Bottleneck Detection of Manufacturing Systems Using Data Driven Method

Transcription

1 Proceedings of the 2007 IEEE International Symposium on Assembly and Manufacturing Ann Arbor, Michigan, USA, July 22-25, 2007 MoB2.1 Bottleneck Detection of Manufacturing Systems Using Data Driven Method Lin Li, Qing Chang, Jun Ni, Guoxian Xiao, and Stephan Biller Abstract Bottlenecks in a production line have been shown to be one of the main reasons that impede productivity. Correctly and efficiently identifying bottleneck locations can improve the utilization of finite manufacturing resources, increase the system throughput, and minimize the total cost of production. Current bottleneck detection schemes can be separated into two categories: analytical and simulation-based. For the analytical method, the system performance is assumed to be described by a statistical distribution. Although an analytical model is good at long term prediction, this type of model is not adequate for solving the bottleneck detection problem in the short term. On the other hand, the simulation-based method has disadvantages, such as long development time and decreased flexibility for different production scenarios, which greatly impede its wide implementation. Because of all these problems, a data driven bottleneck detection method has been constructed based on the real-time data from manufacturing systems. Using this new method, bottleneck locations can be identified in both the short term and long term. Furthermore, the proposed data driven bottleneck detection method has been verified using the results from both the analytical and simulation methods. T I. INTRODUCTION HROUGHPUT is an important parameter to evaluate a production performance. Throughput analysis is also critical for the design, control, and management of production systems. Bottleneck is a machine that impedes the system performance in the strongest manner. Generally, the performance improvement on bottleneck machines results in a significantly higher overall system throughput than the performance improvement on non-bottleneck machines. Much research effort has been made in the area of throughput analysis and bottleneck detection. Generally, previous research can be categorized into two groups: L. Li is with the Department of Mechanical Engineer, University of Michigan, Ann Arbor, MI 48109, USA (phone: ; lilz@umich.edu). Q. Chang is with Manufacturing Systems Research lab, General Motors Research and Development Center, Warren, MI 48090, USA (phone: , cindy.chang@gm.com). J. Ni is with the Department of Mechanical Engineer, University of Michigan, Ann Arbor, MI 48109, USA (phone: ; junni@umich.edu). G. Xiao is with Manufacturing Systems Research lab, General Motors Research and Development Center, Warren, MI 48090, USA ( guoxian.xiao@gm.com). S. Biller is with Manufacturing Systems Research lab, General Motors Research and Development Center, Warren, MI 48090, USA ( stephan.biller@gm.com). detection using an analytical model [1] [4] and detection using a simulation model [5] [6]. For the analytical method, the machine performance metrics such as machine-up-down and processing time are assumed to be exponentially distributed. No closed form expressions have been found for the throughput analysis of serial production lines with more than two workstations. The accepted method for analyzing the longer lines is following the heuristic rule of decomposition. This decomposition approach analyzes the station-buffer-station case iteratively as the building block for longer production lines [7]. Using this heuristic rule, the fundamental challenge is how to model the two-station problem. For the two-station problem, two basic models considering the reliability are often discussed in the literature to establish the closed form expression: the Bernoulli model [8] [10] and the Markovian model [11] [12]. Reference [13] proposed an indirect method to identify the bottleneck. This method described a way of comparison between two neighboring machines: if the blockage time of upstream machine was higher than the starvation time of the downstream machine, bottleneck was downstream; otherwise bottleneck was upstream. By assuming reliability performance follow the Markovian model, analytical verification result was obtained for a scenario with two machines and one buffer. Another widely used method for analyzing system throughput and detecting bottleneck is simulation method, which has been adopted in industry [14] [15]. In the simulation method, discrete event simulation models are often created for a production line. Once these models have been constructed, throughput analysis must be carried out within the simulation model to detect any bottlenecks. The accuracy of the simulation results depends on many factors such as how closely the discrete event models appropriate the actual system and the skill level of the programmer. Good simulation models can significantly improve the design, analysis and management of the production systems. Many corporations have their own tools for analysis. For example, General Motors Corporation created an internal throughput-analysis tool called C-MORE, which is the combination of decomposition-based analytical methods and customized discrete-event-simulation solvers [16]. Although the simulation method is good at analyzing the throughput and detecting the bottleneck locations, it has some disadvantages such as long development time, decreased /07/$ IEEE. 76

