2.810 Manufacturing Processes and Systems. Quiz II (November 19, 2014) Open Book, Open Notes, Computers with Internet Off 90 Minutes

Transcription

1 2.810 Manufacturing Processes and Systems Quiz II (November 19, 2014) Open Book, Open Notes, Computers with Internet Off 90 Minutes Write your name on every page. Clearly box your answers. State any assumptions you have made. Q1. Manufacturing Systems: Automobile Assembly Plant (20 points) Q2. Product Mix on a Transfer Line (20 points) Q3. Process Control (15 points) Q4. TPS Cell (30 points) Q5. Literature (15 points) --- TOTAL: 100 points 1

2 Q1. Manufacturing Systems: Automobile Assembly Plant (20 points) a. (8 points) An automobile assembly plant typically produces a car every minute. Using information from The Machine that Changed the World reading, estimate the average work-in-process (WIP) inventory in terms of vehicles in the assembly line for Japanese assembly plants in Japan, and for All Europe assembly plants. From Chapter 4, Figure 4.7 of The Machine that Changed the World, we know that a Japanese company s Japan plant required 16.8 hours to assemble a vehicle, whereas the All Europe one required 36.2 hours. We apply Little s Law to determine the average inventory in the system. Japanese in Japan: L = λw. That is, L = 60*16.8 = 1008 vehicles. All Europe: L = λw. That is, L = 60*36.2 = 2172 vehicles. b. (12 points) Now consider the Japanese in Japan plant. We assume that there is an assembly station for each vehicle and that the work statistics are identical at each station. Furthermore, if everything worked perfectly the assembly line could actually produce one car every 50 seconds. When an operator observes a problem on the line, he/she can pull an Andon cord which stops the entire line. What fraction of time could an individual station stop the line this way while still meeting the production rate of a car every minute? We are given τ = 50 seconds, P = 1/60 seconds, and n = We assume the assembly line has no buffers and that all processes have equal likelihood of stockouts. We therefore use Buzzacott s formula to determine the downtime. Solving this, we get, MTTR/MTTF = x Or MTTF/(MTTF + MTTR) = 99.98%. So the percentage of time that a station might be stopped this way is 0.02%. 2

3 Q2. Product Mix on a Transfer Line (20 points) Consider a two-machine line as shown below. The machines are perfectly reliable i.e., they do not fail. There is no buffer between the two machines. M 1 M 2 Figure 1: Two-machine zero-buffer line The line is used to make two product types product A and B which have an average demand of 4 and 5 parts per hour respectively. Each machine can process a part of either type in 5 minutes. There is a setup change required for each machine when changing over from part A to B or vice versa. The setup change times are given in Table 1 below. Table 1: Setup change times Setup Change Time required in minutes Machine 1 Machine 2 From A to B From B to A a. (8 points) Assume that the line is constrained to make parts A and B in the ratio 4:5 every hour. For the system shown in Figure 1, what is the maximum production rate of the line with this constraint? Suppose we start with both machines set up to make type A parts. We first make four type A parts. This requires 4 x 5 = 20 minutes. Then we do a setup change on both machines. This is governed by the setup change on Machine 2 and it takes 7.5 minutes. Then both machines work to make five Type B parts. This requires 5 x 5 = 25 minutes. We then do another setup change to prepare to make type A parts which again requires 7.5 minutes. Thus, this cycle requires = 60 minutes. So we can make 9 parts an hour given the constraint of making 4 Type A and 5 Type B parts every hour. 3

4 b. (8 points) Now assume that the constraint is eased so that the line can make the parts in the ratio 4:5 over a shift of 7.75 hours. What is the maximum production rate that you can now achieve? To maximize the production rate, we limit ourselves to two changeovers. We first make 4N type A parts, then do a changeover, then 5N type B parts, and then a changeover to part A. We can add up the times for this sequence and add it up to 7.75 hours to determine what N should be. We need: 4N* N* = 465 minutes. Therefore, we get, 45N = 450 or N = 10. So we should make a batch size of 40 type A parts and then a batch size of 50 type B parts. The production rate would be ( )/(465/60) = parts an hour. c. (4 points) What is the ultimate maximum production rate for the system making parts in the ratio 4:5? And under what conditions would this occur? Again, we need to minimize the number of setups so we get the maximum production rate. We look over an infinitely long time span and repeat the procedure of part b. We need: 4N* N* >. So the batch size tends to infinity for each part. We can make 12 parts of each type in an hour. So the production rate approaches the maximum possible rate of 12 parts an hour. 4

