Monitoring of simple linear profiles and change point estimation in the presence of within-profile ARMA autocorrelation | ||
| Journal of Quality Engineering and Production Optimization | ||
| مقاله 6، دوره 8، شماره 1، مرداد 2023، صفحه 87-114 اصل مقاله (1.24 M) | ||
| نوع مقاله: CFP- Quality Engineering Techniques in Production and Service Systems | ||
| شناسه دیجیتال (DOI): 10.22070/jqepo.2023.17415.1253 | ||
| نویسندگان | ||
| Hooman Fakhimi Kazemi؛ Orod Ahmadi* ؛ Hamidreza Izadbakhsh | ||
| Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran | ||
| چکیده | ||
| In statistical process control applications, the quality of certain processes or products can be accurately described by either a univariate or multivariate distribution. Nonetheless, in certain instances, the quality of a process or product can be defined by a profile, which represents the relationship between independent and response variables. Numerous studies have examined the monitoring of simple linear profiles that incorporate uncorrelated observations. Nevertheless, in practice, this assumption is seldom met as a result of spatial autocorrelation or time collapse, which can result in unsatisfactory outcomes. In numerous studies, the autocorrelation structure between observations is modeled as a first-order autoregressive ( ) model. However, a wide range of autocorrelation between observations might not be modeled by models. Therefore, this paper examines a simple linear profile and assumes an autoregressive moving average autocorrelation structure between each observation, which is more flexible than models. It is assumed that in each profile, random errors follow an model. This article mainly focuses on the Phase II monitoring of simple linear profiles, with a particular emphasis on the estimation of change points, which can lead to substantial reductions in time and cost. This paper aims to estimate the change point for each simple linear profile that possesses an autocorrelation structure of . To achieve this, a maximum likelihood estimator is developed. Simulation experiments are conducted to compare Hotelling's control chart with the proposed control chart. Additionally, the proposed change point estimator is compared to one of the built-in estimators for exponentially weighted moving average ( ) control charts. The results demonstrate that the proposed estimator has accurately estimated the change point regardless of the shift size and the coefficients, and it outperforms the built-in control chart estimator in terms of accuracy. | ||
| کلیدواژهها | ||
| Autocorrelation؛ Autoregressive moving average process؛ Change point estimation؛ EWMA-3 control chart؛ Simple linear profile | ||
| مراجع | ||
|
Amiri, A., & Allahyari, S. (2012). Change point estimation methods for control chart post signal diagnostics: a literature review. Quality and Reliability Engineering International, 28(7), 673-685.
Amiri, A., Derakhshani, R., & Esmaeeli, H. (2022). Monitoring binary response profiles in multistage processes. Journal of Quality Engineering and Production Optimization, 6(2).
Amiri, A., Kazemzadeh, R. B., & Noorossana, R. (2010). Phase II Monitoring of Autocorrelated Polynomial Profiles in AR 1 Processes. International Journal of Science and Technology, Scientia Iranica, 17(1, pp. 12-22).
Asghari Torkamani, E., Niaki, S. T. A., Aminnayeri, M., & Davoodi, M. (2014). Estimating the change point of correlated Poisson count processes. Quality Engineering, 26(2), 182-195.
Atashgar, K., & Adelian, F. (2023). Multivariate Statistical process Control Using Wavelet Approach. Journal of Quality Engineering and Production Optimization, (), -. doi: 10.22070/jqepo.2023.16027.1230
Ayoubi, M., & Ebadi, M. (2022). Estimating step and linear drift change point in contingency tables. Journal of Quality Engineering and Production Optimization, 7(2), 147-160. doi: 10.22070/jqepo.2022.5744.1167
Ayoubi, M., Kazemzadeh, R. B., & Noorossana, R. (2016). Change point estimation in the mean of multivariate linear profiles with no change type assumption via dynamic linear model. Quality and Reliability Engineering International, 32(2), 403-433.
Box, G. E., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society: Series B (Methodological), 26(2), 211-243.
Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: forecasting and control. John Wiley & Sons.
Cheng, T. C., & Yang, S. F. (2018). Monitoring profile based on a linear regression model with correlated errors. Quality Technology & Quantitative Management, 15(3), 393-412.
Chiang, J. Y., Lio, Y. L., & Tsai, T. R. (2017). MEWMA control chart and process capability indices for simple linear profiles with within‐profile autocorrelation. Quality and Reliability Engineering International, 33(5), 1083-1094.
Fallahdizcheh, A., & Wang, C. (2022). Profile monitoring based on transfer learning of multiple profiles with incomplete samples. IISE transactions, 54(7), 643-658.
Ghazanfari, M., Alaeddini, A., Niaki, S. T. A., & Aryanezhad, M. B. (2008). A clustering approach to identify the time of a step change in Shewhart control charts. Quality and Reliability Engineering International, 24(7), 765-778.