2 flexibility for different production scenarios, and high cost greatly impede its wide application. To solve the problems of current bottleneck detection methods, a new data driven bottleneck detection method is developed. The method utilizes production line blockage and starvation probabilities to identify production constraints. The rest of this paper is organized as follows: section 2 gives the definition of a bottleneck and turning point, and then verifies the turning point corresponds to a bottleneck; section 3 explains the data driven bottleneck detection procedures; section 4 discusses the conclusions and future work of this research. B. Definition of Turning Point Based on definition (c), it is difficult to calculate the sensitivity value directly. Therefore, an indirect method is needed to identify the bottlenecks based on the information obtained in the plant floor. Before developing the method, we first introduce a definition of turning point. This definition is the foundation of the proposed data driven bottleneck detection method. Presently, more data are becoming available in modern factories. Fig. 1 shows the blockage and starvation times from a real (serial) production line. II. BOTTLENECK DETECTION FORMULATION A. Bottleneck Detection The notion of a bottleneck does not seem to have a uniformed accepted interpretation [17] [18]. Specifically, the following definitions are often found in the literature: (a) If a machine has the smallest isolation production rate (PR), this machine is the bottleneck. The production rate is defined as the average number of parts produced by a machine per cycle of time. (b) If the work-in-process (WIP) inventory in a buffer is the largest, then the machine right after this buffer is the bottleneck. (c) If the sensitivity value of the system production rate to a machine s production rate is the largest, then this machine Fig. 1. Trend of blockage and starvation times in a production line Usually, bottleneck machines in a production line have many distinct characteristics. For example, a bottleneck machine will often make the upstream machines blocked and downstream machines starved. A bottleneck machine will also have a lower overall sum of blockage and starvation time. Based on these characteristics, the turning point can be defined. DEFINITION: Machine j is the turning point in a n- machine segment with finite buffers if is the bottleneck. It is formulated as if, and then machine i is the bottleneck [18]. In this paper, a bottleneck is defined as the machine which has the maximum ratio of overall system throughput increment to its own standalone throughput increment during a certain period [15]. This definition can be formulated as If, and then machine k is the bottleneck in an n-machine production line. In this definition, is the system throughput increment caused by machine i due to a performance change (e.g., reduction of cycle time or downtime) and is the standalone throughput increment of machine i. Each of these definitions has its advantages and disadvantages [18]. The main advantage of definitions (a) and (b) is that they are based on on-line data, which can be measured during real-time system operation. However, these two definitions are local in nature, and they may not identify the critical bottlenecks from the total system point of view. On the other hand, definition (c) considers both local and global properties, because it defines how each local machine affects the system performance. However, it is not formulated in terms of on-line data, and quantities involved in the definition cannot be measured directly during realtime system operation. This greatly impedes applying definition (c) to detect bottlenecks in a real system. where is the blockage time for machine j; is the starvation time for machine j; j-1 is the nearest upstream machine and j+1 is the nearest downstream machine. We define the turning point to be a machine where the trend of blockage and starvation changes from blockage being higher than starvation to starvation being higher than blockage. Furthermore, the sum of a turning point machine s blockage and starvation is smaller than its neighboring machines. In this way, the turning point machine has the highest percentage of the sum of operating time and downtime compared to the other machines in the segment. This definition of turning point can be further illustrated in Fig. 2, which plots the same actual data as in Fig. 1. In Fig 2, within the segment from machine M8 to machine M17 (a ten-machine segment), blockage is initially higher than starvation (M8). Then, starvation becomes higher than blockage (from M9 to M17). Furthermore, because the relations can be obtained as: 77

