Vol. 17, No. 1, September 2016, pp. 26–33 ISSN 1532-0545 (online) I N F O R M S Transactions on Education http://dx.doi.org/10.1287/ited.2016.0158cs © 2016 INFORMS Case ABCtronics: Manufacturing, Quality Control, and Client Interfaces Arnab Adhikari Indian Institute of Management Calcutta, Joka, Kolkata 700104, India, arnaba10@email.iimcal.ac.in Indranil Biswas Indian Institute of Management Lucknow, Prabandh Nagar, Lucknow 226013, India, indranil@iiml.ac.in Arnab Bisi Johns Hopkins Carey Business School, Baltimore, Maryland 21202, abisi1@jhu.edu Keywords: probability distributions; sampling distribution; confidence interval; hypothesis testing; linear regression; case study History: Received: June 2014; accepted: December 2015. 1. Introduction as an intern, how he could add value to such a discussion? “Today is going to be long,” the thought came to Phil McDermott, as he casually checked the time on his watch while negotiating a busy crowd in the highspeed rail station. After arriving at the station, he started for his office. As an intern at ABCtronics, he never anticipated he would be asked to attend today’s meeting. But Jim was adamant; last evening he had said, “Look at this as a good learning opportunity.” After that, Phil was left with little or no option. The steel and glass-structured gigantic office building was already in sight. The location houses the manufacturing facility of eight-inch fabrication of ABCtronics, along with other departments, such as the quality and reliability team (QRT), the sales and marketing team (SMT), and the customer interface team (CIT). Phil directly reported to Jim Morris, the chief operating officer. Today, all important vertical heads of the plant were meeting for the quarterly review. Quarterly reviews are routine processes in every manufacturing company. Today was different. Complaints from a major client site had increased manifold, and in spite of boom time in the chip industry, ABCtronics had not done well over the last couple of quarters. “Tempers are going to run high today,” Phil thought as he threw his finished coffee cup in the trash can nearby and entered the office. But Phil wondered, 2. Company Background ABCtronics, a semiconductor manufacturing company, was established in 1997. It started its operations on a small scale. Over time, it had become a medium scale enterprise. The company offers a variety of wafer product lines, such as a mixed-signal integrated circuit, analog, and high-voltage circuit boards. ABCtronics is dependent on one major client (XYZsoft) for a good portion of its business. On the other hand, the semiconductor manufacturing industry is affected by a highly cyclical demand pattern.1 During upturns, semiconductor manufacturers have to ensure they have sufficient production capacity to meet high customer demand. During downturns, companies must contend with excess capacity because of weaker demand and high fixed costs associated with manufacturing facilities. Market analysts already predicted that the integrated chip market would face 1 According to noted market analyst Wahlstrom (2014), “Given the cyclical nature of the chip industry, foundries tend to add too much production capacity as they attempt to meet burgeoning demand during the good times, yet are left with excess capacity and are on the hook for the high fixed costs associated with their equipment during the bad times.” 26 Adhikari, Biswas, and Bisi: Case: ABCtronics 27 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS shrinkage in 2008–2009, and growth would resume from 2010 onward (The Economist 2009). Despite the increasing market size from 2010, sales revenue of ABCtronics is not up to the mark compared to its initial year’s sales. 3. Wafer Shaping Process Crystal growth Ingot surface grinding or notching Industry Background With a global sales figure approaching $24.70 billion, the semiconductor industry has experienced continuous sales revenue increases over the last three years (Semiconductor Industry Association 2013). Samsung has the highest installed wafer capacity with a production capacity of approximately 1.9 million wafers per month that represents 12.6% of the world’s total capacity (CdrInfo Report 2014). Other industry leaders are Taiwan Semiconductor Manufacturing Company (10%), Micron (9.3%), Toshiba/SanDisk (8%), and SK Hynix (7%). The industry faces an economic challenge for two reasons: (i) cyclical nature of demand and (ii) the high cost associated with research and development (R&D) (McKinsey Report 2011). Ever increasing costs related to upgrading the existing fabrication plants complicates the scenario further. Demand cycles, though bad for the entire industry, have proved to be a blessing in disguise for underperformers. Semiconductor chip manufacturers have invested heavily in R&D to meet the expectations of Moore’s Law.2 As a result, complexities of the chip design and costs have naturally gone up. A high cost of R&D has also led to substantial capital requirements for building state-of-the-art facilities for wafer fabrication. A McKinsey report indicates that “R&D spending amounted to approximately 17% of industry revenue for semiconductor companies (up from 14% a decade earlier) versus 3% for automakers,” (McKinsey Report 2011). As a result, the industry also focuses on quality assurance processes. In the semiconductor manufacturing lines, the uncertainty regarding the health of processes and wafers often leads to “major scrap events” as well as higher cost. In case of mixed-signal IC chips, it can be as high as 50% of the manufacturing cost. One of the main ways of tackling the quality problem is by monitoring some key parameters for deviations. These kinds of controls stem from statistical process control techniques. 2 Figure 1 Moore’s Law: The number of transistors in a dense integrated circuit doubles approximately every two years. There is no fundamental obstacle to achieving device yields of 100%. At present, packaging costs so far exceed the cost of the semiconductor structure itself that there is no incentive to improve yields, but they can be raised as high as is economically justified (Moore 1965). Wafer slicing by multiple wire saw Edge rounding Lapping/Grinding Edge polish Donor anneal Double/Single side polish Back seal poly-silicon Final polish (CMP) Epitaxy Quality check and packaging Note. CMP: Chemical Mechanical Polishing. 