000). The state of statistical process control as we proceed into the 21st century. Journal of the American Statistical Association, 95(451), 992-998.[53] Tracy, N. D., Young, J. C., & Mason, R. L. (1992). Multivariate control charts for individual observations. Journal of quality technology, 24(2), 88-95.[54] Wang, S., & Reynolds Jr, M. R. (2013). A GLR control chart for monitoring the mean vector of a multivariate normal process. Journal of Quality Technology, 45(1), 18-33.[55] Xue, L., & Qiu, P. (2020). A nonparametric CUSUM chart for monitoring multivariate serially correlated processes. Journal of Quality Technology, 1-14.[56] Yang, S. F. (2016). An improved distribution-free EWMA mean chart. Communications in Statistics-Simulation and Computation, 45(4), 1410-1427.[57] Yang, S. F., & Arnold, B. C. (2014). A simple approach for monitoring business service time variation. The Scientific World Journal, 2014.[58] Yang, S. F., & Arnold, B. C. (2016). Monitoring process variance using an ARL‐unbiased EWMA‐p control chart. Quality and Reliability Engineering International, 32(3), 1227-1235.[59] Yang, S. F., & Jiang, T. A. (2019). Service quality variation monitoring using the interquartile range control chart. Quality Technology & Quantitative Management, 16(5), 613-627.[60] Yang, S. F., Lin, J. S., & Cheng, S. W. (2011). A new nonparametric EWMA sign control chart. Expert Systems with Applications, 38(5), 6239-6243.[61] Yang, S. F., Lin, Y. C., & Yeh, A. B. (2021). A Phase II depth‐based variable dimension EWMA control chart for monitoring process mean. Quality and Reliability Engineering International.[62] Yang, S. F., & Wu, S. H. (2017). A double sampling scheme for process variability monitoring. Quality and Reliability Engineering International, 33(8), 2193-2204.[63] Yeh, A.B., Lin, D. K. J., Zhou, H. and Venkataramani, C. (2003). A multivariate exponentially moving average control chart for monitoring process variability. Journal of Applied Statistics, 30: 507–536.[64] Yen, C. L., & Shiau, J. J. H. (2010). A multivariate control chart for detecting increases in process dispersion. Statistica Sinica, 1683-1707.[65] Yen, C. L., Shiau, J. J. H., & Yeh, A. B. (2012). Effective control charts for monitoring multivariate process dispersion. Quality and Reliability Engineering International, 28(4), 409-426.[66] Zhou, M., Zhou, Q., & Geng, W. (2016). A new nonparametric control chart for monitoring variability. Quality and Reliability Engineering International, 32(7), 2471-2479.[67] Zou, C., & Tsung, F. (2010). Likelihood ratio-based distribution-free EWMA control charts. Journal of Quality Technology, 42(2), 174-196. 描述 碩士
國立政治大學
統計學系
108354012資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108354012 資料類型 thesis dc.contributor.advisor 楊素芬 zh_TW dc.contributor.advisor Yang, Su-Fen en_US dc.contributor.author (Authors) 簡廷安 zh_TW dc.contributor.author (Authors) Chien, Ting-An en_US dc.creator (作者) 簡廷安 zh_TW dc.creator (作者) Chien, Ting-An en_US dc.date (日期) 2021 en_US dc.date.accessioned 4-Aug-2021 14:41:58 (UTC+8) - dc.date.available 4-Aug-2021 14:41:58 (UTC+8) - dc.date.issued (上傳時間) 4-Aug-2021 14:41:58 (UTC+8) - dc.identifier (Other Identifiers) G0108354012 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/136318 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 統計學系 zh_TW dc.description (描述) 108354012 zh_TW dc.description.abstract (摘要) 在監測製造過程中，管制圖是經常使用的手法，現今蒐集到的資料多是高維度且來自未知的分配，使得多維度且無分配假設的管制圖之研究變得更加重要。本文提出一個監控製程共變異數矩陣的管制圖，在母體分配未知或是來自非常態時，使用主成分分析方法 (PCA) 結合符號管制圖 (sign chart) 建立多元製程共變異數矩陣管制圖，並且以平均連串長度 (ARL) 做為衡量此管制圖在製程失控時的偵測能力的指標。此外，本文進一步考慮變動維度 (VD) 的想法，以減少在監測失控製程中的所需偵測時間及抽樣成本，本文採調整後的管制圖偵測出異常訊息的平均時間 (AATS) 來評估管制圖表現。本文與文獻上存在的管制圖偵測能力比較，結果發現提出的管制圖在抽樣樣本數為5且製程的共變異數或相關係數發生小幅度偏移時有較好的偵測能力，最後以半導體製程資料及礫石資料說明所提出的管制圖的應用。 