You are here

BELİRSİZLİK ÖLÇÜMÜNE DAYALI BİR PROSES KONTROL DİYAGRAMI

A PROCESS CONTROL CHART BASED ON UNCERTAINTY MEASUREMENT

Journal Name:

Publication Year:

Author NameUniversity of AuthorFaculty of Author

AMS Codes:

Abstract (2. Language): 
The notion of variation and determining and eliminating it has become a subject that has found a wide application area after total quality approach has become widespread. There is a variety of control charts used in determining variation. Since the 1920’s, when W.Shewhart developed the first control chart, control charts, which have been examined many times in every aspect, are accepted to be one of the seven basic tools of quality. X-R Charts, which are the oldest charts used for variables, are based on the assumption that inner distributions of process samples and distribution of parameter values obtained from the inner distributions of these samples fit the normal distribution. In this study, by setting off from this assumption and the notion of entropy, a new limited process control chart that take the uncertainty in the process into consideration is developed.
Abstract (Original Language): 
Varyasyon ve varyasyonun belirlenmesi, ardından da ortadan kaldırılması toplam kalite yaklaşımının yayılmasıyla birlikte geniş uygulama alanı bulan bir konu haline gelmiştir. Varyasyonun belirlenmesinde kullanılan kontrol diyagramları çok çeşitlidir. W.Shewhart’ın ilk kontrol diyagramını geliştirdiği 1920’lerden bu yana hemen her yönüyle defalarca incelenen kontrol diyagramları bugün kalitenin yedi önemli aracından biri olarak kabul edilmektedir. Ölçülebilen özellikler için kullanılan en eski kontrol diyagramı olan X-R diyagramları, prosesten alınan örneklemlerin (örnek hacmi) iç dağılımlarıyla, bu örneklemlerin iç dağılımlarından elde edilen parametre değerlerinin dağılımlarının da normal dağılıma uyduğu varsayımına dayanırlar. Bu çalışmada, bu varsayımdan ve entropi kavramından yola çıkılarak prosesteki belirsizliği dikkate alan bir limitli yeni bir proses kontrol diyagramı geliştirilmeye çalışılmıştır.
FULL TEXT (PDF): 
63-75

REFERENCES

References: 

