A heuristic fixed limit Bayesian p chart

 

 

M.H. Abooie ^I; M. Amin Nayeri^II

^IDepartment of Industrial Engineering, Amirkabir University of Technology Hafez, Iran
^IIDepartment of Industrial Engineering, Amirkabir University of Technology Hafez, Iran minayeri@aut.ac.ir

 

 

---

ABSTRACT

The paper proposes an efficient approach to detecting an increase in the fraction of nonconforming items. The novelty of the paper is its utilization of the concept of the Bayesian rule and construction of a Bayesian control chart. This approach is significantly better than certain existing effective approaches in detecting small deviations. The major application of the charts is in high-tech industries and short run processes where the detection of small deviations and the evaluation of the initial setup are very important. The simulated results for the average run length profiles demonstrate the superiority of the new approach against the standard p chart, binomial EWMA and moving average approach. The new approach is easy to understand and may be attractive and useful to researchers, while it can also be an effective alternative for other existing approaches.

---

OPSOMMING

Die navorsing hou 'n doeltreffende Bayes-gebaseerde kontrolekaartmetode voor vir die beheer van breukdefekte waar gehalte buite beheer raak vir klein afwykings. Die metode se vertoning word via simulasie teen ander geykte kontrolekaartmetodes vir gemiddelde looplengte beproef. Die nuwe benadering is maklik verstaanbaar en bruikbaar vir navorsers, terwyl dit ook 'n effektiewe alternatief vir ander bestaande benaderings is.

---

 

 

“Full text available only in PDF format” 

 

 

REFERENCES

[1] Vargas, V. Lopes, L. Souza, A. 2004. Comparative study of the performance of the CuSum and EWMA control charts, Computers & Industrial Engineering, 46, pp 707-724.         [ Links ]

[2] Zhang, S. Wu, Z. 2005. Designs of control charts with supplementary runs rules, Computers & Industrial Engineering, 49, pp 76-97.         [ Links ]

[3] Woodall, W.H. 1997. Control charts based on attribute data: Bibliography and review, Journal of quality technology, 29, pp 172-184.         [ Links ]

[4] Reynolds, M. Stoumbos, Z. 1999. A CUSUM chart for monitoring a proportion when inspecting continuously, Journal of quality technology, 31, pp 87-109.         [ Links ]

[5] Roberts, S.W. 1959. Control chart tests based on geometric moving averages, Technometrics, 1, pp 239-250.         [ Links ]

[6] Montgomery, D.C. 2002. Introduction to Statistical Quality Control, Wiley: New York (2002).         [ Links ]

[7] Hunter, J.S. 1986. The exponentially weighted moving average, Journal of quality technology, 18, pp 203-210.         [ Links ]

[8] Crowder, S.V. 1987a. Computation of ARL for combined individual measurement and moving range charts, Journal of quality technology, 19, pp 98-102.         [ Links ]

[9] Crowder, S.V. 1987b. A simple method for studying run-length distributions of exponentially weighted moving average charts, Technometrics, 29, pp 401-407.         [ Links ]

[10] Lucas, J.M. Saccucci, M.S. 1990. Exponentially weighted moving average control schemes: properties and enhancements, Technometrics, 32, pp 1-29.         [ Links ]

[11] Gan, F.F. 1990. Monitoring Poisson observations using modified exponentially weighted moving average control charts, Communication in statistics, 19, pp 103-124.         [ Links ]

[12] Borror, C.M. Champ, C.W. Rigdon, S.E. 1998. Poisson EWMA control charts, Journal of quality technology, 30, pp 352-36.         [ Links ]

[13] Somerville, S.E. Montgomery, D.C. Runger, G.C. 2002. Filtering and smoothing methods for mixed particle count distributions, International Journal of Production Research, 40, pp 2991-3013.         [ Links ]

[14] Khoo, M. 2004. A Moving Average Control Chart for Monitoring the Fraction of non-conforming, Quality and reliability engineering, 20, pp 617-635.         [ Links ]

[15] Nenes, G. Tagaras, G. 2007. The economically designed two-sided Bayesian X control chart, European journal of operational research, 183, pp 263-277.         [ Links ]

[16] Calabrese, J. 1995. Bayesian Process Control for Attributes, Management science 41: pp 637-645.         [ Links ]

[17] Marcellus R. 2007. Bayesian Monitoring to Detect a Shift in Process Mean, quality and reliability engineering 2007; DOI: 10.1002/qre.895.         [ Links ]