IJE TRANSACTIONS A: Basics Vol. 27, No. 10 (October 2014) 1591-1600   

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A. Sherbaf Moghaddam, A. Amiri and M. Bashiri
( Received: February 26, 2014 – Accepted: June 26, 2014 )

Abstract    Cumulative Count of Conforming (CCC) charts are utilized for monitoring the quality characteristics in high-quality processes. Executive cost of control charts is a motivation for researchers to design them with the lowest cost. Usually in most researches, only one objective named cost function is minimized subject to statistical constraints, which is not effective method for economic-statistical design of control charts. In this paper, a multi-objective model for the economic-statistical design of the CCC control chart is developed. Then, multi-objective evolutionary algorithm (NSGA-II) for obtaining the Pareto optimal solution of the model is proposed. A numerical example is applied to illustrate the effectiveness of the proposed model. This model leads to lower cost and smaller probability of Type I and Type II errors, compared with economic model. In addition, a sensitivity analysis is done to investigate the effect of input parameters on the best solutions of the proposed model.


Keywords    Statistical Process Control, Cumulative Count of Conforming Charts, High-Quality Processes, Multi-Objective Economic-Statistical Design, NSGA-II Algorithm


چکیده    نمودار هاي کنترل CCC براي پايش مشخصه هاي كيفي در فرآيندهاي با كيفيت بالا به كار برده مي شوند. هزينه عملياتي نمودارهاي كنترل به عنوان محركي براي محققان در طراحي نمودارها با كمترين هزينه مي باشد. در بسياري از پژوهش ها، تابع هزينه به عنوان يك تابع هدف با در نظر گرفتن محدودیتهای آماری مينيمم مي شود كه اين رويكرد موثري در طراحي اقتصادي-آماري نمودارهاي كنترل نمي‏باشد.در اين مقاله، يك مدل چند هدفه براي طراحي اقتصادي-آماري نمودار كنترل CCC توسعه داده شده است. سپس الگوريتم تكاملي چندهدفه (NSGA-II) براي بدست آوردن جواب بهينه پارتو مدل پيشنهاد شده است. براي نشان دادن اثر مدل پيشنهادي، از يك مثال عددي استفاده شده است. اين مدل اقتصادي- آماري پيشنهادي منجر به هزينه كمتر و احتمالات خطاي نوع اول و دوم كوچكتر در مقايسه با مدل اقتصادي مي شود. همچنین آناليز حساسيتي براي بررسي اثر پارامترهاي ورودي روي بهترين جواب هاي مدل پيشنهاد شده انجام شده است.


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