A Design for Quality Management Information System in Short Delivery Time Processes 37 40 50 60 70 80 90 100 110 120 0.05 1176.9 1302.2 1377.4 1422.1 1448.7 1464.6 1474.0 1479.5 1482.7 0.10 1090.8 1135.5 1155.3 1163.8 1167.3 1168.6 1169.05 1169.06 1168.9 0.15 1017.8 1023.5 1024.6 1024.8 1024.6 1024.4 1024.15 1023.88 1023.6 0.20 961.3 949.7 944.8 942.8 941.9 941.4 941.03 940.71 940.4 0.30 890.0 863.6 855.2 852.0 850.6 849.9 849.47 849.11 848.8 0.35 860.0 836.8 827.7 824.2 822.8 822.0 821.58 821.21 820.9 0.40 840.0 816.2 806.6 802.9 801.4 800.6 800.12 799.74 799.4 0.46 824.1 796.0 786.0 782.1 780.5 779.7 779.25 778.87 778.5 0.50 810.0 786.4 776.1 772.2 770.5 769.7 769.25 768.87 768.5 0.55 800.0 775.2 764.8 760.8 759.1 758.3 757.79 757.40 757.1 0.60 799.0 765.9 755.2 751.1 749.5 748.6 748.13 747.74 747.4 0.65 791.0 757.9 747.1 742.9 741.2 740.4 739.88 739.49 739.1 0.70 781.4 751.0 740.0 735.8 734.1 733.3 732.76 732.37 732.0 0.75 775.7 744.9 733.9 729.7 727.9 727.1 726.55 726.15 725.8 0.80 770.6 739.6 728.5 724.2 722.4 721.6 721.08 720.68 720.3 0.85 766.2 734.9 723.7 719.4 717.6 716.7 716.23 715.83 715.5 0.90 762.1 730.7 719.4 715.1 713.3 712.4 711.90 711.50 711.1 0.95 758.5 726.9 715.5 711.2 709.4 708.5 708.01 707.61 707.3 1.00 755.3 723.5 712.0 707.7 705.9 705.0 704.50 704.10 703.7 Pa T Table 2. The balance of Pa, T and Ct From Tables 2, it also can be understood that how much total expectation cost should be paid by the different power, when the delivery time is strictly demanded; how much total expectation cost should be paid by different delivery time, when the power of process is strictly demanded. Because Table 2 shows the relation (concrete value) of power, the delivery date and the total expectation cost, it would become a reference for business plan. D. The balance of k, T and Ct In this section, we study the relations between the delivery time and ACT time and the total expectation cost, then we investigate the balance of control limits width (k) and delivery time (T) and the total expectation cost (Ct) by numerically analyzing the above design. Where, c 0 =1 ， c 1 =0.1 ， c 2 =10, c 3 =50, c 4 =25, a c β = p c β = d c β =200, c c β =2400, n 1 =4, v 1 =0.0316, Tp=1, 1 φ =0.01, 2 φ =0.001, λ 1 =1. Table 3 show the balance of the quality (control limits width) and delivery time and the total expectation cost of the above case, which is useful for setting the optimal delivery time and control limits width to the supplier. Process Management 38 Table 3. The balance of k, T and Ct A Design for Quality Management Information System in Short Delivery Time Processes 39 From Table 3, it can be understood that this tables are divided into two areas by the changed control limits width: in the colorlessness area, the expected total cost per unit time (Ct) increases with the increase of delivery time (T); in the blue area, the expected total cost per unit time (Ct) decreases with the increase of delivery time (T). From Table 3 and Figure 5, it can be noted that the expected total cost per unit time (Ct) increases with the increase of control limits width (k). This is because that the cost of defective goods increases by the increase of control limits width. Fig. 5. The relation between k and Ct (T=2, T=5). Fig. 6. The relation between T, k and Ct. From Table 3, it also can be understand that a longer delivery time should be set when the high quality (when k is small) is demanded, while a shorter delivery time should be set when the low quality is demanded from an economic aspect. In addition, to clarify it more, we also show the Figure 6 which is the same as the case of Table 3. Ct(T=2)>Ct(T=5) Ct(T=2)<Ct(T=5) Process Management 40 Table 4. The balance of a, T and Ct A Design for Quality Management Information System in Short Delivery Time Processes 41 E. The relation between T, a and Ct Fig. 7. The relation between a and Ct (T=2, T=10) Fig. 8. The relation between T, a and Ct Figure 7 show the relation between the delivery time and ACT time and the total expectation cost, which is useful for setting the optimal delivery time and ACT time to the supplier. From Figure 7, it can be understood that this tables are divided into two areas by the changed ACT time: in the