3 M9 must be the turning point by definition. Following the same procedure, M2, M4 and M6 are the other turning points in this example. Because each machine only has four statuses (blocked, starved, down, and operating), the equations based on time summation for each machine can be expressed as: Fig. 2. Case to show how turning points are determined The on-line information of blockage and starvation reflects production line performance during a projected time periods. For short time periods, the turning points reflect short-term dynamic bottlenecks. For long time periods, the turning points reflect long-term statistic bottlenecks C. Analytical Verification for Three-Machine-No-Buffer Segment After introducing the definitions of a bottleneck and turning point, two kinds of verification methods analytical verification and simulation verification are performed to prove the conclusion that turning points correspond to bottlenecks. The analytical verification is on a simple three-machineno-buffer line. We give a pictorial representation of this segment in Fig. 3. By analyzing the relationship between these three machines; we see that is mainly caused by, and is mainly caused by. Furthermore, is mainly caused by and, and is mainly caused by and. Therefore, four additional equations according to these conditions can be obtained as where. When both machines and are failed, if there is a part on machine, then machine is blocked during the failure; else if there is no part on machine when both machine and machine are failed, then machine is starved. Therefore, parameter is the random value between 0 and 1 to describe this kind of uncertainty in (4) and (5). By solving these seven equations, the expressions for can be calculated as Fig. 3. Selected segment for analytical verification The assumptions and simplifications in the verification include: (1) The first machine is never starved, and the last machine is never blocked. (2) Reasonably assume the cycle time for each machine to be same, because the cycle time for each machine in the actual system of different types of machine is quite close. (3) Machine is the turning point. We define the parameters as follows: - Blockage time for machine j, j = i-1, i - Starvation time for machine j, j = i, i+1 - Down time for machine j, j = i-1, i, i+1 - Working time for machine j, j = i-1, i, i+1 T- Sampling time (e.g., one shift) TC - Cycle time of machines - Overall system throughput - Standalone throughput for individual machine j, j = i-1, i, i+1 - Intersection of sets which means the working time of each machine during the segment is the same. Since machine is the turning point, the additional relations can be obtained as and. Therefore, from (1), (2) and (3), we see that and. The system throughput of the three-machine segment can be obtained: According to the definition of standalone throughput, three more equations can be obtained as Now, change each machine s parameter to calculate the sensitivity value. We reduce the total downtime of each machine by a certain small value respectively to calculate the throughput increment by each machine and the standalone throughput increment of each machine. Then the sensitivity values and can be 78

4 obtained. Finally, the bottleneck location can be identified by comparing the sensitivity values. When is reduced by, according to (8) and (9) As a result, D. Simulation Verification Besides the analytical verification on a three-machine-nobuffer serial line, simulation-based verification is utilized to verify the turning point is a bottleneck in complex production lines More than five hundred cases have been studied, and over 95% of cases show good agreement that the data driven bottleneck detection method works well and finds the actual bottleneck. The simulation models studied include twomachine-one-buffer model (2M1B), three-machine-twobuffer model (3M2B), four-machine-three-buffer model (4M3B), five-machine-four-buffer model (5M4B), sixmachine-five-buffer model (6M5B), several-machine-nobuffer models, and models of real production lines from two automotive plants. One case of a 6M5B production line is shown to not only illustrate the simulation verification but also highlight the main advantage of data driven method over the traditional simulation-based bottleneck detection method. The 6M5B production line is drawn schematically in Fig. 4. Therefore, Following the same procedures, we calculate sensitivity values when reducing downtime by one at a time for other two machines and as Fig. 4. A 6M5B production line The simulation running conditions include: buffer capacity =10, initial buffer content = 0, part inter-arrival time = 0.1 sec, running period = 8 hours, and machine running parameters are listed in TABLE І. TABLE I SIMULATION PARAMETERS IN A 6M5B LINE Cycle time MTTR (min) MTBF (min) M1 10 sec 2 31 M2 10 sec 3 25 M3 10 sec 2 28 M4 10 sec 2 26 M5 10 sec 3 21 M6 10 sec 2 29 Therefore, which verifies that the turning point (machine bottleneck. ) is the Fig. 5. A simulation result for verification on 6M5B line By running the simulation, the blockage and starvation results are shown