Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. Vol. 10, No. 2, January 2010, pp. 90–94 issn 1532-0545 10 1002 0090 informs ® doi 10.1287/ited.1090.0041tn-a © 2010 INFORMS I N F O R M S Transactions on Education Teaching Note The MotoTech Manufacturing Company: Process Control and Improvement Prakash Mirchandani Katz Graduate School of Business, University of Pittsburgh, 358 Mervis Hall, Pittsburgh, Pennsylvania 15260, [email protected] D istribution: To maintain the integrity and usefulness of cases published in ITE, distribution of these teaching notes to any other party is prohibited. Please refer interested instructors to ITE for access to the teaching notes. Key words: process control charts; X-bar chart; capability indices; six sigma History: Received: June 2009; accepted: November 2009. Part A help develop readiness plans for use whenever the need arises. Should John Tagole have “waited out the storm,” hoping that Semicon will relax its new, more stringent, specifications? Would this strategy have worked in the short term? in the long term? Business environments are becoming increasingly more competitive and global in every industry. Even in industries typically thought of as being high technology, such as electronics, medical diagnostics, and computers, in which U.S. companies had an advantage, the center of production is shifting to China and other Far-Eastern nations. Semicon, therefore, is likely facing competitive pressures of its own to improve its product offerings. It is therefore highly improbable that Semicon would be willing or able to relax its proposed more stringent requirements. Even if we assume that Semicon’s threat is only partially warranted at this stage, the future may not bode well for MotoTech Manufacturing (MM) unless it is proactive in responding to Semicon’s concerns. Semicon might give preference to suppliers with more advanced processes when it introduces its next generation of products. Given that electronics products have a short technological life cycle, it might not be long before this happens. In any case, it makes sense for John Tagole to investigate and find out exactly what Semicon is looking for in its proposed specifications and what changes are needed at MM for meeting those specifications. Even if the situation does not warrant immediate process changes, John Tagole’s proactive approach will Part B John Tagole provides your group, The Famous Five, with the data set in the worksheet “Pre_Improvement.” The data in the worksheet were taken from the diffusion process. Samples of three wafers, were randomly selected from each batch of 200 wafers, and the thickness of the silicon dioxide deposition was measured on the wafers. The data are from 72 batches. Answer the following questions for this data set. 1. For this data set, construct the X-bar and range control charts. Attach a printout showing your X-bar and range control charts. See the attached Excel file, MotoTech (PCI) Solution. xls, for the control charts. 2. Use the range chart to determine if the process variation is in control. The process variation is not in control. In particular, the sample range for samples 8 and 40 exceeds the upper control limit of the range chart. Because we have already determined that the range chart is out of control, it is not necessary to check whether the sample data violates any of the other rules that may indicate that the process variation is out of control. 3. Use the X-bar chart to determine if the process mean is in control. The process mean is out of control because several sample means fall outside of the control limits of the 90 Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Process Control and Improvement Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. INFORMS Transactions on Education 10(2), pp. 90–94, © 2010 INFORMS X-bar chart. (For example, observations 5, 27, 40, and 41 are over the upper control limit, and 32, 33, 61, 64, 70, and 72 are under the lower control limit). However, see the answer to Part B.4 below. 4. If the process variation is found to be out of control in Part B2, would the control limits of the X-bar chart have been valid? Why or why not? If the process variation is out of control, the control limits of the X-bar chart do not have any meaning. This is because the control limits of the X-bar chart depend on the mean range value. The much higher value of the range for sample 40 skews the computation of the mean range value and, thus, the upper and lower control limits of the X-bar chart. Therefore, when the range chart is out of control, as is the case here, the X-bar chart should not be constructed. Part C After observing the control charts in Part B, The Famous Five investigate the reasons for the identifiable causes of variation. They find that the process went out of control during times when the plant air conditioning system was shut down for preventive maintenance. They recommend that a back-up air conditioner be installed and the temperature in the diffusion room be maintained at 60 F. This recommended temperature setting is based on The Famous Five’s general experience, although local atmospheric conditions and raw-material composition can also potentially affect the recommended temperature. Until the new air conditioner can be installed, The Famous Five recommend that the preventive maintenance be carried out on weekend nights, when the diffusion process is stopped. They ask John Tagole to collect data for an additional 72 batches under these controlled conditions. These data are enclosed in the worksheet “Post_Improvement.” 