colorlessness area, the expected total cost per unit time (Ct) increases with the increase of delivery time (T); in the blue area, the expected total cost per unit time (Ct) decreases with the increase of delivery time (T). From Figure 7 and Table 5, it can be noted that the expected total cost per unit time (Ct) increases with the increase of Act time (a). This is because that the cost of defective goods increases by the increase of ACT time. Also it can be understand that a longer delivery time should be set when the ACT time is long, while a shorter delivery time should be set when the ACT time is short from an economic aspect. In addition, to clarify it more, we also show the Figure 8 which is the same as the case of Figure 7. Ct(T=2)>Ct(T=10) Ct(T=2)<Ct(T=10) Process Management 42 4. Conclusions In this research, from an economic viewpoint, a design of the x control chart is analyzed for quality management information system used in short delivery time processes. Because of competition in markets, studying the balance of quality and the delivery time and cost has become a new problem to manager. To resolve this problem, the mathematical formulations which correspond to this design were shown, and then by numerically consideration using the data from real situation, the relations of the power of process and delivery time and the total expectation cost, the balance of quality (control limits width) and delivery time and the total expectation cost, the relations between the delivery time, ACT time and the total expectation cost are discussed, respectively. Moreover, the presented design based on the judgment rules of JIS Z 9021 was studied. Some comments are drawn as follows, which would become useful references for setting the optimal delivery time, ACT time and the power of process to manager. 1. The expected total cost per unit time decreases with the increase of the power of process. 2. The power by the two rules (3σ rule and 9 ARL rule) increases with the increase of sample size n, and the speed of increase of 9 ARL rule is faster. 3. A longer delivery time should be set when the higher power for higher quality is demanded from an economic aspect. 4. A longer delivery time should be set when the ACT time is long, from an economic aspect. 5. References [1] K. Amasaka, ed., “Manufacturing Fundamentals: The Application of Intelligence Control Chart- Digital Engineering for Superior Quality Assurance” , Japanese Standards Association , 2003 (in Japanese). [2] Y. Kanuma, and Y. Suzuki, and T. Kamagata, “Application and Efficiency of FDAS for Strengthening Real Working Front Ability”, Proceedings on the 37st Research Conference of Japanese Society for Quality Control , pp.161-164, 2007 (in Japanese). [3] Y. Ando, “An activity report of ‘control chart practical applications study group’ in JSQC”, Proceedings on the 5th ANQ Quality Congress, 2007. [4] S. Yasui, “On key factors for effective process control based on control charts through investigating literature cases”, Proceedings on the 37st Research Conference of Japanese Society for Quality Control , pp.169-172, 2007 (in Japanese). [5] J. Sun, M. Tsubaki and M. Matsui, “The comparisons between two quality control cycles-when the time of in-control and time of out-of-control is independent”, Proceedings on the 31st Research Conference of Japanese Society for Quality Control , pp.227-230, 2003 (in Japanese). [6] J. Sun, M. Tsubaki and M. Matsui, “Economic considerations in CAPD Model of P Control Chart for Quality Improvement”, International Conference on Quality ’05- Tokyo Proceedings , pp.VI-10, 2005. [7] J. Sun, M. Tsubaki and M. Matsui, “Economic Models of x Chart with Tardiness Penalty in Finite Due Time Processes,” Journal of Japan Industrial management Association, (in Japanese), vol. 57, no.5, pp.374-387, 2006. [8] Japanese Industrial Standards Committee (1998): “ JIS Z 9021: The Shewhart Control Chart”, Japanese Standards Association (in Japanese). [9] Y. Katou, “Verification of judgment rules of Shewhart control chart (JIS Z 9021)”, Proceedings on the 37st Research Conference of Japanese Society for Quality Control, pp.165-168, 2007 (in Japanese). [10] S. P. Ladany and D. N.Bedi, “Selection of the Optimal Setup Policy,” Naval research Logistics Quarterly , vol. 23, pp.219-233, 1976. 