[1] Alwan L.C., Ebrahimi N., Soofi E.S., “Information Theoretic Framework for Process
Control”, European Journal of Operational Research, 111, 3, 526-542, 1998.
[2] Atienza O.O., Tang L.C., Ang B.W., “A CUSUM Scheme for Autocorrelated
Observations”, Journal of Quality Technology, 34, 2, 187-199, 2002.
[3] Baray A., “Entropi ve Karar Verme”, Yönetim (İÜ İşletme Fak. İşletme İktisadı Enstitüsü
Dergisi), Yıl :14, 44, 7-21, 2003.
[4] Besterfield D.H., “Quality Control”, 6th. Ed., Prentice Hall, USA, 2001.
[5] Bischak D.P., Silver E.A., “Estimating the rate at which a process goes out of control in a
statistical process control context”, International Journal of Production Research, 39, 13,
2957-2971, 2001.
[6] Boyles R.A., “Phase I Analysis for Autocorrelated Processes”, Journal of Quality
Technology, 32, 4, 395-409, 2000.
[7] Bushuyev S.D., Sochnev S.V., “Entropy measurements as a project control tool”,
International Journal of Project Management, 17, 6, 343-350, 1999.
[8] Chen Y.K., “Economic design of X control charts for non-normal data using variable
sampling policy”, International Journal of Production Economics, 92, 1, 61-74, 2004.
[9] Costa A.F.B., “Joint Economic Design of X and R Control Charts for Processes Subject
To Two Independent Assignable Causes”, IIE Transactions, 25, 6, 27-33, 1993.
[10] Costa A.F.B., Rahim M.A., “Joint X and R Charts with Two-stage Samplings”, Quality
and Reliability Engineering International, 20, 7, 699-708, 2004.
[11] Çambel A.B., “Applied Chaos Theory A Paradigm For Complexity”, Academic Press,
USA, 1993.
[12] Djauhari M.A., “Improved Monitoring of Multivariate Process Variability”, Journal of
Quality Technology, 37, 1, 32-39, 2005.
[13] Fang S.-C., Rajasekera J.R., Tsao H.-S.J., 2nd.Ed., “Entropy Optimization and
Mathematical Programming”, 2nd.Ed., Kluwer Academic Publishers, USA, 1999.
[14] Fomby T.B., Hill R.C., “Applying Maximum Entropy to Econometric Problems”, Jai
Press, USA, 1997.
[15] Fu J.C., Shmueli G., Chang Y.M., “A unified Markov chain approach for computing the
run lenght distribution in control charts with simple or compound rules”, Statistics and
Probability Letters, 65, 4, 457-466, 2003.
[16] Fu J.C., Spiring F.A., Hansheng X., “On the average run lenghts of quality control
schemes using a Markov chain approach”, Statistics and Probability Letters, 56, 4, 369-
380, 2002.
[17] Grant E.L., Leavenworth R.S., “Statistical Quality Control”, 6nd.Ed., McGraw Hill,
Singapore, 1988.
[18] Greven A., Keller G., Warnecke G. (editors), “Entropy”, Princeton University Press,
USA, 2003.
[19] Gültekin M., English J.R., Elsayed E.A., “Cross-correlation and X-trend control charts for
process with linear shift”, International Journal of Production Research, 40, 5, 1051-1064,
2002.
[20] Hawkins D.M., Zamba K.D., “A Change-Point Model for a Shift in Variance”, Journal of
Quality Technology, 37, 1, 21-31, 2005.
[21] Hawkins D.M., Zamba K.D., “Statistical Process Control for Shifts in Mean or Variance
Using a Changepoint Formulation”, Technometrics, 47, 2, 164-173, 2005.
[22] He D., Grigoryan A., “Joint statistical design of double sampling X and s charts”,
European Journal of Operational Research, 168, 1, 122-142, 2006.
[23] Jiang W., “Multivariate Control Charts for Monitoring Autocorrelated Processes”, Journal
of Quality Technology, 36, 4, 367-379, 2004.
[24] Johnston R.B., “From Efficiency to Flexibility: Entropic Measures of Market Complexity
and Production Flexibility”, 02.11.2002, www.csu.edu.au/ci/vol03/finalst3/finalst3.html.
[25] Kapur J.N., Kesavan H.K., “Entropy Optimization Principles with Applications”,
Academic Press, USA, 1992.
[26] Kim K., Reynolds Jr. M.R., “Multivariate Monitoring Using an MEWMA Control Chart
with Unequal Sample Sizes”, Journal of Quality Technology, 37, 4, 267-281, 2005.
[27] Lu C.-W., Reynolds Jr. M.R., “EWMA Control Charts for Monitoring the Mean of
Autocorrelated Processes”, Journal of Quality Technology, 31, 2, 166-188, 1999.
[28] Lu C.-W., Reynolds Jr. M.R., “Control Charts for Monitoring the Mean and Variance of