1. For this data set, construct the X-bar and range charts. Attach a printout showing your control charts. See the attached Excel file, MotoTech (PCI) Solution.xls, for the control charts. 2. Use the range chart to determine whether the process variation is in control. If we check whether or not the sample range values are within the upper and lower control limits of the range control chart, we do not see any evidence of the process being out of control. However, several other rules can indicate that the process is likely to be out of control. These rules all look for a pattern of some sort, and the basic underlying idea is that these patterns all have the same probability of occurring if the process is in control. Because there are many such rules, I only ask my students to check three others (beyond the basic one that checks for the sample statistic falling outside of the upper and lower control limits). The other rules require that the region between the upper 91 control limit and the center line be split up into three regions; similarly, the region between the lower control limit and the center line also needs to be split up. The three rules that I do ask the students to check are as follows: (a) Nine consecutive points that are all above or all below the center line on either the either the range or the X-bar chart1 ; (b) Six consecutively increasing or decreasing observations on either the range or the X-bar chart; and (c) Fourteen consecutive points that alternately increase and decrease. Using these three rules, the process variation is in control. 3. Use the X-bar chart to determine whether the process mean is in control. Using the same rules as above the process mean is in control. Sometimes, I change the data so that one of the sample means or one of the range values falls close to control limits (either within or outside the control limits). I want students to think through and recognize that there is a 0.0027 chance that a sample mean will fall outside of the control limits, even when the process is in control. If there are several points that are, for instance, close to, but do not fall beyond, the control limits, none of the rules discussed above for identifying an out-of-control process may be violated. Yet, the process may be out of control. Therefore, the idea is that students should use judgment along with the statistics in determining whether a process is in control or out of control. Part D Based on your analysis in Parts B and C, what would you recommend? The analysis in Parts C and D seems to indicate that temperature in the diffusion room is an important factor in keeping the process under control. Therefore, a first (short-term) recommendation is keep the diffusion room temperature at 60 F. This can be done by scheduling preventive maintenance on weekends or by upgrading the air conditioning system. MM should implement tighter temperature controls, so that the identifiable or special cause variation associated with temperature does not cause quality problems. There are some other issues that the Famous Five need to consider. They should check whether the differences seen between Parts C and D were indeed 1 If the process is centered, the probability of this happening is 2∗ 1/29 = 00039. This is about the same as the probability of an observation falling outside of the upper and the lower control chart limits (0.0027). Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. 92 Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Process Control and Improvement attributable to stabilizing the air conditioning system and are not attributable to some other factor (such as raw material supplies, or a change in one of the manufacturing stages that precedes the diffusion stage). The case does not mention any of these factors. However, it is important to determine that none of the other factors changed between Parts C and D, before a cause-and-effect relationship between temperature and diffusion quality can be ascertained. Some students immediately jump to conclusions about causeand-effect relationships with the data provided, not recognizing that there may be a confounding factor that is affecting the results. Another point that students are expected to make is that, even if the relationship between temperature and diffusion quality holds, and the process is in control as in Part D, MM will have to make further improvements. That is, even when the process is in control, its output need not meet the specifications: a stable process is not necessarily capable. For this reason, once the process is brought under control, one should check the capability of the process. One can do so by determining the proportion of output falling outside of the control limits, computing the Cpk for the process, or by computing the sigma level of the process. We compute these metrics in Part E. Finally, is 60 F the best temperature? Does 58 F, or 62 F, produce better output than 60 F? What other factors affect the quality, and what are the best settings for these other factors? Some statistics courses cover design of experiments. A discussion of how to find the best temperature and its interaction with other factors