4 Design Cycle Period Management Bahram Soltanmohammad Sharif University of Technology IRAN 1. Introduction As competition increases and new technologies emerge, the civil aerospace industries need relatively better appropriate frameworks to guarantee their success. Efficient and close interactions among all disciplines involved in the aircraft design process from manufacturing, to the flight testing, are essential for improving the quality of the product. However, such necessities generally lead to a lengthy design cycle. Because of this, a strategy for cycle time reduction (CTR) must always be available. This process is called Integrated Airframe Design (IAD), (AGARD Report 814). A proper CTR leads to lessened costs which is essential in surviving a competition since time, cost and quality are three parameters that are normally used to evaluate the efficiency of a design process (Ullman, 2003). Researches on CTR could be categorized into four branches: 1- reducing engineering man hours; 2- reducing tooling hours; 3- reducing testing activities 4- implementing process and information technologies(NASA/CR-2001-210658). In the design process of complex systems, similar to that of an airplane, engineering tasks are either: coupled, sequential, parallel or compound ones. The design process of such a product is naturally in an iterative form (Eppinger & Whitney, 1994). In the scientific modeling of a design process, iterations are considered as specific features to be addressed (NSF, 1996). Iterations of a design process could be divided into two types (Browning, 1998): 1. Intentional iterations, performed between any two disciplines which help converging toward a satisfying solution. 2. Unintentional iterations that occur due to arrival of new information into the design process. In this chapter we concentrate on the first type. The very existence of iterations in the design process is the primary source of the increase in the development cycle time and its associated cost. Several studies have documented iteration effects as the driver of the overall development cycle time (Clark, 1993, Eisenhardt, 1995). Therefore, one expects that managing iterations and keeping them to a minimum leads to a more efficient design process. In this chapter, we investigate reducing man-hours by improving iteration characteristics. According to Smith and Eppinger there are two main strategies in increasing the speed of the design process: 1- faster execution of iterations; 2- reducing the number of necessary iterations in the design process (Smith & Eppinger, 1997). Extensive studies have been carried out by different researchers for either strategy. For example, the information flow model in designing tasks and distinguishing their cyclic Process Management 44 loops has been investigated by Steward in the form of a design structure matrix (DSM) (Steward, 1981). Eppinger continued this work and the information cycle in a design process was modeled in a clearer fashion while different strategies for the process management were investigated (Eppinger and Whitney, 1994). Browning developed a new methodology to understand product development cost, schedule, and performance (Browning, 1998). These works could be assessed from different points of views such as; presenting a systematic method for "Cycle Time Reduction" that allows each design topic to be analyzed according to its specific features. This approach allows managers to involve contractors in designing a big system in an efficient manner. One might also consider the approach in the broader subject of "Subcontracting". The fact that the WTM Concept could suggest what part of the project would be a good candidate for subcontracting, does not necessarily means that such implementation is an economic solution as well. That is WTM deals only with controlling the duration of the project and not the financial aspect of it. This chapter however, focuses on controlling iterations by means of iteration dynamic order reduction or tear-out "Controlling Features" (C.F.s) of a design process. To show how the new approach could be implemented, we use the WTM of a GENERAL AVAITION(G.A.) AIRPLANE. Following an introduction, we briefly discuss the application of Design Structure Matrix (DSM) to describe the so called Work Transformation Matrix (WTM). Then, we describe the main idea of the current chapter and how it is used to reduce the dynamic order of the iterations in a typical design process. Finally, we present a case study together with discussions on a G. A. airplane design process, and discuss the results. 