Gupta, S., Montgomery, D. C., & Woodall, W. H. (2006). Performance evaluation of two methods for online monitoring of linear calibration profiles. International journal of production research, 44(10), 1927-1942.
Haq, A., Bibi, M., & Shah, B. A. (2022). A novel approach to monitor simple linear profiles using individual observations. Communications in Statistics-Simulation and Computation, 51(11), 6269-6282.
He, S., Song, L., Shang, Y., & Wang, Z. (2021). Change-point detection in Phase I for autocorrelated Poisson profiles with random or unbalanced designs. International Journal of Production Research, 59(14), 4306-4323.
Jensen, W. A., Birch, J. B., & Woodall, W. H. (2008). Monitoring correlation within linear profiles using mixed models. Journal of Quality Technology, 40(2), 167-183.
Kamranrad, R., & Amiri, A. (2016). Robust Holt-Winter based control chart for monitoring autocorrelated simple linear profiles with contaminated data. Scientia Iranica, 23(3), 1345-1354.
Kang, L., & Albin, S. L. (2000). On-line monitoring when the process yields a linear profile. Journal of quality Technology, 32(4), 418-426.
Kazemzadeh, R. B., Amiri, A., and Mirbeik, H. (2016b). Step Change Point Estimation of the First-Order Autoregressive Autocorrelated Simple Linear Profiles, Scientia Iranica. Transaction E, Industrial Engineering, 23(6), 2995-3008.
Kazemzadeh, R. B., Noorossana, R., & Ayoubi, M. (2015). Change point estimation of multivariate linear profiles under linear drift. Communications in Statistics-Simulation and Computation, 44(6), 1570-1599.
Khedmati, M., & Niaki, S. T. A. (2015). Identifying the time of a step change in AR (1) auto-correlated simple linear profiles. Journal of Industrial Engineering International, 11, 473-484.
Khedmati, M., Soleymanian, M. E., Keramatpour, M., & Niaki, S. T. A. (2013). Monitoring and change point estimation of AR (1) autocorrelated polynomial profiles. International Journal of Engineering, 26(9), 933-942.
Kim, K., Mahmoud, M. A., & Woodall, W. H. (2003). On the monitoring of linear profiles. Journal of Quality Technology, 35(3), 317–328.
Koosha, M., & Amiri, A. (2013). Generalized linear mixed model for monitoring autocorrelated logistic regression profiles. The International Journal of Advanced Manufacturing Technology, 64, 487-495.
Mahmoud, M. A., & Woodall, W. H. (2004). Phase I analysis of linear profiles with calibration applications. Technometrics, 46(4), 380–391.
Mahmoud, M. A., Parker, P. A., Woodall, W. H., & Hawkins, D. M. (2007). A change point method for linear profile data. Quality and Reliability Engineering International, 23(2), 247–268.
Maleki, M. R., Amiri, A., Taheriyoun, A. R., & Castagliola, P. (2018). Phase I monitoring and change point estimation of autocorrelated poisson regression profiles. Communications in statistics-Theory and Methods, 47(24), 5885-5903.
Nadi, A. A., Yeganeh, A., & Shadman, A. (2023). Monitoring simple linear profiles in the presence of within‐and between‐profile autocorrelation. Quality and Reliability Engineering International.
Narvand, A., Soleimani, P., & Raissi, S. (2013). Phase II monitoring of auto-correlated linear profiles using linear mixed model. Journal of Industrial Engineering International, 9, 1-9.
Niaki, S. T. A., Khedmati, M., & Soleymanian, M. E. (2015). Statistical monitoring of autocorrelated simple linear profiles based on principal components analysis. Communications in Statistics-Theory and Methods, 44(21), 4454-4475.
Nie, B., & Du, M. (2017). Identifying change-point in polynomial profiles based on data-segmentation. Communications in Statistics-Simulation and Computation, 46(4), 2513-2528.
Nishina, K. (1992). A comparison of control charts from the viewpoint of change‐point estimation. Quality and reliability engineering international, 8(6), 537-541.
Noorossana, R., & Shadman, A. (2009). Estimating the change point of a normal process mean with a monotonic change. Quality and Reliability Engineering International, 25(1), 79-90.
Noorossana, R., Amiri, A., & Soleimani, P. (2008). On the monitoring of autocorrelated linear profiles. Communications in Statistics—Theory and Methods, 37(3), 425-442.
Noorossana, R., Saghaei, A., & Dorri, M. (2010). Linear profile monitoring in the presence of non-normality and autocorrelation.
Perry, M. B., & Pignatiello Jr, J. J. (2010). Identifying the time of step change in the mean of autocorrelated processes. Journal of Applied Statistics, 37(1), 119-136.
Pini, A., Vantini, S., Colosimo, B. M., & Grasso, M. (2018). Domain-selective functional analysis of variance for supervised statistical profile monitoring of signal data. Journal of the Royal Statistical Society. Series C (Applied Statistics), 67(1), 55-81.