zh_TW dc.description.abstract (摘要) The control chart is a widely used approach to monitor manufacturing processes. In the era big data, most of the collected data are high dimensional from an unknown distribution. In statistical process control (SPC), the effectiveness of univariate Shewhart control charts is challenged by monitoring highly correlated quality variables simultaneously. The development of nonparametric multivariate statistical process control (MSPC) is critically important these days.In this article, we propose a new Phase II nonparametric multivariate expone-ntially weighted moving average (EWMA) control chart for monitoring the process covariance matrix, which is based on the principal component analysis (PCA) and sign statistics. We use the average run length (ARL) to measure the detection performance of the proposed control chart. The proposed control chart surpasses the existing nonparametric control charts in some out-of-control scenarios, especially with sample size 5 and small shifts in the covariance or the correlation coefficients. The application of the proposed control is demonstrated by gravel and semiconductor process data.Further, we extend the proposed control chart by considering of variable dimension (VD) to diminish the detection time and the sampling cost under an out-of-control process. We use the adjusted average time to signal (AATS) to measure the detection efficiency of the VD control chart for various sampling plans. en_US dc.description.tableofcontents Chapter 1. Introduction 11.1 Literature review and research motivation 1Chapter 2. The EWMA Control Chart for Monitoring Process with In-Control Identity Covariance Matrix 52.1 A Principal component analysis (PCA) based covariance matrix chart 52.2 Determination of the control limits of the proposed control chart 112.3 Detection performance of the proposed ZEWMAV control charts 152.4 Out-of-control detection performance comparison 29Chapter 3. The EWMA Control Charts for An In-Control Prcoess with Non-Identity Covariance Matrix 513.1 Construction of the ZEWMAV1 and ZEWMAV2 charts 513.2 Determination of the control limits of the proposed control charts 573.3 Out-of-control detection performance of the proposed two control charts 593.4 Illustrative examples for the application of the proposed covariance matrix control chart 71Chapter 4. The Variable Dimension EWMA Control Charts for Monitoring the Process Covariance Matrix 974.1 Construction of the VD ZEWMAV charts 974.2 Determination of the control limits and warning limits of the proposed VD ZEWMAV charts 1044.3 Detection performance of the VD ZEWMAV charts 1094.4 Out-of-control detection performance comparison between the FD ZEWMAV and VD ZEWMAV charts 1234.5 An illustrative example of VD ZEWMAV charts 132Chapter 5. Conclusions and Future Study 149References 150 zh_TW dc.format.extent 12083835 bytes - dc.format.mimetype application/pdf - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108354012 en_US dc.subject (關鍵詞) 多維度管制圖 zh_TW dc.subject (關鍵詞) 主成分分析方法 zh_TW dc.subject (關鍵詞) 符號管制圖 zh_TW dc.subject (關鍵詞) 平均連串長度 zh_TW dc.subject (關鍵詞) 維度變動 zh_TW dc.subject (關鍵詞) 調整後的管制圖偵測出異常訊息的平均時間 zh_TW dc.subject (關鍵詞) Adjusted average time to signal en_US dc.subject (關鍵詞) Average run length en_US dc.subject (關鍵詞) Multivariate control chart en_US dc.subject (關鍵詞) Principal component analysis en_US dc.subject (關鍵詞) Sign chart en_US dc.subject (關鍵詞) Variable dimension en_US dc.title (題名) 以主成分分析法建立製程共變異數矩陣管制圖之研究 zh_TW dc.title (題名) The Study of Covariance Matrix Control Chart Based on the Principal Component Analysis Method en_US dc.type (資料類型) thesis en_US dc.relation.reference (參考文獻) [1] Alt, F. B. (1985). Multivariate Quality Control, in Encyclopedia of Statistical Sciences, Vol. 6, 110-122.[2] Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.[3] Aparisi, F., Epprecht, E. K., & Ruiz, O. (2012). T2 control charts with variable dimension. Journal of quality technology, 44(4), 375-393.[4] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.[5] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.[6] Bell, R. C., Jones-Farmer, L. A., & Billor, N. (2014). A distribution-free multivariate phase I location control chart for subgrouped data from elliptical distributions. Technometrics, 56(4), 528-538.