2. Design process modeling by means of (DSM) Most designers believe that the first step in design process management is creating a comprehensive model which contains all the design tasks and their relationship. According to Yassine and Falkenburg, and Chelst; one of the main problems in the design process is the existence of the information cycles in tasks (Yassine et al., 1999). Any information cycle means the information interchanges among different disciplines in the design process. According to Pahl and Bietz the reason for the very existence of information cycles is related to the complexity in disciplines of the coupled design parameters (Pahl& Bietz, 1996);. Using a comprehensive model one could break the information cycles in suitable points, thus the complexity of the design process will be reduced. A comprehensive model should contain two characteristics: 1. Ability to identify information cycles 2. Ability to identify effective dynamic elements or suitable points to break information cycles The DSM method decomposes a more general design problem into separate tasks and while representing the relation among tasks as X; it provides a systematic way to analyze the design process structure. Each of the tasks is placed in rows and columns of a square matrix and the relationship among the tasks shown by the X marks. The X marks along each row show the input data which is needed for carrying out the tasks of that row. The X marks along each column show the output data which is supplied by that column task for other tasks. As a result the X marks above the diagonal show the feedback information and the X marks under the diagonal show the feed forward information; thus, the coupled part of the design process is then readily available (Figure – 1). Design Cycle Period Management 45 Fig. 1. Sample DSM Representing Coupled Tasks Thus DSM provides the aforementioned characteristics in a systematic way. In order to study of the behavior of iterations, a numerical DSM, called the Work Transformation Matrix (WTM), can be used (Smith&Eppinger 1997). Works done by the mentioned researchers suggest that three assumptions enable us to use linear algebra to analyze a WTM; as follows: 1. All iterations are done parallel. 2. The rework done is a linear function of the work done in the previous step. 3. The relationships among the tasks do not change in time. In this Chapter, we accept the aforementioned assumptions as the basis of the work; however, from a theoretical point of view, assumption number (1) applies to a big design organization where all engineering disciplines are available. This assumption basically means that members of engineering teams are fixed and that they work simultaneously on the same design problem. Also, this assumption gets closer to the reality wherever "Concurrent Engineering" is exercised. Assuming "time of conducting an iteration" to be a linear function of previous ones, is generally not a precise assumption. However, due to an engineer’s cognitive learning, it is believed that as the design process proceeds, performing iterations become both simpler and faster. Considering this, a linear decrease in conducting iterations would be somehow meaningful; as we would expect with a linear decrease in work associated with iterations. It is worth noting however, that at the moment there is no other approach to quantitatively model the nature of iterations. Besides linear approximation, one might think of a bi-linear model or tri-linear one. Nevertheless, different case studies by the authors show that such models would not effectively change the behavior of iterations (Soltanmohammad, PhD Thesis, 2007). One of the factors that influence the validity of the linear model is the very existence of some