4. Semiconductor Fabrication Process The fabrication of integrated circuit (IC) chips is a highly complex process that involves hundreds of separate steps. The overall process lasts for several weeks. At ABCtronics, hundreds of IC chips are fabricated simultaneously on a six by eight-inch disc of silicon, termed as a “wafer” (see Figure 1). The wafers are processed in groups called “lots.” The circuit elements such as transistors, resistors, and capacitors are manufactured in layers on the wafer, with alternate deposition of material and exposure to light through a mask; finally they are subjected to an etching process that removes the unexposed material. The exposure to light is referred as photo-lithography (see Figure 2). This process itself contributes to the variability in the quality of the IC chips. The features created in this way are currently as small as 0.16 Œm (1 micrometer (Œm) = 1 × 10−6 meter), and therefore, fabrication is required to be done in a virtually sterile environment, often referred to as a “clean room.” ABCtronics Adhikari, Biswas, and Bisi: Case: ABCtronics 28 Figure 2 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS avenues to improve upon the quality checks and customized design of such control measures. Similarly, ABCtronics is also concerned about maintaining high quality. From an internal investigation, the fabrication process is currently facing two major problems: high downtime and chemical impurities. Photo-Lithography Oxidation Photoresist coating 5. Stepper exposure Optical mask Photoresist development Acid etch Spin, rinse, and dry Plasma etching Process steps Metal deposition Ion implantation Photoresist removal enforces a strict quality control policy. Samples of wafers from each lot are subjected to quality checks at various steps during the process to assess the impact of particular defects, the thickness of different layers, and the performance of test structures created in the areas between the chips. At the end of the line, each chip on every wafer is subjected to functionality tests (to reduce probing time, testing of each chip is stopped after the first failed functionality test; this serves as an equivalent of a rejection rule). The quantity and the complexity of the process and associated testing have forced the quality improvement efforts to focus primarily on summary statistics such as the number of salable IC chips per lot. This kind of figure has the advantage of suggesting simple and unambiguous screening rules (e.g., mark a lot if less than a particular proportion of the IC chips are usable). However, such one-dimensional analysis fails to address more pressing issues such as the possible causes of the defects, and crucial information for process improvement. Large manufacturing houses of IC chips are therefore always looking for Quality Control Tests The cost of quality assurance in manufacturing IC chips is very high. Moreover, as the complexity of IC chip design increases, the probability of faulty production also goes up. Since it is practically impossible to attain 100% yield on any IC chip manufacturing, quality checks are incorporated at several stages of the manufacturing process. Industry experts put emphasis on the requirement for routinely designing statistical procedures to monitor the presence of defect clustering. The entire industry is increasingly turning toward statistical methods for quality control. ABCtronics has also adopted a similar approach. Analysis of production data has revealed that the probability of producing a defective chip is 0.004. The company is currently considering whether to incorporate a new IC growth technology, namely, “defect-free manufacturing,” which can bring down the probability of producing a defective chip to 0.002. ABCtronics currently applies the Lot Acceptance Testing Method (LATM) for quality check. An automated machine is employed to take a sample of 25 IC chips one by one randomly from a lot of 500 without replacement. It means the chip already drawn from the lot is not returned to the lot when the next chip is selected, and the lot size goes down. If the sample has less than two defectives then the lot is accepted; otherwise it gets rejected. The in-house testing team has conducted their analysis and found that every lot of 500 IC chips contains two defectives on average. The QRT has proposed a new design for quality control to the board for approval. Scrapping the existing quality control policy, LATM, they want to bring in a new type of testing called Individual Chip Testing Method (ICTM), designed based on “defect-free manufacturing.” According to the proposal from QRT, a sample of 25 IC chips is to be taken one by one from a lot of 500, but this time they will allow replacement. It signifies the chip already drawn from the lot is returned to the lot when the next chip is selected, and the lot size remains the same for each selection. If a defective chip is found, the rework will immediately be done on that chip. The rework is usually done by performing a functional test on the internal circuitry of that IC chip (Tsai and Ho 2000). The proposal was aimed at establishing ABCtronics as a reliable brand in the IC chips market and also for retaining a good relationship with its biggest customer, XYZsoft. Adhikari, Biswas, and Bisi: Case: ABCtronics 29 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS Figure 3 ABCtronics Organizational Structure Shareholders Board of directors Audit committee Chairman Vice-chairman Internal audit team Chief executive officer Chief financial officer Research and development Customer interface team Chief operating officer Sales and marketing team Operations (plant president) Marketing Materials management XYZsoft, one of the major clients of ABCtronics, uses IC chips on their personal computers (PCs). In a component of each of these PCs, three IC chips are connected in series. It is known that the life (measured in years) of any IC chip follows an exponential distribution. XYZsoft uses chips with an identical specification in series. The ABCtronics