A control chart for heavy tailed distributions

 

 

K. Thaga

Department of Statistics, University of Botswana, Botswana thagak@mopipi.ub.bw

 

 

---

ABSTRACT

Standard control charts with control limits determined by the mean and standard error of the mean are constructed based on the assumption that the distribution of the quality characteristic being monitored follows a normal distribution. However, this assumption is not always valid. It is proposed to use a chart based on computing the control limits using the process mean and the standard error of the least absolute deviation for the case where the process quality characteristics follow a heavy tailed t distribution. Such a control chart is more effective than the normal distribution based chart since it has a low out-of-control average run length for both small and large values of process shift.

---

OPSOMMING

'n Kontrolekaart wat gebruik maak van kontrolelimiete gebaseer op die standaardafwyking van die geringste absolute limiet word ontwerp vir 'n t-verdeling met 'n betekenisvolle stert. Simulasietoetse vir vergelyking van die voorgestelde kontrolekaart met normaalverdeelde kontrolekaarte toon dat korter gemiddelde looplengtes voor diagnose van beheerverlies uitgewys word, bereik word.

---

 

 

“Full text available only in PDF format” 

 

 

REFERENCES

[1] Ferrell, Ε.Β. 1953. Control charts using midranges and medians. Industrial Quality Control, 9, 30-34.         [ Links ]

[2] Gourieroux, C. and Monfort, A. 1995. Statistics and econometric models, 1. Cambridge University Press, Cambridge.         [ Links ]

[3] Johnson, N. L. and Kotz, S. 1970. Continuous univariate distributions, Vols. 1 & 2. Houghton Mifflin Company, Boston.         [ Links ]

[4] Langenberg, P. and Iglewicz, B. 1986. Trimmed mean X and R charts, Journal of Quality Technology, 18, 152-161.         [ Links ]

[5] Page, E.S. 1961. Cumulative sum charts. Technometrics, 3, 1-9.         [ Links ]

[6] Roberts, S.W. 1959. Control charts test based on geometric moving averages. Technometrics, 1 , 239-250.         [ Links ]

[7] Rocke, D.M. 1989. Robust control charts. Technometrics, 31, 173-184.         [ Links ]

[8] Shewhart, W.A. 1931. Economic control of quality of manufactured product. Van Nortrand Inc., New York.         [ Links ]

[9] Thaga, K. 2008. Control chart for autocorrelated processes with heavy tailed distributions. Economic Quality Control. 23, 1-10.         [ Links ]

[10] Thavaneswaran, A. and Heyde, C.C. 1999. Prediction via estimating functions. Journal of Statistical Planning and Inference, 77, 89-101.         [ Links ]

[11] White, E.M. and Schroeder, R. 1987. A simultaneous control chart. Journal of Quality Technology, 19, 1-10.         [ Links ]