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In most cases we deal with more than one requirement needed to be satisfied. In this paper we present the proposed methodology which improves the six sigma methodology based on the multi-objective techniques and Design of experiment. El Santty, et al. It was the result of a series of changes in the quality area starting in the late s, with ambitious ten-fold improvement drives. In section 2 we present an over view on the multi objective definition and techniques, in section 3 we present the six sigma definition and methodology, in section4 we present an over view on the design of experiments DOE , in section 5 we present overview on chromojet printing, in section 6 we present the proposed methodology, in section 7 we present the application details in chromojet printing, section 8 discussion and conclusion.

Multi objective optimization In this section we present the definition and mathematical model and solution technique of multi objective optimization problems. Belong to the nonempty feasible region set S , which is a subset of the decision variable space. Kaisia Miettinen, , Multi-objective problems as a rule present a possibly uncountable set of solutions. Two Euclidean spaces from Rn are considered in multi-objective problems. The set of solutions is found through the use of the Pareto Optimality Theory M.

Ehrgott, Solution techniques: The solving of multi-objective optimization problem helps the decision maker in finding the best solution that fits the specified preferences. The decision maker can be one or more experts in the problem domain with the main task of selecting one of the Pareto optimal solutions.

Multi-objective optimization is a multi-disciplinary field which combines ideas from mathematical programming with multiple criteria decision making, glued together by the computer programming techniques. Multiple criteria decision making is the research domain which considers decision problems with multiple conflicting objectives Branke et al.

Methods available for multi-objective optimization can be classified in different ways. In the classification adopted by Miettinen , multi-objective optimization methods are split into two main groups: generating methods and preferences-based methods.

Methods from the first class generate one or more Pareto-optimal solutions without any inputs from the decision maker. The solutions obtained are then provided to the decision maker for selection. The generating methods are divided into two subgroups: no-preference methods in which additional preference information are not required from the decision maker and a posterior methods which use posterior information to select a solution from the generated Pareto front.

Preference-based methods use the preferences specified by the decision maker at some stage in solving the multi-objective optimization problem. These have been divided in a priori methods Pareto optimal solution is found using preference information given by the decision maker at the beginning of the process and interactive methods.

Interactive methods require multiple interactions with the decision maker during the optimization procedure. For each interaction, the decision maker analyzes the generated Pareto optimal solution s and specifies preferences.

These preferences are used in formulating and solving the optimization problem during the next iteration. The main steps of an interactive method are Branke et al. Generation of a Pareto optimal starting point; 3. Requesting preference information from the decision maker; El Santty, et al. Generation of a new Pareto optimal solution s based on specified preferences; 5.

If several solutions were generated, the decision maker is asked to select the preferred one; 6. If the decision maker is satisfied with the obtained solution it comes to the end, else it goes to step3. Weighting Method: In the weighting method the idea is to associate each objective function with a weighting factor and minimize the weighted sum of objectives.

In this way the multiple objective functions are transformed into single objective function. We suppose that weighting coefficients are real numbers such that for all it usually supposed to the weight are normalized, that is and the multi objective optimization problem will modified to the following problem Kaisia Miettinen, Six Sigma Methodology In this section we present the definition of six sigma and main phases of six sigma methodology known as DMAIC and the main target of each phase.

Six Sigma is defined by Linderman et al. Design Of experiments DOE : Design of Experiments provides the foundation for experimenters to systematically investigate hypotheses about systems and processes. By outlining a series of structured tests in which well thought out adjustments are made to the controllable inputs of a process or system, then the effects of these changes on a pre-defined output or response variable can be observed and their significance evaluated.

The importance of applying such a structured method is found in its ability to minimize the number of factors influencing a system, maximize the responses deemed desirable in the system by manipulating the factors, and minimize the amount of experimentation required to effectively cover the design space characterized by the factors.

In comparison DOE plans for all of the possible combinations of input variables initially. It then imposes data requirements which enable the experimenter to determine the significance of that effect on the system response, and the independence of that effect from the influence of others Ahmed Abdallah, DOE can be used in a wide variety of circumstances.

Typically though the most common uses of DOE are in the following situations A. Dean and A. These methods are well established and have been widely used in other fields of engineering. Their application fields are widely varied and include manufacturing, industry, fabrication, IC design and process calibration, biological science, social science, medicine, marketing, and even software engineering. Chromjet printing Chromo jet is a computer-controlled design system, which applies the air-pressurized printing dye point by point by means of high speed valves jets to the material to be printed.

An intensity control is not available. To apply the printing dye according to the pattern stored in the PC in a point-precise way onto the material, jets are used to control the dye which is under air pressure. To obtain a precise switching on and cutting off of the dye streams, the El Santty, et al. All jets are located on a jet carriage, which is movable across the transport direction of the material.

To reach every point on the surface of the material, which appears in the pattern, the jet carriage is moved crosswise across the material. At the same time the position of the carriage is determined. The accuracy of the measurement corresponds to the particular resolution or point size of the pattern.

The position of the carriage is compared in the PC with the stored pattern information by the accompanying program.

The result of this comparison is, which jets of which color for this position of the carriage are opened or closed.

After each stroke of the carriage the material is moved by the transport or feeding device by a specified distance in production direction, and the carriage carries out its movement in the opposite direction see figure 1[10].

Figure 1: Main component of chromojet line. The separation of improve phase to Modeling, Optimization, and Implementation enable us to deal with process improvement and optimization for two or more process output simultaneously. In modeling phase we ling key process outputs with the key process inputs mathematically using design of experiment DOE for one or several responses outputs see Figure 3.

Process Figure 3: Process illustration of inputs and outputs. In optimization we formulate the multi objective mathematical model and solving the model using multi objective optimization technique to get efficient solution.