fabrication team is now contemplating the option of rework on returned and defective IC chips from XYZsoft to investigate any problem with series connectivity of the IC chips. QRT is proposing immediate rework on IC chips with ICTM. 6. Review Meeting with the Manufacturing Unit and QRT As Phil entered the board room, most of the executives of ABCtronics had already arrived. Mark, the head of QRT, and Robert, the head of SMT, were there. They were having a last look at their respective files before the start of the meeting. ABCtronics was a hierarchy-centric organization, typical of any manufacturing-based firm (see Figure 3). He saw that Stuart, the president of the fabrication plant, was scribbling down something in his file. Stuart would give the first presentation of the review meeting. They were waiting for Jim. Phil found a corner seat in the room for himself. Legal advisory team Quality and reliability team Manufacturing As Phil was going to settle, Jim entered the room. Like a meticulous taskmaster, he set the agenda for the meeting first: “Gentlemen, last evening, I received yet another complaint from XYZsoft. It is the third time in last six months. I have assured them that I will personally look into the matter and ensure all possible rectification measures. So, let’s get started. We have a number of things such as improvement of operational efficiency, rework issue, customer feedback, and sales growth potential to discuss today.” Stuart immediately started. After detailing out the overall production of IC chips, he said, “We are currently producing 500 IC chips per lot. However, our plant is also facing the problem of downtime. This issue is particularly critical with our ion implanter.” It immediately reminded Phil about one of the reports that he read earlier. Downtime of this equipment is a matter of concern for semiconductor companies. Minimization of the downtime would lead to improvement of operational efficiency (Globenewswire 2007). At this point, Jim interrupted and asked, “In terms of downtime, what are we looking at, Stuart? How big is the problem?” Stuart said, “We ran some analysis and based on our estimate, average downtime of the machine is 6 hours (see Table 1). We need to curtail it down to 5.” “How good is that chance?” Jim enquired. Stuart glanced at Mark, the head of QRT, and said, “Mark and I agree that a replacement Adhikari, Biswas, and Bisi: Case: ABCtronics 30 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS Table 1 Data on Downtime and Chemical Impurity Figure 4 Report on Chemical Impurity Found in Raw Materials (Probability Density Function of the Percentage of Impurity in Chemical X) Excerpt from the fabrication plant report on downtime of ion implantation Data on monthly downtime of ion implantation (for last one year) July, 2012 August, 2012 September, 2012 October, 2012 November, 2012 December, 2012 January, 2013 February, 2013 March, 2013 April, 2013 May, 2013 June, 2013 Downtime 3 hours 36 minutes 4 hours 48 minutes 4 hours 36 minutes 6 hours 40 minutes 5 hours 24 minutes 5 hours 40 minutes 7 hours 20 minutes 9 hours 24 minutes 8 hours 40 minutes 5 hours 06 minutes 6 hours 20 minutes 4 hours 40 minutes is needed. I have a minor disagreement with Mark regarding the possibility of achieving 5 hours of the downtime.” Mark was ready with his reply, “QRT ran some tests and found that downtime of ion implanter has a gamma distribution pattern and based on that we have calculated the chance of reducing the downtime to 5 hours. But Stuart says the ion implanter impacts the overall production. As per his opinion, downtime of ion implanter and subsequent activities follows a uniform distribution instead. Here lies the difference in opinions.” Jim looked at Stuart and asked, “Are you sure that we are left with no other option but replacing this machine?” Stuart nodded silently. Jim pondered over the matter for some time and said, “Well, let me think over this. Now, I will look at the status of the chemical impurity problem we had last month.” IC chip fabrication process of ABCtronics involves the chemical vapor deposition method. In this technique, several chemicals such as ammonia, hydrochloric acid, sulfuric acid, etc., used in various steps of manufacturing, often contain impurities. To avoid contamination, the percentage of impurities per lot in a chemical should not go beyond a specific limit; otherwise, it results in producing defective IC chips. The manufacturing company itself sets the upper threshold of chemical impurity percentage based on the desired operating level of the production process. Stuart went on to explain, “From the analysis of historical data, we have concluded that the percentage of impurities per lot in a chemical approximately follows a beta distribution (see Figure 4). Based on this, we have decided that if the percentage of impurities per lot in any chemical is more than 30%, it is not used in the fabrication process.” Jim did not look convinced. “Is that good enough?” Mark came to Stuart’s aid this time. He said, “QRT has checked that the policy is Probability density function Month 2.5 2.0 1.5 1.0 0.5 0 0 10 20 30 40 50 60 70 80 90 100 Percentage of impurity Note. The percentage of impurity in chemical X follows beta distribution with shape parameters  = 4 and ‚ = 2. working fine.” Jim remained skeptical. He waved at Phil. As Phil approached him, Jim handed him over a stack of papers and said, “Keep these with you, we will work on this issue, later.” At this point Mark commented, “Regarding the proposed quality check technique ICTM, we need to make a decision. Are we going to adopt this method or not?” Now, Stuart commented, “But don’t you see, our current system is flawed, and client complaints will not stop coming?” Robert supported Stuart and opined that it would affect the product delivery system. At the table, everybody seemed clueless. Jim intervened and said, “QRT gave me a report on ICTM last week. I have asked Phil to look into the analysis. Next Monday we will take the final decision on the matter of ICTM.” Phil scribbled on his scratch-pad, “ICTM Report— urgent.” The truth was that he was yet to figure out the flaw in the current testing procedure. The meeting at hand was entering into the second phase. 