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Paper Information

Journal:   JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)   SUMMER 2010 , Volume 7 , Number 2 (25); Page(s) 91 To 104.
 
Paper: 

ECONOMIC STATISTICAL DESIGN OF HOTELLING'S T2 CONTROL CHART USING VARIABLE SAMPLE SIZES, SAMPLING INTERVALS AND CONTROL LIMITS

 
 
Author(s):  TORABIAN MOHSEN*, MOGHADAM M.B., FARAZ ALIREZA, NEMATOLLAHI NADER
 
* SCIENCE AND RESEARCH BRANCH, ISLAMIC AZAD UNIVERSITY (IAU), TEHRAN, IRAN
 
Abstract: 
The Hotelling's T2 control chart, is the most widely used multivariate procedure for two or more related quality characteristics, but it’s power lacks the desired performance in detecting small to moderate shifts. Recently, the variable sampling intervals and Control Limits (VSICL) control scheme has been proved to have a very good performance on detecting small to moderate shifts when it is compared to the fixed ratio sampling (FRS) T2 control chart. Moreover, it is shown that the VSICL scheme is more economical than the classical one. This article studies the economic consequences of a new control scheme named variable sample sizes, sampling intervals and control limits (VSSICL) in that the sample size n, sampling interval h and control limit k vary between minimum and maximum values. We apply the cost model proposed by Costa and Rahim (2001). This model considers the cost of false alarms, the cost of finding and repairing an assignable cause, the cost of producing out of control items and the cost of sampling and testing. Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. Finally, the both VSICL and VSSICL T2 control charts are compared with respect to the expected cost per unit time.
 
Keyword(s): ECONOMIC DESIGN (ED), ECONOMIC STATISTICAL DESIGN (ESD), HOTELLING’S T2 CONTROL CHART, VARIABLE SAMPLING INTERVALS AND CONTROL LIMITS (VSICL), VARIABLE SAMPLE SIZES SAMPLING INTERVALS AND CONTROL LIMITS (VSSICL), MARKOV CHAIN, GENETIC ALGORITHM (GA)
 
 
References: 
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Citations: 
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+ Click to Cite.
APA: Copy

TORABIAN, M., & MOGHADAM, M., & FARAZ, A., & NEMATOLLAHI, N. (2010). ECONOMIC STATISTICAL DESIGN OF HOTELLING'S T2 CONTROL CHART USING VARIABLE SAMPLE SIZES, SAMPLING INTERVALS AND CONTROL LIMITS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 7(2 (25)), 91-104. https://www.sid.ir/en/journal/ViewPaper.aspx?id=191846



Vancouver: Copy

TORABIAN MOHSEN, MOGHADAM M.B., FARAZ ALIREZA, NEMATOLLAHI NADER. ECONOMIC STATISTICAL DESIGN OF HOTELLING'S T2 CONTROL CHART USING VARIABLE SAMPLE SIZES, SAMPLING INTERVALS AND CONTROL LIMITS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS). 2010 [cited 2021June22];7(2 (25)):91-104. Available from: https://www.sid.ir/en/journal/ViewPaper.aspx?id=191846



IEEE: Copy

TORABIAN, M., MOGHADAM, M., FARAZ, A., NEMATOLLAHI, N., 2010. ECONOMIC STATISTICAL DESIGN OF HOTELLING'S T2 CONTROL CHART USING VARIABLE SAMPLE SIZES, SAMPLING INTERVALS AND CONTROL LIMITS. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), [online] 7(2 (25)), pp.91-104. Available: https://www.sid.ir/en/journal/ViewPaper.aspx?id=191846.



 
 
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