In implementation phase we implement the solution get from the optimization phase and evaluate the results and validate the benefit from the solutions.

Application: We implement the proposed Multi-Objective Six Sigma Methodology for improving the chromojet carpet printing process using DMAMOIC phases to minimize the quantity of printing paste and maximize the penetration of the colors into pile of the carpet. Define phase In define phase as shown in table 1 we need to identify the objective for improvement In the chromojet printing process we have two important process output one of them is the quantity of dye paste using in carpet printing which affect the cost of printing process and the cost of waste water treatment in case of excess color used and the second is the penetration of dye on carpet pile see figure 4 , which needed to be full covered with dye solution in order to prevent the effect on the printed design.

So we need to minimize the quantity of the printing dye with keeping the full penetration of the dye on carpet pile. In six sigma methodology we cannot deal with those two outputs simultaneously. Penetration Carpet pile 7. Measure In measure phase we need to define the details application and the how we will measure the defined two process output.

We will print on the white carpet and measure the quantity of dye get out from the jet and the penetration on the carpet pile. Printing paste specification: Acid dye low viscosity poly acrelate solution yellow, blue and gray colors. Analyze : In analyze phase we need to get the details of the machine setting and the condition of the printing process will be used and the most effective factors affecting the two defined process output.

From the application and machine constraint we define the detailed application and machine setting as the following. Color solution with viscosity vary from 50 - mPa. Modeling: In modeling phase we need to link the defined key process output and most affecting factor s in mathematical model. So the model layout begin to be clear we have two responses Y1 Quantity of printing paste and Y2 Penetration of the color on the pile , and three factors X1 Speed of jet carriage , X2 Viscosity of printing paste , and X3 Pressure of the pump see Figure 5.

The details of runs and the details of the factors change seen in the Table 1. We will apply the 19 runs illustrate in table 1 and for each run we measure the quantity of dye solution come out of one jet in one struck in gram by collecting the dye in cretin container and determine the weight difference between empty and full container and measure the penetration of the dye solution on the pile in millimeter as and the detailed run results in table 2. We can conclude that for the response Y1 Quantity of the printing paste we will take in consideration the Main effects of factors speed, Viscosity, and Pressure, and the neglect the other effects, For response Y2 Penetration of dye on pile we will take in consideration the main effects of Factors speed, Viscosity, and Pressure, and El Santty, et al.

Figure 6: Minitab session of estimates coefficients of quantity and penetration. Now the Multi-objective Model can be formulated to minimize the Quantity of the paste and maximize the penetration simultaneously. Optimization: In optimization phase we need to solve the previous model to get the value of Xi which satisfy the constraint and achieve acceptable solution for the objective functions efficient solution.

In control phase we develop and implement control plan that maintain and sustain the results we got from the previous phases such that written procedure, written work instruction, written, and machine setup. Discussion and conclusion: In this paper, we develop a new methodology for using multi objective optimization technique within six sigma methodology for improve quality to modify DMAIC methodology to DMAMOIC and implement the modified methodology in Chromjet printing process to improve two key process output responses simultaneously quantity of printing past and penetration of printing paste on carpet as application and validation of the methodology.

The results indicates that the integration between six sigma as continuous quality improvement methodology classified as professional methodology and operations research technique can add and enhance the methodology and add new dimensions to it which can use in process improvement and optimization in many sectors such as manufacturing ,services, and health care.

Also we can use the same methodology for more than two key process output used in this paper according to the complicity of the process under El Santty, et al.

The challenge now how to merge the operations research tools and techniques in the quality improvement methodologies to be easy to use for non academic teams.

References 1. Balakrishnan, A. Ezutn mtri x f ormb an meg ad juk a h l zat ad atai t. A Cras h T i me az erl-tetett men etb en rv -n yes i d tartamot jelen ti. Az ad atok at tb lzatos f ormb an rd emes meg -ad n i. O K Ezutn b eg p elj k a p rojek tet le r ad atok at, s elmen tj k a mod ellt. Az alb b i tb lzat els os zlop a azt mutatja, h og y az 1. A tb lzatb an az 1. Ilyen a 2. N yeres g t az alb b i tb lzat mutatja.

Ezutn meg ad juk az elzetes val s z n s g ek et, s a n yeres g tb lzat elemei t. Ezen a p on ton rd emes elmen ten i a mod ellt. Az ered m n y mag t l rtetd. A es rt k n ek s n ek a s lyozott s zmtan i k zep e 0. Vi zs g ljuk a k vek ez f elad atot! Id -eg ys g n ek a p erc et vlas ztjuk. Cus tomer arri val rate p er p erc. Ezutn b eg p elj k az i n p ut-ad atok at, s elmen tj k a mod ellt.

A jelen t s i g en terjed elmes , ez rt a k lts g ek et tartalmaz s orok at ez ttal k i h ag yjuk. Az ad atok at a k vetk ezk p p en rtelmezz k.

Eg y p erc alatt tlag os an 0. Author eszter-oerdoeg View 34 Download 0. Nhny fontosabb modul ismertetse Eb b en a r s zb en azok at a mod ulok at i s mertetj k , melyek az O p erc i k utats tan trg y temati k ja s zemp on tjb l a leg f on tos ab b ak. L P P mod ellt! O p erc i k utatsi feladatok meg oldsa W inQ S B -v el 3.

K eres s k az 1-es vros b l a 6-os vros b a vezet leg r vi d eb b tvo- n alat! O K Ezutn mtri x f ormb an meg ad juk a h l zat ad atai t. O K Ezutn meg ad juk az elzetes val s z n s g ek et, s a n yeres g tb lzat elemei t. O K Ezutn b eg p elj k az i n p ut-ad atok at, s elmen tj k a mod ellt.

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