is a good lead-in to design of experiments. A companion case (MotoTech Manufacturing Company: Design of Experiments/ANOVA) covers that issue. Part E In Part C, we found that the process is in control when we set the temperature in the diffusion room to 60 F. The Famous Five construct a histogram of the “Post_Improvement” observations and conclude that the distribution is normal.2 Answer the following questions for the data used in Part C. 1. What is the cumulative probability for a single wafer to have a thickness of 3000 angstroms? The process mean is 3061.3 angstroms, and the process standard deviation is 38.3 angstroms. Therefore, 2 If checking for normality has been covered, then the instructor can ask the students to fit the process output data. Although Excel does not do so, commercial packages such as SPSS and SAS will construct the P-P (acronym for probability-probability) plot or perform statistical tests (such as the 2 test, Kolmogorov-Smirnov test, or the Anderson-Darling test. A visual test can be done in Excel by constructing a histogram.) INFORMS Transactions on Education 10(2), pp. 90–94, © 2010 INFORMS the cumulative probability for a single wafer having, a thickness of 3000 angstroms is 0.0550. (Please see “Parts E and F” worksheet of the Excel Solution file.) Students sometimes make a mistake in computing the standard deviation to be used for computing this probability. They incorrectly use the standard deviation of the 72 sample mean values (which is an estimate of the standard error) in computing the cumulative probability. This problem helps students learn that an estimate of the standard deviation of the process is the standard deviation of the entire output of the process, that is, the entire 216 values. This part also serves to review the concept of cumulative probability. The students may have seen cumulative probability earlier, but such a review is important because this concept is important for simulation, which they will see in subsequent courses. 2. What is the percentage of defectives being produced under the current setup? A wafer does not meet the specifications if its thickness is less than 2900 angstroms or more than 3100 angstroms. The probability of this happening is 0.156. (Please see the “Parts E and F” worksheet of the Excel solution file.) Some students will find the proportion of nonconforming wafers being produced by the current process (by counting the number of observations in the sample that fall outside of the 2900–3100 interval and dividing this number count by 216). This proportion is an estimate of the probability that we want; however, we can obtain a better estimate of the probability if we first fit the data to a distribution. We are told that the output process is normal; we can compute the mean and the standard deviation of this distribution to estimate the probability we want. 3. Compute the process capability index, Cp , for this situation. Is the process capable of meeting the customer’s requirements? Is Cp the appropriate metric for measuring process capability in this case? If so, why? If not, why not? What other metric would you suggest using? If LSL denotes the lower specification limit and USL denotes the upper specification limit, and Process Std. Dev. denotes the process standard deviation, Cp equals USL − LSL/6 ∗ Process Std. Dev., which in this particular case is 0.87. Because the process is not centered, Cp may overestimate the process capability, and a better capability index to use when a process is off-center as in this situation, is Cpk . If LSL denotes the lower specification limit and USL denotes the upper specification limit, and Process Mean and Process Std. Dev. denote the process mean and process standard deviation, Process Mean−LSL USL−Process Mean Cpk = min 3∗Process Std. Dev. 3∗Process Std. Dev. Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Process Control and Improvement Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. INFORMS Transactions on Education 10(2), pp. 90–94, © 2010 INFORMS Because we do not know the true process mean or the true process standard deviation, we use our estimates of these two parameters, and for our data, Cpk is 0.337. (When the process is not centered, Cpk is always lower than Cp .) A generally accepted value of Cpk for the corresponding process to be considered capable is 4/3. Some people (and some industries) might consider a value of Cpk as low as 1 to be capable; however, a Cpk of 0.337 does not indicate a capable process by any standards. 4. Is this a six sigma process? If not, what is its sigma level? Assuming that the process mean shifts by at most 1.5 sigma in either direction of the target, compute the approximate number of defectives out of a million. (Hint: In Motorola’s experience, process mean shifts of up to 1.5 sigma can go undetected, and that is why they use this assumption to calculate the proportion of defectives.) Sigma level equals USL−LSL/2∗Process Std. Dev. = 3100−2900/2∗383 = 2609. Therefore, this is not a six sigma process. To compute the number of defectives, 1.5 sigma should be subtracted from the sigma level. This is because, in the original computation of proportion of defectives given the sigma level, Motorola had assumed that shifts in the process mean of up to 1.5 sigma are difficult to detect. So, the process mean may shift by up to 1.5 sigma without our realizing