in the histogram in Fig. 5. By applying the data driven bottleneck detection method, we find that M2 and M5 are the two turning points in this case. For comparison, we run the simulation for sensitivity analysis. Under normal conditions, system throughput is 2,362 parts. Two approaches are adopted to perform sensitivity analysis for simulation-based bottleneck detection. The first approach is to eliminate the downtime of each machine respectively to check which elimination results in the highest new throughput. The bigger the new throughput (or throughput increment) is, the higher the importance of a potential bottleneck becomes. A second approach, similar to the first, includes a reduction of the total downtime of each machine by a certain small value (5 minutes in this case). This reduction of downtime is used for each machine individually, instead of eliminating the downtime altogether. The results for these two kinds of 79

5 sensitivity analysis approaches are listed in TABLE II. TABLE II RESULTS OF SENSITIVITY ANALYSIS OF A 6M5B LINE when MTTR=0 when downtime decreased by 5 minutes M1 2,363 2,363 M2 2,403 2,371 M3 2,408 2,376 M4 2,431 2,384 M5 2,461 2,388 M6 2,378 2,378 Both approaches show M5 and M4 are the most important bottleneck. In fact, M5 is definitely the primary bottleneck with highest throughout increment, and M2 (not M4) is the actual secondary important bottleneck. To verify this conclusion, we eliminated the down time of the primary bottleneck (M5) and performed the sensitivity analysis on the other five machines again. The results are shown in TABLE III. TABLE III SENSITIVITY ANALYSIS OF A 6M5B LINE WHEN M5 IS PERFECT when MTTR=0 when downtime decreased by 5 minutes M1 2,480 2,480 M2 2,622 2,487 M3 2,500 2,486 M4 2,474 2,473 M6 2,461 2,461 In TABLE III, both sensitivity analysis methods show that M2 is the primary bottleneck in the new condition, which verifies that M2 is the actual secondary bottleneck in the original system (not M4). In fact, in the original condition, the higher throughput increment of M4 comes from the effect of the primary bottleneck M5. In this way, the primary bottleneck dominates the throughput change: on one hand, the function and influence of M2 has been concealed and abated by the primary bottleneck M5; on the other hand, M4 is the dependent machine of the primary bottleneck M5 and achieves high throughput with M5. Therefore, M4 is the dependent bottleneck (not the independent one). These dependencies cause actual independent bottlenecks to be missed. Furthermore, some unimportant, dependent bottlenecks are treated as independent bottlenecks. In summary, this case study verifies an important advantage of data driven bottleneck detection method over the simulation based bottleneck detection method: the data driven method can identify independent local bottlenecks, while the simulation based method sometimes reflects dependencies. E. Verification Discussion In fact, the most important task for bottleneck detection is to identify all the independent local bottlenecks, which are often located in independent segments and divided by the effective buffer locations. Buffer locations in the production line are used to receive and store the finished parts from the upstream machines and provide parts to the downstream machines to be processed. Buffer content level is an important factor which strongly affects system performance. If a buffer content is seldom zero or full and often close to a certain level (e.g., half of the total capacity), then the machines ahead of this buffer are independent of the machines after this buffer because the buffer can provide or store enough parts and the production is not affected no matter how good or bad the performance is upstream or downstream. This kind of buffer is defined as an effective buffer, and segments divided by an effective buffer can be studied independently. On the other hand, if the content of a buffer is often zero or full, this kind of buffer is defined as non-effective buffer and machines ahead of this buffer are dependently related to machines after this buffer because the blockage and starvation times of upstream machines affect the blockage and starvation times of downstream machines (and vice versa). However, the effective buffer and non-effective buffer can only be defined qualitatively not quantitatively because there is no unified standard accepted to determine the boundary between effective and non-effective buffers. It is obvious that a buffer in which the content is never zero or full can be considered an ideally effective buffer. However, it is less straightforward to define whether a buffer is effective or non-effective when the buffer is full or empty 10 percent of the time. Fortunately, buffer dynamic movement (including both effective and non-effective buffers) can be considered as a blockage/starvation change, and the global trend of blockage/starvation automatically decouples long production lines into many independent segments. The turning point is defined in both a local and a global sense; in this way, it can identify independent