7. Review Meeting with SMT and CIT “Where are we with our client Customer PQRsystems?” Jim directed his question toward Robert. “They are looking for specifications such that the product can work for six years smoothly. I have asked Mark to give you a copy of our internal RT report3 (see Figure 5). After looking at it, we have replied to their query. I think we have a good chance of securing this order.” Mark commented, “I think we should be able to meet their expectations. I have checked the data myself. Our chips will easily last more than six years.” After hearing this, Jim said, “Mark, send me a copy of RT. I would also like to have a look at the details.” Mark nodded. 3 RT report refers to Rigorous Testing (RT) report. This process checks for the lifespan of any product. Adhikari, Biswas, and Bisi: Case: ABCtronics 31 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS Figure 5 Related Portion of Rigorous Testing Report (Probability Density Function of Time Before Failure (in Years) of IC Chips) Excerpt from the Rigorous Testing Report on Life Expectancy of IC Chips Probability density function The following graph represents the Early Life Failure Test (the chip is tested to check whether it can survive for 40 years or not) result of the LM98XX chip that was carried out. The result is presented in the figure below. 5.6 5.1 4.6 4.1 3.6 3.1 2.6 2.1 1.6 1.1 0.6 0 5 10 15 20 25 30 35 40 Time before IC chip failure (in years) Salient data points from the Early Life Failure Test are presented below. Time before failure (in years) 5 10 15 20 25 30 Cumulative distribution function of failure time 22.55 40.00 53.53 64.01 72.13 78.41 Notes. The time before failure of IC chips is exponentially distributed. The figure depicts the probability density function of IC chips failure time, whereas the cumulative distribution function of the same is presented in the table. “OK. Now, the next issue is XYZsoft. Why has the number of complaints increased? What has happened, Robert?” Jim said as he was finishing his cup of coffee. Stuart immediately quipped, “They have again started experimenting with their quality control.” Robert smiled at him and said, “A few months ago, XYZsoft started a module-wise testing of their product. Circuit module M (CM) has a path where three chips from ABCtronics get connected in a series. Before the new testing process, XYZsoft reported that in a typical lot comprising 20 CMs they are finding three defective items. In most of those cases, they observed that the problem was with our chips. Now, they have put a stricter policy in place. They have now started to calculate the number of nondefectives before they encounter a particular number of defectives, and they started the count of 3. Till this point of time nothing happened.” Robert paused. Phil could sense that the new policy did not have much impact compared to the previous one. He pondered in his mind, how would that be possible? Robert started after taking a sip of his coffee, “The problem began as their testing team proposed that they should send back the whole lot for rework and recheck as soon as one defective item is found. All hell has broken loose since then. We are now flooded with requests for rechecks from XYZsoft.” At this point, Mark commented, “I am telling you, Jim, we can easily tackle this problem if we implement ICTM at our end.” Jim looked at Mark but said nothing. The entire episode puzzled him. How can a change in the quality control policy of XYZsoft have serious implications on the business of ABCtronics? Jim replied, “We need to tackle this problem quickly. XYZsoft is our biggest client. We simply cannot afford to lose their business.” Phil also found this development of events to be fascinating. He had quietly jotted down whatever Robert has said and looked at his pad. “What am I missing?” he wondered on his own. Robert continued, “I had a talk with Stuart regarding this matter. He told me that [the] Susceptible High Voltage Problem (SHVP)4 could contribute to this kind of issue. His team is looking into this aspect on the priority basis.” After hearing this, Jim looked at Stuart and said, “I thought we dealt with this problem a couple of years ago.” Stuart replied, “We are checking to be sure of the fact that it is not due to SHVP. Tests would be complete within next week.” Jim replied, “Do you have any preliminary report on this test?” Stuart said, “As per historical data, our IC chips produce [a] minimum 2.7 V output on an average, as HIGH signal. The variance of the HIGH signal output voltage remains 1.8 V. We have received a number of complaints from XYZsoft that the IC chips are not producing the expected voltage. Then, I ordered to take a random sample of 100 IC chips across the lots and test them for SHVP. Initial reports suggest the average voltage produced by the IC chips is around 2.3 V.” At this point, Mark commented, “Is it possible that we are overestimating the output of the IC chips?” Stuart replied, “It may be the case. We would not know for sure unless the detailed report comes.” Phil could sense that the entire XYZsoft episode had caused a fluttering feeling across the power corridor of ABCtronics. They need a fast fix for the problem and as of now none was in sight. A stifled silence prevailed over the board room. 4 Susceptible High Voltage Problem (SHVP): Ideally, every IC should produce HIGH signal output at 3.5 V, LOW signal output at 0.1 V, whereas 0.4 V–2.4 V is the undefined region of signal where signal remains neither HIGH nor LOW. In reality, it is often found that the HIGH signal output is around 2.5 V–3.0 V for a good IC. A problem starts if the HIGH signal output of an IC’s lies between 0 V and 2.4 V. Then the signal is LOW or undefined, whereas it should be HIGH. This problem is defined as SHVP (Tokheim 2004). Adhikari, Biswas, and Bisi: Case: ABCtronics 32 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS Table 2 Customer Score Sheet Sl. no. Customer name Customer score Range Customer A Customer B Customer C Customer D Customer E Customer F Customer G Customer H Customer I Customer J Customer K Customer L Customer M Customer N Customer O Customer P Customer Q Customer R Customer S Customer T Customer U