Rahimi, S. B., Amiri, A., & Ghashghaei, R. (2021). Simultaneous monitoring of mean vector and covariance matrix of multivariate simple linear profiles in the presence of within profile autocorrelation. Communications in Statistics-Simulation and Computation, 50(6), 1791-1808.
Saghaei, A., Mehrjoo, M., & Amiri, A. (2009). A CUSUM-based method for monitoring simple linear profiles. The International Journal of Advanced Manufacturing Technology, 45, 1252-1260.
Salmasnia, A., Tavakoli, A., Noroozi, M., & Abdzadeh, B. (2019). Robust economic-statistical design of the EWMA-R control charts for phase II linear profile monitoring. Journal of Industrial Engineering and Management Studies, 6(1), 46-67.
Shadman, A., Mahlooji, H., Yeh, A. B., & Zou, C. (2015). A change point method for monitoring generalized linear profiles in phase I. Quality and Reliability Engineering International, 31(8), 1367-1381.
Shadman, A., Zou, C., Mahlooji, H., & Yeh, A. B. (2017). A change point method for Phase II monitoring of generalized linear profiles. Communications in Statistics-Simulation and Computation, 46(1), 559-578.
Sharafi, A., Aminnayeri, M., & Amiri, A. (2012). Identifying the change point in monitoring Poisson regression profiles with linear trend disturbance. Journal of Quality Engineering and Management, 1(1), 39-44.
Sharafi, A., Aminnayeri, M., & Amiri, A. (2012). Identifying the time of step change in binary profiles. The International Journal of Advanced Manufacturing Technology, 63, 209-214.
Sharafi, A., Aminnayeri, M., & Amiri, A. (2013). An MLE approach for estimating the time of step changes in Poisson regression profiles. Scientia Iranica, 20(3), 855-860.
Sharafi, A., Aminnayeri, M., Amiri, A., & Rasouli, M. (2013). Estimating the Change Point of Binary Profiles with a Linear Trend Disturbance (Quality Engineering Conference Paper). International Journal of Industrial Engineering & Production Research, 24(2), 123-129.
Sogandi, F. (2015). Estimating the time of a step change in Gamma regression profiles using MLE approach. International Journal of Engineering, 28(2), 224-233.
Sogandi, F., & Amiri, A. (2014). Change point estimation of gamma regression profiles with a linear trend disturbance. International Journal of Quality Engineering and Technology, 4(4), 352-368.
Sogandi, F., & Amiri, A. (2017). Monotonic change point estimation of generalized linear model-based regression profiles. Communications in Statistics-Simulation and Computation, 46(3), 2207-2227.
Sogandi, F., & Vakilian, F. (2015). Isotonic change point estimation in the AR (1) autocorrelated simple linear profiles. International Journal of Engineering, 28(7), 1059-1067.
Soleimani, P., Noorossana, R., & Amiri, A. (2009). Simple linear profiles monitoring in the presence of within profile autocorrelation. Computers & Industrial Engineering, 57(3), 1015-1021.
Soleimani, P., Noorossana, R., & Niaki, S. T. A. (2013). Monitoring autocorrelated multivariate simple linear profiles. The International Journal of Advanced Manufacturing Technology, 67(5-8), 1857-1865.
Stover, F. S., & Brill, R. V. (1998). Statistical quality control applied to ion chromatography calibrations. Journal of Chromatography A, 804(1-2), 37-43.
Taghipour, M., Amiri, A., & Saghaei, A. (2017). Phase I monitoring of within-profile autocorrelated multivariate linear profiles. Journal of Engineering Research, 5(4).
Tamirat, Y., & Wang, F. K. (2016). Sampling plan based on the exponentially weighted moving average yield index for autocorrelation within linear profiles. Quality and Reliability Engineering International, 32(5), 1757-1768.
Wang, F. K., & Tamirat, Y. (2015). Process yield analysis for linear within‐profile autocorrelation. Quality and Reliability Engineering International, 31(6), 1053-1061.
Wang, K., & Tsung, F. (2005). Using profile monitoring techniques for a data‐rich environment with huge sample size. Quality and reliability engineering international, 21(7), 677-688.
Woodall, W. H. (2007). Current research on profile monitoring. Production, 17, 420-425.
Woodall, W. H., Spitzner, D. J., Montgomery, D. C., & Gupta, S. (2004). Using control charts to monitor process and product quality profiles. Journal of Quality Technology, 36(3), 309-320.
Zhang, Y., He, Z., Zhang, C., & Woodall, W. H. (2014). Control charts for monitoring linear profiles with within‐profile correlation using Gaussian process models. Quality and Reliability Engineering International, 30(4), 487-501.
Zou, C., Zhang, Y., & Wang, Z. (2006). A control chart based on a change-point model for monitoring linear profiles. IIE transactions, 38(12), 1093-1103. | ||
|
آمار تعداد مشاهده مقاله: 410 تعداد دریافت فایل اصل مقاله: 75 |
||