[7] Capizzi, G., & Masarotto, G. (2017). Phase I distribution-free analysis of multivariate data. Technometrics, 59(4), 484-495.[8] Chakraborti, S., & Eryilmaz, S. (2007). A nonparametric Shewhart-type signed-rank control chart based on runs. Communications in Statistics—Simulation and Computation®, 36(2), 335-356.[9] Chakraborti, S., & Van de Wiel, M. A. (2008). A nonparametric control chart based on the Mann-Whitney statistic (pp. 156-172). Institute of Mathematical Statistics.[10] Cheng, C. R., & Shiau, J. J. H. (2015). A distribution‐free multivariate control chart for phase I applications. Quality and Reliability Engineering International, 31(1), 97-111.[11] Chen, N., Zi, X., & Zou, C. (2016). A distribution-free multivariate control chart. Technometrics, 58(4), 448-459.[12] Chou, Y. M., Polansky, A. M., & Mason, R. L. (1998). Transforming non-normal data to normality in statistical process control. Journal of Quality Technology, 30(2), 133-141.[13] Costa, A. F., & Machado, M. A. (2008). A new chart for monitoring the covariance matrix of bivariate processes. Communications in Statistics—Simulation and Computation®, 37(7), 1453-1465.[14] Costa, A. F. B., & Machado, M. A. G. (2009). A new chart based on sample variances for monitoring the covariance matrix of multivariate processes. The International Journal of Advanced Manufacturing Technology, 41(7-8), 770-779.[15] Crosier, R. B. (1988). Multivariate generalizations of cumulative sum quality-control schemes. Technometrics, 30(3), 291-303.[16] Das, N. (2008). Non-parametric control chart for controlling variability based on rank test.[17] Doornik, J. A., & Hansen, H. (2008). An omnibus test for univariate and multivariate normality. Oxford Bulletin of Economics and Statistics, 70, 927-939.[18] Douglas M. Hawkins & Edgard M. Maboudou-Tchao (2008) Multivariate Exponentially Weighted Moving Covariance Matrix, Technometrics, 50:2, 155-166.[19] Epprecht, E. K., Aparisi, F., & Ruiz, O. (2018). Optimum variable-dimension EWMA chart for multivariate statistical process control. Quality Engineering, 30(2), 268-282.[20] Farokhnia, M., & Niaki, S. T. A. (2020). Principal component analysis-based control charts using support vector machines for multivariate non-normal distributions. Communications in Statistics-Simulation and Computation, 49(7), 1815-1838.[21] Ghute, V. B., & Shirke, D. T. (2008). A multivariate synthetic control chart for process dispersion. Quality Technology & Quantitative Management, 5(3), 271-288.[22] Haq, A., & Sohrab, K. (2021). Directionally sensitive MCUSUM mean charts. Quality and Reliability Engineering International.[23] Hawkins, D. M. (1991). Multivariate quality control based on regression-adjusted variables. Technometrics, 33(1), 61-75.[24] Holmes, D. S., & Mergen, A. E. (1993). Improving the performance of the T2 control chart. Quality Engineering, 5(4), 619-625.[25] Hotelling, H. (1947) Multivariate quality control-illustrated by the air testing of sample bombsights, Techniques of Statistical Analysis, Eisenhart, C., Hastay, M.W. and Wallis, W.A. (eds), McGraw-Hill, New York, NY, pp. 111–184.[26] Huwang, L., Lin, P. C., Chang, C. H., Lin, L. W., & Tee, Y. S. (2017). An EWMA chart for monitoring the covariance matrix of a multivariate process based on dissimilarity index. Quality and Reliability Engineering International, 33(8), 2089-2104.[27] Huwang, L., Lin, L. W., & Yu, C. T. (2019). A spatial rank–based multivariate EWMA chart for monitoring process shape matrices. Quality and Reliability Engineering International, 35(6), 1716-1734.[28] Jackson, J. E. (1959). Quality Control Methods for Several Related Variables, Technometrics,Vol. 1(4),pp. 359–377.[29] Kaiser, H. F. (1960). The application of electronic computers to factor analysis. Educational and psychological measurement, 20(1), 141-151.[30] Khilare, S. K., & Shirke, D. T. (2012). 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