Customer V Customer W Customer X Customer Y Customer Z Customer AA Customer AB Customer AC Customer AD Customer AE Customer AF Customer AG Customer AH Customer AI Customer AJ Customer AK Customer AL Customer AM Customer AN 79 56 33 79 66 49 47 34 88 77 67 51 53 74 85 56 39 51 26 43 77 97 73 57 66 45 28 33 56 68 32 93 60 29 41 42 72 48 59 47 Good Satisfactory Needs improvement Good Good Satisfactory Satisfactory Needs improvement Very good Good Good Satisfactory Satisfactory Good Very good Satisfactory Needs improvement Satisfactory Needs improvement Satisfactory Good Very good Good Satisfactory Good Satisfactory Needs improvement Needs improvement Satisfactory Good Needs improvement Very good Good Needs Improvement Satisfactory Satisfactory Good Satisfactory Satisfactory Satisfactory 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 Table 3 Note. Customer Score Range is defined as follows—Below 40: Needs improvement, 40–59: Satisfactory, 60–79: Good, and 80–100: Very good. Breaking the silence of the room, Jim spoke, “This brings us to the last issue of the discussion today. Where are we, regarding the analysis of customer feedback?” Robert picked up a thick file and said, “It’s all here. We ran the survey through 40 randomly chosen customers of the 74XX chip family. Four of them have rated us Very Good, eight have rated us Needs Improvement, and 28 have given us either Good or Satisfactory (see Table 2). So, I think we are good. Most of them are happy with our products.” Jim noted something in his diary. Then he said to Robert, “That would be your hunch. That cannot be your analysis.” Then Jim remembered something from an earlier meeting. He asked Robert, “In the last meeting, there was some discussion on redesigning the survey alto- Historical Sales Figure of ABCtronics ABCtronics’ sales Overall market demand Price per Economic Year volume (in millions) (in millions) chip (in $) condition∗ 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2.39 3.82 3.33 2.49 1.56 0.97 1.32 1.42 1.48 1.85 297 332 195 182 93 98 198 188 285 264 0.832 0.844 0.854 1.155 1.303 1.265 1.368 1.208 1.234 1.282 0 1 0 1 0 0 1 0 1 1 Note. ∗ Economic condition: 1 signifies favorable market condition and 0 signifies otherwise. gether. Why?” Robert looked visibly uncomfortable with this question. He cleared his throat and replied, “We have a mean customer rating of about 56. But the overall spread of the score is very high. If we want to conduct the survey to be sure of this average score with 90% confidence, even with a margin error of 4 the required sample size may exceed our total customer base.” Jim said, “What is the total number of customers for 74XX?” Robert said, “Including the new clients, the total is 70.” Jim said, “Sample more customers if needed. And tell me how good would be our estimate of the customer score?” Robert presented the report on the sales figure (see Table 3). ABCtronics was using a simple linear regression model for predicting the sales figure. However, the new interns, who recently joined SMT, indicated a few problems with the existing method. They proposed a new method to predict sales. They argued that their multiple linear regression model had better explanatory power and was devoid of multicollinearity problems. Looking at the presentation, Phil figured out that he was also asked to predict the sales figure for various demand scenarios. But Phil adopted a different approach. While looking at the screen, he did some quick mental calculation, and the results were not matching with the one presented. He nervously glanced at Jim. Jim was listening to Robert’s analysis with rapt attention. As the meeting was coming to an end, Phil could sense that ABCtronics needed to deal with a number of issues, and they needed to do it quickly. The company was entering into the second quarter of the year. ABCtronics immediately had to take corrective measures; otherwise it might be too late. As Stuart, Mark, and Robert were leaving the board room, Phil waited quietly for Jim. He knew that he was asked to attend today’s meeting for a reason. Adhikari, Biswas, and Bisi: Case: ABCtronics 33 INFORMS Transactions on Education 17(1), pp. 26–33, © 2016 INFORMS Table 4 Market Demand Estimate Total market demand for PCs (in millions) XX > 200 100 ≤ XX ≤ 200 XX < 100 Sub-total Sales volume 4Y Y 5 (in millions) YY > 3 105 ≤ Y Y ≤ 3 Y Y < 105 0.10 0.20 0.10 0.10 0.10 0.20 0.00 0.10 0.10 0.20 0.40 0.40 Joint probability matrix of the sales volume and total market demand Total market demand of PCs 4XX 5 (in millions) Subtotal 0.40 0.40 0.20 1 Average sales volume 4Y Y 5 (in millions) XX > 200 100 ≤ XX ≤ 200 XX < 100 2.385 2.140 1.265 Average sales volume in different demand scenarios Note. Based on the sales figure of ABCtronics in Table 3, Phil has calculated the joint probability matrix for the sales volume and total market demand, as well as the average sales volume in different demand scenarios. 8. The Road Ahead As everybody left the room, Jim turned to Phil and asked, “What do you think of today’s meeting?” Phil kept quiet. Many aspects of the meeting left him confused. Jim went on, “I need an honest opinion before going ahead. Look at all the reports and analyze. Tell me what do you think? You have two days to prepare. Let us meet on Monday.” As Jim uttered those words, only one thought came to Phil’s mind, “There goes my weekend plan!” “Have you prepared an analysis of the sales figures I asked for?” Phil said yes (see Table 4). “Do you think we can sell more than 3 million chips this year?” Phil said nothing. He has done the calculation; the possibility stands below 50% level. Jim figured out the answer from Phil’s silence. He asked, “What about 2.5?” Phil replied, “I think we will fall short of that number, the industry overall is experiencing a medium level demand. But the difference is not very large. If we get an order from Customer PQRsystems, probably we can make it.” Jim sighed for a moment and said, “Let us see where we arrive independently with our analysis. On Monday, after our meeting, I shall meet with Stuart and Mark. We have gone through a prolonged rough patch. The time has come to take some course correction; otherwise competition will knock us to the ground.” 