it. This gives us 2609 − 15 = 1109. Therefore, the probability of defectives is 0.1337, or 133,700 defectives out of one million. As expected, this figure is much higher than the six sigma level of 3.4 defectives out of 1 million. Part F 1. Should The Famous Five recommend that MM lease the new equipment?3 Why or why not? (In the computation of the expected costs, you can ignore the time value of money because some of you may not yet know how to incorporate it. You can also ignore inflation.) From the analysis in the worksheet, Parts E and F, of the Excel solutions file, we see that in each of the five years that we have considered in our planning horizon, the rework and reject cost savings associated with new equipment more than compensates for the leasing expense of the new equipment.4 The difference in the contribution, after accounting for the cost of the new equipment starts at about $3.8 million and increases to about $24 million as the demand increases. Therefore, regardless of the discount rate, from an economic perspective, it makes sense to lease 3 To find the probabilities, one can use the normal tables or can use Excel’s = NORMDIST function. 4 This analysis assumes that each year MM’s total production quantity equals the expected demand for that year. Thus, if any wafers are rejected because of poor quality, then the quantity sold is lower than the demand. 93 the new equipment. (If the students are familiar with present value analysis, they can be given a discount rate and asked to compute the net present value.) There may be other reasons for leasing the new equipment, such as positive impact, that a more consistent product can have on market perception, revenue, and profitability. If time is available, I discuss whether it is appropriate to use the rework and reject costs as described in Part F of the case. The cost structure as depicted is convex—the further away we are from the target value (of 3000 angstroms), the greater is the rework cost. In principle, this form is similar to the form of the quadratic Taguchi loss function. Taguchi loss function reflects the fact that a customer’s level of dissatisfaction increases the further product characteristics are from the target values. In this case, the rework cost for the manufacturer increases the further the product is from the target value. 2. What else would you recommend for the future? Whether an investment is made in the new equipment or not, by better regulating the air-conditioning temperature, MM has brought the diffusion process under control. MM should continue to undertake continuous improvement activities at the diffusion stage. It should do controlled experimentation regarding other factors that might affect quality, such as correct raw material specifications, and atmospheric conditions, such as humidity levels and barometric pressure settings. The variation in quality may also be attributable to other stages of production (such as plasma etching, ion implantation, chemical deposition, etc.) An evaluation of these departments can lead to further improving the output quality. The production stages that follow diffusion, including final packaging and transportation, should also be studied to ensure that quality is not adversely affected at these stages. Finally, MM should also keep a close watch on alternative semiconductor technologies that are being developed, as these might affect both acceptable quality levels and process investment decisions. Comments on Assigning the Questions Instructors may note that some of the later parts of Case 1 implicitly “give away” the solution to previous parts. (Part C implicitly implies that the data in Part B would indicate that the process is out of control. Part D mentions that Part C data satisfy the normality assumption.) I believe that immediate feedback (partial) about work done correctly, or a hint that the students have made a mistake in a previous analysis, can actually aid learning and boost student confidence. Of course, other instructors may not agree with this assessment and may decide to split up the case questions into multiple assignments. If they decide to do so, then a suggested split is Parts A and B, followed by Parts C and D, and then Parts E and F. (In Additional information, including supplemental material and rights and permission policies, is available at http://ite.pubs.informs.org. 94 Mirchandani: Teaching Note: The MotoTech Manufacturing Company: Process Control and Improvement Case 2, none of the later parts give any hints to a previous part, and so this situation does not arise.) Second, I often change the data somewhat from year to year to prevent information transfer among the different classes. I also do this to sometimes highlight some other conceptual issues. For example, I might change the data so that one of the sample means or sample ranges lies close to (but not beyond) the control chart limits, and then see if students INFORMS Transactions on Education 10(2), pp. 90–94, © 2010 INFORMS recognize the managerial impact of observing such a data point. Also, cost figures can be changed from year to year (it is easy to check, using the Excel solution spreadsheet, whether or not the decision to invest in new equipment changes with a change in costs). Supplementary Material Files that accompany this paper can be found and downloaded from http://ite.pubs.informs.org.