5 Q3. Process Control (15 points) Consider a process for which an X-bar control chart has been established. a. (5 points) What is the probability that an observed data point would fall outside the UCL? We assume that the UCL is at 3σ from the mean. From the standard normal table, we get Φ(3) = So on each side, the area outside the 3σ limit is ( ) = or 0.135%. This is the probability that a point will fall outside the UCL. b. (10 points) Assume that the process changes and there is a mean shift but the variance stays the same. If the old control chart is being used and the mean shift is equal to plus one standard deviation, what is the probability that an observed data point would fall outside the UCL? This scenario is shown in the figure below. With the process now operating at 1σ from the mean, the UCL is 2σ from the new mean. For a normally distributed process, the fraction of parts outside the 2σ limit are (1 Φ(2)) = ( ) = or 2.27%. 5

6 Q4. TPS Cell (30 points) Consider the TPS manufacturing cell shown below. There are 4 machines and 5 walking segments. The manual time/machine times are indicated next to each machine in seconds. In the present scenario, there is only one operator in the cell, and there are no de-couplers. The walking time between the machines are shown next to the arrows. 10 s/ 5 1/ s/ 30 s 1/ 3 a. (10 points) For the present scenario, determine the production rate, average inventory and time spent by a part in the system. The time chart is as shown in the table. Time in seconds Operation Walking + Manual Machine Finish Thus, the production rate is constrained by the pace of the operator. It is λ = 1/85 part per second. The average number of parts in the system is 5 (four parts in four machines and one in the operator s hands). The time spent in the system is, W = 5/(1/85) = 42econds. 6

7 b. (20 points) The desired production rate is one part every 50 seconds. We need to add one more worker to the cell. The cell could be split horizontally (operations 1 and 2 by one worker, operations 3 and 4 by the other worker) or vertically (operations 1 and 4 by one worker, and operations 2 and 3 by another worker). Which system would meet the desired production rate? Are there any other changes required to the system? The two scenarios are analyzed below. In either case, we add a de-coupler between each pair of machines. Also, machine 1 is the bottleneck since it requires 5econds. So we add another machine there. Horizontal Split 10 s/ s/ 5 1/ s s/ 30 s 1/ Time in seconds Operation Walking + Manual Machine Finish Worker Worker Note that this system is still limited by worker 2 and we cannot meet a production rate of a part every 50 seconds. 7

8 Vertical Split 10 s/ s/ 5 1/ s/ 30 s 1/ 3 Time in seconds Operation Walking + Manual Machine Finish Worker 1 50 Worker 2 45 This configuration would satisfy the production rate of one part every 50 seconds. 8

9 Q5. Literature (15 points) In your answers, state which reading and the page number of the information you are citing. a. (5 points) What did Taiichi Ohno and others at Toyota think of the Mass Producers management of their supply chains? Name at least two features utilized by the Mass Producers that the Japanese thought irrelevant and/or unproductive. From Womack, chapter 3, page 58-59, we learn that Ohno thought that the make-vs-buy decision was irrelevant and the bidding system seemed unsatisfactory. Ohno thought that suppliers had little incentive to improve their processes and worked to the plan given to them by the automaker. The suppliers were also competing amongst themselves which limited the exchange of information. b. (4 points) What argument did Henry Ford use to justify his plan to use more castings and forgings instead of sheet metal stamping in the Model A? Hounshell, chapter 7, page : Henry Ford had reservations about using stampings in his cars. He used the thermal argument saying that a cast part had to go through fewer heating operations compared to production of sheet steel. c. (3 points) How many people were employed at the River Rouge plant in the early 1930s? (And just for fun, guess how many people work at the plant today. The plant now makes the Ford F-150 truck and has a capacity of about 420,000 vehicles a year.) From Hounshell chapter 7 page 296 the River Rouge plant had 75,000 employees. On the previous page, Hounshell says that the plant produced 1.4 million vehicles from January 1 to September This indicates a productivity of 18.6 vehicles per employee. In the present day, according to Wikipedia and Ford s online sources, we know that the River Rouge complex hires about 6,000 employees. This means a productivity of 70 vehicles per employee. d. (3 points) According to Womack et al, of the high volume automobile producers which plant had the best quality performance in the world? From Womack s chapter 4, page 87 we learn that Ford s plant at Hermasillo, Mexico plant had the best assembly quality. 9

10 10