9. Note This case has been prepared to form the basis for class discussion rather than to illustrate either effective or ineffective handling of a business situation. Supplemental Material Supplemental material to this paper is available at http://dx .doi.org/10.1287/ited.2016.0158cs. Acknowledgments We sincerely thank the editor-in-chief, the associate editor, and two anonymous referees for their insightful comments and helpful suggestions. Their efforts have significantly improved the case. References CdrInfo Report (2014) Samsung, TSMC, and Micron Top List of IC Capacity Leaders. Accessed November 2, 2015, http://www .cdrinfo.com/. Economist, The (2009) The semiconductor industry: Under new management. Accessed November 2, 2015, http://www.economist .com/. Globenewswire (2007) ATMI Announces Revolutionary Auto clean Technology Offering Greater Process Efficiency by Reducing Ion Implant Equipment Downtime. Accessed November 2, 2015, http://globenewswire.com/. McKinsey Report (2011) Creating value in the semiconductor industry. Accessed November 2, 2015, http://www.mckinsey.com/. Moore GE (1965) Cramming more components onto integrated circuits. Electronics (April 19), 114-117. Semiconductor Industry Association (2013) Global semiconductor sales jump by largest margin in over three years. Accessed November 2, 2015, http://www.semiconductors.org/. Tokheim RL (2004) Digital Electronics: Principles and Applications, 6th ed. (McGraw-Hill, New York). Tsai MC, Ho HC (2000) U.S. Patent No. 6,159,838. Washington, DC: U.S. Patent and Trademark Office, Alexandria, VA. (Accessed November 2, 2015). Wahlstrom P (2014) Mobile chips are driving strong demand for TSMC’s manufacturing services. Accessed November 2, 2015, http://analysisreport.morningstar.com/. Reading Material for Students Arnab Adhikari Indian Institute of Management Calcutta, Joka, Kolkata 700104, India, arnaba10@email.iimcal.ac.in Indranil Biswas Indian Institute of Management Lucknow, Prabandh Nagar, Lucknow 226013, India, indranil@iiml.ac.in Arnab Bisi Johns Hopkins Carey Business School, 100 International Drive, Baltimore, Maryland 21202, abisi1@jhu.edu Probability Distributions Binomial distribution. The Binomial distribution describes the probability of exactly 𝑥 successes out of 𝑁 trials; the probability associated with a success in a single trial is given by 𝑝 and that with a failure is given by 1 − 𝑝 (also designated by 𝑞). The expression of the probability mass function (pmf) of this distribution is as follows 𝑝(𝑥; 𝑁, 𝑝) = (𝑁𝑥)𝑝 𝑥 (1 − 𝑝)𝑁−𝑥 , where the variable 𝑥 and the parameter 𝑁 are integers, satisfying the conditions 0 ≤ 𝑥 ≤ 𝑁 and 𝑁 > 0. The parameter 𝑝 is a real quantity and 𝑝 ∈ [0,1]. The expected value and the variance of a random variable X having binomial distribution can be expressed as follows: EX  Np and V ar  X   N p (1  p ) . Hypergeometric distribution. The hypergeometric distribution describes the experiment where out of total 𝑁 elements, 𝑀 possesses a certain attribute [and the remaining (𝑁 – 𝑀) does not]; if we then choose 𝑛 elements at random without replacement, 𝑝(𝑥; 𝑛, 𝑁, 𝑀) gives the probability that exactly 𝑥 of the selected n elements have come from the group of 𝑀 elements that possesses the attribute. Let the number of elements with that certain attribute be denoted by X. The probability mass function (pmf) of X with hypergeometric distribution is given by 𝑓(𝑥; 𝑛, 𝑁, 𝑀) = (𝑀 )(𝑁−𝑀 ) 𝑥 𝑛−𝑥 (𝑁𝑛) where 𝑥 is discrete and its range is given by: 𝑥 ∈ [max(0, 𝑛 − 𝑁 + 𝑀) , min(𝑛, 𝑀)]. The parameters 𝑛, 𝑁 and 𝑀 are all integers and satisfy the following conditions: 1 ≤ 𝑛 ≤ 𝑁, 𝑁 ≥ 1 1 and 𝑀 ≥ 1. Let probability of success be represented by p  M . Then, the expected value and N the variance of X under hypergeometric distribution can be expressed as follows: E X  np and Var  X   np (1  p ) ( N  n ) ( N  1) . In real life, when a marketing group is trying to understand their customer base by testing a set of known customers for over-representation of various demographic subgroups, they use hypergeometric test designed based on hypergeometric distribution. Negative Binomial distribution. The negative binomial distribution (also known as Pascal distribution) gives the probability of waiting for exactly 𝑥 trials until 𝑘 𝑡ℎ success has occurred. Let the number of trials before 𝑘 𝑡ℎ success be denoted by X. Here 𝑝 and 𝑞(= 1 − 𝑝) designates the probability of a success and a failure in a single trial, respectively. The probability mass function (pmf) of this distribution is given by 𝑓(𝑥; 𝑘, 𝑝) = (𝑥−1 )𝑝𝑘 (1 − 𝑝)𝑥−𝑘 , 𝑘−1 where the variable 𝑥 and parameter 𝑘 are integers and satisfies the following condition: 𝑥 ≥ 𝑘 > 0. Now, the expected value and the variance of a random variable X under negative binomial distribution can be expressed as follows: E X   k (1  p ) p and Var  X   k (1  p ) p 2 . The negative binomial distribution has applications in the insurance industry, where for example the rate at which people have accidents is affected by a random variable like the weather condition. Geometric distribution. The geometric distribution is a special case of the negative binomial distribution discussed above with 𝑘 = 1. It expresses the probability of waiting for exactly x trials before the occurrence of the first successful event. Let the number of trials before the first success be denoted by X. Then, the probability mass function (pmf) of X with this distribution is given by 𝑓(𝑥; 𝑝) = 𝑝(1 − 𝑝)𝑥−1 , where p denotes the probability of success in each trial. The expected value and the variance of a random variable X under geometric distribution can be expressed as follows: 2 E X   (1  p ) p and Var  X   (1  p ) p . 