local bottlenecks in each independent segment of the production line. Under the ideal condition, for the segment between two effective buffers, if only one turning point exists, the segment possibly can be aggregated into a three-machineno-buffer segment. As shown in Fig. 6, if machine is the turning point, by definition, for each machine from to, blockage is higher than its own starvation. However, for each machine from to, blockage is smaller than its own starvation. Therefore, the machines in the small segment before are blocked while the machines after are starved. Because of these characteristics, the m-machine segment (including buffers) can be simplified and aggregated into a three-machine-no-buffer segment including, and. Because the analytical 80

6 verification solution has been obtained in three-machine segment, analytical verification on m-machine segment is also solved. However, the conditions, under which a long segment can be aggregated into three-virtual-machine segment, are still unknown. It will be our further work. Fig. 6. Long line aggregation into three-machine segment III. CONCLUSIONS AND FUTURE WORK This research proposed a new data-driven methodology to detect serial production line bottlenecks. It is shown that manufacturing blockage and starvation measurements play crucial roles in bottleneck identification. The method is verified to be compatible with the bottleneck definition for simple three-machine-no-buffer serial line. The analytical verification uses the actual cumulative values instead of traditional statistical values. For complex production line, simulation-based verification is utilized. It is convinced that the data driven method can provide quick bottleneck identification. This offers a possibility for a unified approach to bottleneck analysis. It is noticed that the new method can apply for most cases in our studies, however a few exceptions exist. To learn the limitation of the method and to gain deep understandings of production performance from on-line production measurements such as blockage and starvation are subjects of future work [9] D. Jacobs, and S. M. Meerkov, A system-theoretic property of serial production lines: Improvability, Int. J. System Science, 1995, Vol. 26, No. 4, pp [10] J. Li, and S. M. Meerkov, Bottlenecks with respect to due-time performance in pull serial production lines, Mathematical Problem in Engineering, 2000, Vol. 5, pp [11] J. A. Buzacott, and J. G. Shanthikumar, Stochastic Models of Manufacturing Systems, Englewood Cliffs, NJ: Prentice Hall, [12] S. Y. Chiang, C. T. Kuo, and S. M. Meerkov (2000), DT-bottlenecks in serial production lines: theory and application, IEEE Transactions on Robotics and Automation, 2000, Vol. 16, No. 5, pp [13] S. Y. Chiang, C. T. Kuo, and S. M. Meerkov, c-bottlenecks in serial production lines: identification and application, Mathematical Problem in Engineering, 2001, Vol. 7, pp [14] C. Roser, M. Nakano, and M. Tanaka, Comparison of bottleneck detection methods for AGV systems, Proceedings of the 2003 Winter Simulation Conference, 2003, pp [15] Q. Chang, and J. Ni, Supervisory factor control based on real-time production feedback, Ph.D dissertation, Program in Manufacturing in the University of Michigan, [16] J. M. Alden, L. D. Burns, T. Costy, R. D. Hutton, C. A. Jackson, D. S. Kim, K. A. Kohls, J. H. Owen, M. A. Turnquist, and D. J. Vander Veen, General Motors Increases Its Production Throughput, Interfaces, 2006, Vol. 36, No. 1, pp [17] S. R. Lawrence, and A. H., Buss, Economic Analysis of Production Bottlenecks, Mathematical Problems in Engineering, 1995, Vol. 1, No. 4. [18] C. T. Kuo, J. T. Lim and S. M. Meerkov, Bottlenecks in serial production lines: a system-theoretic approach, Mathematical Problem in Engineering, 1996, Vol. 2, pp Reference [1] S. B. Gershwin, Manufacturing Systems Engineering, Englewood Cliffs, NJ: Prentice Hall, 1994, pp [2] S. Y. Chiang, C. T. Kuo, and S. M. Meerkov, (1998), Bottlenecks in Markovian production lines: a systems approach, IEEE Transactions on Robotics and Automation, 1998, Vol. 14, No. 2, pp [3] J. C. Wang, M. C. Zhou, and Y. Deng, Throughput analysis of discrete event systems based on stochastic Petri nets, International Journal of Intelligent Control and Systems, 1999, Vol. 99. [4] D. E. Blumenfeld, and J. Li, An analytical formula for throughput of a production line with identical stations and random failures, Mathematical Problems in Engineering, 2005, Vol. 3, [5] A. M. Law, and M. G. McComas, Simulation of manufacturing systems, Proceedings of the 1998 Winter Simulation Conference, 1998, pp [6] D. A. Bonder, and L. F. McGinnis, A structured approach to simulation modeling of manufacturing systems, Proceedings of the 2002 Industrial Engineering Research Conference. [7] S. B. Gershwin, An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking, Operations Research, 1987, Vol. 35, No. 2, pp [8] J. T. Lim, S. M. Meerkov, and F. Top (1990), Homogeneous, asymptotically reliable serial production lines: theory and a case study, IEEE Transactions on Automatic Control, 1990, Vol. 35, No. 5, pp. 81