technological jumps that might occur during the execution of the project. In such cases, one might use a new approach based on "Time Dependent Complexity" (TDC) of coupled design parameters (Suh, 2003). In general, the second and third assumptions will be correct if we are not dealing with too many iterations. Moreover, since assumption number (3) does not support the effect of the so called "Learning Curve" in an organization it must be used very carefully. Based on what was described earlier, one can describe any iteration as a vector u t with dimension "n" where "n" is the number of coupled design tasks, relation (1). Each entries of the iteration vector shows the iteration job done after the t th stage of iteration. If matrix A is a part of WTM, which contains the data about the dependency intensity of tasks to one another, then according to Smith and Eppinger the work vector and total work vector U are (Smith and Eppinger, 1997): Process Management 46 1+ =⋅ tt uAu (1) 0 00== ⎛⎞ == ⎜⎟ ⎝⎠ ∑∑ MM t t tt Uu Au (2) That t is the iteration stage, u is the work vector, and M is the total number of iterations and u 0 is the initial work vector, that, all entries of u 0 are equal to 1.0. After decomposing matrix A, one might derive a relationship between U and eigenstructure of A as follows: () 1 1 0 − − =⋅ −Λ ⋅USI Su (3) Where S and Λ are eigenvectors and diagonal eigenvalues of matrix A respectively. According to (3), the dynamics (structure) of a design process is related to the time needed for conducting that design and from there to the nature of the eigenvalues and eigenvectors of the WTM. According to (3) the eigenvalues which are real and positive values close to unity, have a major role in the work vector U and in contrary role of the negative eigenvalues which are close to -1.0 are not important. The effect of complex eigenvalues is established by their real parts. If the real part is positive and near 1, then the eigenvalue plays an important role; otherwise it does not. Based on Perron-Frobenius theory, the biggest eigenvalue of a matrix like WTM, where all entries are non-negative, is always a real and positive number (Minc, 1988). In this way, the design mode associated with the largest eigenvalue can be selected as the most dominant design mode. This design mode has an eigenvector which is strictly positive and relatively larger elements of the eigenvector determine the contribution of the corresponding tasks to the dominant design mode. From a mathematical point of view, one might interpret the entries of this eigenvector to be more effective in the dominant design mode. In this way the C.F.s of the design process are identified as the tasks inside the most dominant design mode which have relatively greater contribution in convergence/divergence of iterations. By thoroughly examining the eigenvector entries, one can understands the C.F.s of the design process (Smith& Eppinger 1997). It can be stated that the number and characteristics of iterations are function of the C.F.s of a design process. Unlike what we interpret from Smith and Eppinger’s work, we might say that the contribution of each task and the number of effective tasks are different in generating iterations. The differences are related to the nature of the WTM. Based on the mentioned reasoning, C.F.s can be selected by following the simple relation: max > i d V K V (4) i V : th i Entry of dominant mode eigenvector max V : Maximum entry of dominant mode eigenvector d K : A decision parameter based on the designers experience (usually 0.5) If (4) holds, then i V is a C.F. Obviously, C.F.s each design processes differs, of course, this adapt with designers experiences and observations. To optimize a DSM, one might take advantage of four mathematical operations as follows: [...]... "tearing" 40% 31 .60% Convergence Improvement 30 % 23. 49% 22.62% 20% 18.20% 10% 3. 80% Cases Fig 8 Convergence Improvement in each scenario case5 case4 case3 case2 Case1 0% 61 Design Cycle Period Management 7 6 6 4 4 3 2 2 2 case2 3 Case1 No of C.F.s 5 2 1 case5 case4 case3 Basic 0 Cases Fig 9 No of C.F.s in basic WTM and in each scenario 90% 80% 77% C.F Weight Improvement(%) 70% 66% 67% 60% 50% 40% 37 % 30 % 26%... Case 5. 