2 In real life, if a NGO wants to know the number of male births before one female birth regarding the study of sex ratio in human population then it can use this kind of distribution. Poisson distribution. The Poisson distribution gives the probability of finding occurrence of exactly 𝑥 events in a given length of time when the events are independent in nature and happens at a constant rate, given by  . The probability mass function (pmf) of this distribution is given by f (x ;)  e   x , x! where the variable 𝑥 is a positive integer and the parameter  is a real positive quantity. Now, the expected value and the variance of a random variable X under Poisson distribution can be expressed as follows: E X    and Var  X    . When the value of N is very large and p is very small in the binomial distribution described before, then it can be approximated by a Poisson distribution with expected value = Np. Poisson distribution is applied to determine the probability of rare events like birth defects, genetic mutations, car accidents, etc. Uniform distribution. If a continuous random variable X follows the uniform distribution, then its probability density function (pdf) is given by the expression 1 𝑓(𝑥; 𝑎, 𝑏) = 𝑏−𝑎 for 𝑎 ≤ 𝑋 ≤ 𝑏. The expected value and the variance of a random variable X under uniform distribution can be expressed as follows E X   ba 2 and Var  X   b  a  2 . 12 In oil exploration, the position of the oil-water contact in a potential prospect is often considered to be uniformly distributed. Exponential distribution. If a continuous random variable X follows the exponential distribution, then its pdf can be expressed as follows: 3 1 𝑥 𝑓(𝑥; 𝜃) = 𝜃 𝑒 −𝜃 , where 𝜃 represents the scale parameter. The expected value and the variance of a random variable X under exponential distribution are given by: E X    and Var  X    2 . In real life, the radioactive or particle decays is considered to follow exponential distribution. Normal distribution. The normal distribution (also called the Gauss distribution) is one of the most important distributions in statistics. The pdf of normal distribution is given by the following expression: 𝑓(𝑥; 𝜇, 𝜎 2) 1 = 𝜎√2𝜋 𝑒 1 𝑥−𝜇 2 ) 2 𝜎 − ( , where 𝜇 is the mean or expected value and 𝜎 2 is the variance of the distribution. For 𝜇 = 0 and 𝜎 = 1, the distribution is called the standard normal distribution. It has widespread applications in natural and social sciences, financial models, etc. Beta distribution. The beta distribution has been applied to model the behavior of random variables limited to intervals of finite length in a wide variety of disciplines. The pdf of beta distribution is given by: 1 𝑓(𝑥; 𝛼, 𝛽) = 𝐵(𝛼,𝛽) 𝑥 𝛼−1 (1 − 𝑥)𝛽−1 , where the shape parameters 𝛼 and 𝛽 are positive real numbers, and the variable 𝑥 satisfies the condition 0 ≤ 𝑥 ≤ 1. 𝐵(𝛼, 𝛽) designates the beta function and is given by the following expression 𝐵(𝛼, 𝛽) = Γ(𝛼)Γ(𝛽) Γ(𝛼+𝛽) . For 𝛼 ∈ ℝ+ , the gamma function Γ(𝛼) is defined by the integral ∞ Γ(𝛼) = ∫0 𝑡 𝛼−1 𝑒 −𝑡 𝑑𝑡. When 𝛼 = 𝛽 = 1 , the beta distribution assumes the form of the uniform distribution between 0 and 1; when 𝛼 = 𝛽 = 2 the distribution takes parabolic shape; when 𝛼 = 2 and 𝛽 = 1 or vise versa the distribution takes triangular shaped distribution. The expected value and the variance of a random variable X under beta distribution can be expressed as follows:   E  X           .  and Var  X    2    (     1 )       4 Beta distribution is usually applied to determine the time allocation in project management/ control systems, heterogeneity in the probability of HIV transmission, etc. Gamma distribution. It is a two-parameter family of continuous probability distributions. Exponential distribution is a special case of the gamma distribution. The pdf of gamma distribution can be represented by the following functional form: 𝑥 − 𝑥 𝑘−1 𝑒 𝜃 𝑓(𝑥; 𝑘, 𝜃) = 𝜃 𝑘 Γ(𝑘) , where the shape parameter 𝑘 and the scale parameter 𝜃 are positive real numbers (𝑘 ∈ ℝ+ and 𝜃 ∈ ℝ+ ) and the variable 𝑥 is also a positive real number (𝑥 ∈ ℝ+ ). The expected value and the variance of a random variable X under gamma distribution are given by: E X   k  and Var  X   k  2 . Sampling Distribution and Confidence Interval. If we take repeated samples from the same population, samples means  x  would vary from sample to sample and form a sampling distribution of sample means. It explains the random behavior of a sample mean. The variability of x from  can be obtained by determining the variance of x . The variance of the sample mean with a sample of size n is given by:  2 x   2 . n Next, the confidence interval contains the true population parameter. A confidence interval comprise point estimate, i.e., the best estimate of the population parameter from the sample statistic and the margin of error or maximum sampling error (the maximum accepted difference between the true population parameter and a sample estimate of that parameter). The confidence interval where  lies can be determined by the following expression: x  z  / 2         x  z   n  / 2   .    n  The confidence level is denoted by 1 0 0  1    % . The margin of error denoted by E is given by the following formula: E  z  / 2 5     n    . From the formula given above, the required minimum sample size can be easily obtained and it is given by:   n   z ( / 2 )  E  2   .  Hypothesis Testing. Hypothesis testing is a technique to check with the help of a sample data whether a claim or hypothesis about a population parameter is true or not. In hypothesis testing, the stated conjecture  defined as the null hypothesis  can be disproved, but it cannot be proved. However, by disproving the null hypothesis, one can prove that the contrary is true. The contrary of the null hypothesis is termed as the alternative hypothesis. The test statistic represents the value determined using the sample data. A test statistic for testing a hypothesis on population mean is given by the following formula: z  x   0        n  , where  0 denotes the hypothesized value of the population mean. Following are the null ( H 0 ) and alternative ( H A ) hypotheses for three standard tests on population mean: The “Two-Tailed” Test. H 0 :   0 H A :   0 z x  0  n reject H 0 if z  z  / 2 or z   z  / 2 . The “One-Tailed” Test to the Right H 0 :   0 H A :   0 z x  0  n reject H 0 if z  z  . 