Autocorrelated Processes”, Journal of Quality Technology, 31, 3, 259-274, 1999.
[29] Lu C.-W., Reynolds Jr. M.R., “Cusum Charts For Monitoring An Autocorrelated
Processes”, Journal of Quality Technology, 33, 3, 316-334, 2001.
[30] Molnau W.E., Runger G.C., Montgomery D.C., Skinner K.R., Loredo E.N., “A Program
for ARL Calculation for Multivariate EWMA Charts”, Journal of Quality Technology, 33,
4, 515-521, 2001.
[31] Montgomery D.C., “Introduction to Statistical Quality Control”, 5th.Ed., John Wiley &
Sons, sf.153, sf. 200-205, USA, 2005.
[32] Montgomery D.C., Mastrangelo C.M., “Some Statistical Process Control Methods for
Autocorrelated Data”, Journal of Quality Technology, 23, 3, 179-197, 1991.
[33] Rahim M.A., Costa A.F.B., “Joint economic design of x and R charts under Weibull
shock models”, International Journal of Production Research, 38, 13, 2871-2889, 2000.
[34] Reynolds Jr. M.R., Kim K., “Multivariate Monitoring of the Process Mean Vector With
Sequential Sampling”, Journal of Quality Technology, 37, 2, 149-162, 2005.
[35] Reynolds Jr. M.R., Stoumbos Z.G., “Should Exponentially Weighted Moving Average
and Cumulative Sum Charts Be Used With Shewhart Limits?”, Technometrics, 47, 4,
409-424, 2005.
[36] Roegen N.G., “The Entropy Law and The Economic Process”, Harvard University Press,
USA, 1971.
[37] Runger G.C., “Assignable Causes and Autocorrelation: Control Charts for Observations
or Residuals?”, Journal of Quality Technology, 34, 2, 165-170, 2002.
[38] Runger G.C., Willemain T.R., “Model-Based and Model-Free Control of Autocorrelated
Processes”, Journal of Quality Technology, 27, 4, 283-292, 1995.
[39] Saniga E.M., “Joint Economically Optimal Design of X and R Control Charts”,
Management Science, 24, 4, 420-431, 1977.
[40] Shannon C.E., “A Mathematical Theory of Communication”, The Bell System Technical
Journal, vol.:27, 379-423, 623-656, 1948.
[41] Shore H., “A new approach to analysing non-normal quality data with application to
process capability analysis”, International Journal of Production Research, 36, 7, 1917-
1933, 1998.
[42] Smith G.M., “Statistical Process Control and Quality Improvement”, 5th.Ed., PerasonPrentice Hall, sf.247-248, USA, 2004.
[43] Summers D.C.S., “Quality”, 2nd.Ed., Prentice Hall, sf.204, USA, 2000.
[44] Tsiamyrtzis P., Hawkins D.M., “A Bayesian Scheme to Detect Changes in the Mean of a
Short-Run Process”, Technometrics, 47, 4, 446-456, 2005.
[45] Tsung F., Zhao Y., Xiang L., Jiang W., “Improved Design of Proportional Integral
Derivative Charts”, Journal of Quality Technology, 38, 1, 31-44, 2006.
[46] Vasilopoulos A.V., Stamboulis A.P., “Modification of Control Chart Limits in the
Presence of Data Correlation”, Journal of Quality Technology, 10, 1, 20-30, 1978.
[47] Vaughan T.S., “The Effect of Process Adjustment Error on X Chart Design”, Naval
Research Logistics, 46, 6, 597-612, 1999.
[48] Vaughan T.S., “Variables Inspection for SPC-Quarantined Production”, Naval Research
Logistics, 48, 2, 159-171, 2001.
[49] Wang M.-C., Yue J., “Economic design of process adjustment for on-line control”,
International Journal of Production Research, 39, 5, 809-823, 2001.
[50] Weindling J.I., Littauer S.B., De Oliveira J.T., “Mean Action Time of the X Control Chart
with Warning Limits”, Journal of Quality Technology, 2, 2, 79-85, 1970.
[51] Wheeler D.J., “Advanced Topics in Statistical Process Control The Power of Shewhart’s
Charts”, SPC Press, USA, 1995.
[52] Wise S.A., Fair D.C., “Innovative Control Charting”, ASQ Quality Press, USA, 1998.
[53] Yang S.-F., “An approach to controlling process variability for short production runs”,
Total Quality Management, 10, 8, 1123-1129, 1999.
[54] Zhang N.F., “A Statistical Control Chart for Stationary Process Data”, Technometrics, 40,
1, 24-38, 1998.
[55] Zhang S.Z., Wu Z., “Designs of control charts with supplementary runs rules”, Computers
& Industrial Engineering, 49, 1, 76-97, 2005.

Thank you for copying data from http://www.arastirmax.com