730 0.700 1-Structure design &analysis 2-Mathematical surface model 3- Aerodynamic analysis 4-Stability &Control Analysis Case-1 2.280 0.480 1-Structure analysis Case-2 3. 490 0. 530 1-Structure analysis Case -3 3.510 0.540 1-Structure analysis Case-4 5. 430 0.570 1-Structure analysis 2-Weight & Balance 3- Stability & Control Case-5 4.980 0.680 1-Mathematical surface model 2-Aerodynamic analysis 3- Stability... Distributions 13 Structural Analysis 14 Preliminary Production Program 15 Concept Selection 16 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Table 2 Partitioned G.A airplane DSM Tasks No 3 4 5 6 7 8 9 10 11 12 13 14 15 Select Preliminary Configuration Alternative 3 0 0 0 0 0 .3 0 0 .3 0 0.2 0... Integration Propulsion No 3 7 9 3 0 .3 0 .3 7 0.2 0 9 0 0.4 Table 14 The WTM after partitioning and tearing (Third case minor block-a) 57 Design Cycle Period Management Tasks No 4 5 Mathematical Surface Models 4 0.4 Aerodynamics Calculation 5 0.5 Table 15 The WTM after partitioning and tearing (Third case minor block-b) Fig 7 Architecture of major and minor blocks and tear-out tasks at Case -3 Case – 4: In this... major and minor blocks and tear-out tasks at Case-2 Tasks No 3 Select Preliminary Configuration Alternative 3 Prepare for cabin & Fuselage Design 7 0 .3 0 .3 7 0.2 Integration Propulsion 9 9 0 0 0.4 Table 11 The WTM after partitioning and tearing (second case minor block) Tasks Preliminary Structural Arrangement No 6 8 10 12 13 14 15 6 0 0 0.1 0 0 0 .3 0.1 Develop Structural Design Conditions 8 0.2 0 0 0 0... Internal Load Distributions 13 0 0 0 0 0 0.5 0 0.5 0 0 .3 0 0 0 Structural Analysis 14 0 0 0 0 0 0.5 0.2 0 0 0.1 0.1 0 0 Preliminary Production Program 15 0 0 0 0.2 0.1 0 0.1 0 0 0 0 0.1 0 Table 3 WTM of the G.A airplane Project Showing Coupled part 2 Coupled part Reduction: This criterion presents the effect of tearing most important C.F.s on work volume of design process coupled part and is calculated as... Tearing − (CW )After Tearing Tear Task Weight CPR : Couple Part Re duction 53 Design Cycle Period Management Task Name Eigenvector Elements Task No V-n Diagram Aerodynamics Calculation Internal Load Distributions Preliminary Structural Arrangement Mathematical Surface Models Stability & Control Analysis 0.2 83 0 .30 2 0 .32 2 0.424 0.425 0.482 12 5 13 6 4 11 Table 4 Controlling Feature of the most dominant... 0.679 13 Table 7 C.F.s of the most dominant design mode after tearing (First case) Tasks No 3 Select Preliminary Configuration Alternative 3 Prepare for cabin & Fuselage Design 7 0 .3 0 .3 7 0.2 Integration Propulsion 9 9 0 0 0.4 Table 8 The WTM after partitioning and tearing (First case minor block) Tasks No 6 Preliminary Structural Arrangement Develop Structural Design Conditions 6 0 8 10 12 13 14 0... torn After the tearing and repartitioning of the WTM, the table of the tasks of the G.A airplane will change into Table (16) This table shows that after tear-out, number of coupled tasks will change to 11 tasks The C.F.s of the most dominant design mode are shown in Table (17) Tasks No 3 Select Preliminary Configuration Alternative 3 6 7 8 9 10 11 12 13 14 15 0 0 0 .3 0 0 .3 0 0.2 0 0 0 0 0 Preliminary... Production Program 15 0 0.2 0.1 0 0.1 0 Table 16 The WTM after partitioning and tearing (Fourth case) 0 0 0 0.4 0 0 0 0 0 0.1 0.1 0 0 0 0 0 0.1 0 58 Process Management Task Name Eigenvector Elements Task No Perform Preliminary Weight & Balance 0 .30 0 10 Stability & Control Analysis 0.407 11 V-n Diagram 0.476 12 Internal Load Distributions 0.5 73 13 Table 17 Controlling feature of the most dominant design . 758 .3 757.79 757.40 757.1 0.60 799.0 765.9 755.2 751.1 749.5 748.6 748. 13 747.74 747.4 0.65 791.0 757.9 747.1 742.9 741.2 740.4 739 .88 739 .49 739 .1 0.70 781.4 751.0 740.0 735 .8 734 .1 733 .3 732 .76. 732 .76 732 .37 732 .0 0.75 775.7 744.9 733 .9 729.7 727.9 727.1 726.55 726.15 725.8 0.80 770.6 739 .6 728.5 724.2 722.4 721.6 721.08 720.68 720 .3 0.85 766.2 734 .9 7 23. 7 719.4 717.6 716.7 716. 23 715. 83. 1155 .3 11 63. 8 1167 .3 1168.6 1169.05 1169.06 1168.9 0.15 1017.8 10 23. 5 1024.6 1024.8 1024.6 1024.4 1024.15 10 23. 88 10 23. 6 0.20 961 .3 949.7 944.8 942.8 941.9 941.4 941. 03 940.71 940.4 0 .30 890.0 8 63. 6