6 The “One-Tailed” Test to the Left H 0 :   0 H A :   0 z x  0  n reject H 0 if z   z  . Regression Models Simple linear regression Here we present a simple linear regression model to determine the relationship between the dependent variable Y and the independent variable X, captured by the following equation: E( 𝑌 | 𝑋) = 𝛼 + 𝛽𝑋. Then the regression model can be designated as: 𝑌 = 𝛼 + 𝛽𝑋 + 𝜖, where 𝜖 = 𝑌 − E( 𝑌 | 𝑋) is a random variable or an error term with E(𝜖) = 0 and 𝑉𝑎𝑟 ( 𝜖) = 𝜎 2 . If 𝛼̂ and 𝛽̂ denote the best estimates of the parameters α and β , respectively, then the estimated linear regression equation of Y on X is: 𝑌̂ = 𝛼̂ + 𝛽̂ 𝑋. Multiple linear regression The effect of independent variables 𝑋1 , 𝑋2 and 𝑋3 on the dependent variable Y can be captured by the following equation: E( 𝑌 | 𝑋1 , 𝑋2 , 𝑋3 ) = 𝛼 + 𝛽1 𝑋1 + 𝛽2 𝑋2 + 𝛽3 𝑋3, where 𝜖 = 𝑌 − E( 𝑌 | 𝑋1 , 𝑋2 , 𝑋3 ) is a random variable or an error term with E(𝜖) = ̂1 , 𝛽 ̂2 , and 𝛽 ̂3 denote the best estimates of the parameters 0 and 𝑉𝑎𝑟( 𝜖) = 𝜎 2 . If 𝛼̂ , 𝛽 α , β1 , β2 , and β3 , respectively, then the estimated multiple linear regression equation of Y on 𝑋1 , 𝑋2 and 𝑋3 is given by: ̂1 𝑋1 + 𝛽 ̂2 𝑋2 + 𝛽 ̂3 𝑋3. 𝑌̂ = 𝛼 + 𝛽 Multicollinearity check Often regression model is affected by linear relationship between independent variables termed as ‘multicollinearity’. Variance Inflation Factor (VIF) is one of the conventional techniques employed to check whether any multicollinearity exists or not. VIF between two independent variables X1 and X2 can be determined by the following expression: 7 VIF𝑋1 ,𝑋2 = 1 1−𝑅𝑋1 ,𝑋2 2 , where 𝑅𝑋1 ,𝑋2 2 denotes the co-efficient of determination between 𝑋1 and 𝑋2 . If the value of VIF is greater than 5, then it indicates multicollinearity and the overall regression model gets affected by it. Sources  Anderson, D., Sweeney, D., Williams, T., Camm, J., Cochran, J. 2011. Statistics for Business & Economics, 11th ed. Cengage Learning, Mason.  Berenson, M., Levine, D., Krehbiel, T. C. 2011. Basic business statistics: Concepts and applications. Pearson Education, New Jersey.  Groebner, D. F., Shannon, P. W., Fry, P. C., Smith, K. D. 2013. Business statistics: a decision making approach, 9th ed. Pearson Education, New Jersey.  Hildebrand, D. K. and O. Lyman. 1998. Statistical Thinking for Managers, 4th ed. Duxbury Press, California.  Levin, R. I. and D. S. Rubin. 1997. Statistics for Management, 7th ed. Prentice Hall International, New Jersey.  http://wps.aw.com/wps/media/objects/15/15512/formulas.pdf  http://www.nzqa.govt.nz/assets/qualifications-and-standards/qualifications/ncea/NCEAsubject-resources/Mathematics/L3-Stats-Formulae-2013.pdf 8 Case Write-up: ABCtronics Submission Rule: You must work individually on this case. Submit as MSWord document. Mechanics: Page length limitation: Not more than Title + 7 pages, laid out as follows: • Title page: fill in the template on following page with your name. • Page 1: A memo addressed to Jim Morris following the template format (see following page), 1.5 or double spaced, stating your findings in the categories listed. • Pages 2-7: Detailed analytical support for your Page 1 memo. Layout: • Page size: US standard 8.5” x 11” • Margins: Minimum of 1” on all four sides • Font Size: 12 pt (or larger) • Spacing: 1.5 or double Please delete this first page, fill in your name on the cover page that follows. In the pages that follow, keep the section headings, but replace the instructions with your own content that addresses the issues called for in the instructions. In your writing, please pay attention to layout for readability (bulleting, use of white space, figures/tables, etc.). Finally, leave in place the last page as a separate page, which contains a grading key, which will be filled in when your case is graded. Notice that this key tells you how many points each part of the case analysis is worth. Try as best as you can. Good luck! ABCtronics Case Report Author_____________________________ To: Jim Morris From: RE: ABCtronics Analysis Memo One-page (1.5 or double-spaced) memo that summarizes key findings of analysis and recommendations (citing analytical justifications and evidence) for ABCtronics. The memo should clearly state how different quality and production issues get intertwined at ABCtronics, and what possible are the avenues for ABCtronics to improve its manufacturing as well as quality control processes. While it should not include detailed calculations, the memo should give the reader a clear sense of how you logically arrived at your conclusions concerning the causes of problems and your recommendations for actions with which to address them. Supporting Analysis Your analysis should address the issues below. (Note: In doing your analysis, you will need information from the text of the case and from many exhibits.) Downtime and Chemical Impurity Problem Regarding the analysis of downtime, why do you think that Mark and Stuart differ in their opinion? Would you recommend for changing the ion-implementer? Do you agree with Mark’s analysis on the chemical impurity problem? Comparison of Quality Control Methods Compare the existing quality control policy of LATM and the proposed policy ICTM. Can you comment upon the ‘flaw’ with the existing system? Analysis on Client Interfaces Explain why Mark is confident that ABCtronics should be able to meet the expectation of the client Customer PQRsystems. How the change at XYZsoft’s testing policy contributes to increase in the number of complaints regarding ABCtronics’ IC chips? Comment on the issue of SHVP. Do you think that ABCtronics is over-estimating the output of IC chips? Customer Feedback Assuming that customer scores in Table 2 follow a normal distribution, find the parameters of this distribution. Do you agree with Robert’s analysis of the customer scores? Find the 90% confidence interval for the average customer score. For the given margin of error 4, what do you think would be the minimum sample size for analyzing the mean customer score with 90% confidence? Sales Prediction Models What do you think of the sales prediction model proposed by SMT interns? According to Phil, what is the expected sales figure for ABCtronics in this year? How good is their chance to reach the target sales volume of 3 million chips? Conclusions Describe the main insights from this case and your recommendations to address the problems in the ABCtronics system. Grade: 40 points, allocated as follows Element Points Possible Memo contents 8 Downtime and chemical impurity problem 6 Comparison of quality control methods 6 Analysis on Client Interfaces 6 Customer Feedback 6 Sales Prediction Models 6 Conclusions 2 Total 40 Points Received Comments
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