6 Running head: Case Study Questions HOMEWORK ASSIGNMENT 6 Charles V. Nash Allied American University Author Note This paper was prepared for MGT 305: Quality Management, Homework Assignment 6 taught by Dr. Stan Reeley. Homework Assignment 6 Directions: Please complete the following case studies in your textbook. Ensure that your responses are at least one to two pages in length. Please use citations from the textbook when appropriate. Please visit the Academic Resource Center (ARC) for concise APA guidelines. Case Study 8.1 Parts 1, 2, and 3 (p. 299) 1. Find the probability that in a lot of 15 forms, a sample of 4 forms will have no errors. Answer: 2. Given that the process has a fraction nonconforming (p) of 5 percent (p = 0.05), what is the probability that in a sample of 10 forms, 3 or fewer will be found with errors? Answer: 3. Find the probability that in any given minute, five new customers will arrive. What is the probability that more than seven new customers will arrive in a given minute? Answer: Case Study 9.1 Parts 1 and 2 (pp. 341-343) Max's B-B-Q Inc. manufactures top-of-the-line barbeque tools. The tools include forks, spatulas, knives, spoons, and shish-kebab skewers. Max's fabricates both the metal parts of the tools and the resin handles. These are then riveted together to create the tools (Figure C8.2.1). Recently, Max's hired you as a process engineer. Your first assignment is to study routine tool wear on the company's stamping ma- chine. In particular, you will be studying tool-wear patterns for the tools used to create knife blades. In the stamping process, the tooling wears slightly during each stroke of the press as the punch shears through the material. As the tool wears, the part features become smaller. The knife has specifications of 10 mm; 0.025 mm; under- sized parts must be scrapped. The tool can be re-sharpened to bring the parts produced back into specification. To reduce manufacturing costs and simplify machine scheduling, it is critical to pull the tool and perform maintenance only when absolutely necessary. It is very important for scheduling, costing, and quality purposes that the average number of strokes, or tool run length, be determined. Knowing the average number of strokes that can be performed by a tool enables routine maintenance to be scheduled. It is the plant manager's philosophy that tool maintenance be scheduled proactively. When a tool is pulled unexpectedly, the tool maintenance area may not have time to work on it immediately. Presses without tools don't run, and if they are not running, they are not making money. As the process engineer studying tool wear, you must develop a prediction for when the tool should be Homework Assignment 6 pulled and re-sharpened. The following information is available from the tool maintenance department. The average number of strokes for a tool is 45,000. The standard deviation is 2,500 strokes. A punch has a total of 25 mm that can be ground off be- fore it is no longer useful. Each regrind to sharpen a punch removes 1 mm of punch life. The cost to regrind is 2 hours of press downtime to remove and reinsert tool, at $300 per hour 5 hours of tool maintenance time, at $65 per hour 5 hours of downtime while press is not being used, at $300 per hour The average wait time for unplanned tool regrind is 15 hours at $300 per hour. Because of the large number of strokes per tool regrind, this is considered to be a continuous distribution. The normal curve probability distribution is applicable. 1. One percent of the tools wear out very early in their expected productive life. Early tool wear out and, thus, an unplanned tool pull can be caused by a variety of factors, including changes in the hardness of the material being punched, lack of lubrication, the hardness of the tool steel, and the width of the gap between the punch and the die. Key part dimensions are monitored using X and R charts. These charts reveal when the tool needs to be reground in order to preserve part quality. Use the normal probability distribution and the information provided to calculate the number of strokes that would result in an early wear out percentage of 1 percent or fewer. If the plant manager wants the tool to be pulled for a regrind at 40,000 strokes, what is the chance that there will be an early tool wear out failure before the tool reaches 40,000 strokes? Answer: Now that you have been at Max's B-B-Q Inc. for a while, the plant manager asks you to assist the production scheduling department with pricing data on a high volume job requiring knife blades for the company's best customer. As you know, it is the plant manager's philosophy to be proactive when scheduling tool maintenance (regrinds) rather than have to unexpectedly pull the tool. However, pricing will be a very important factor in selling this job to the customer. Essentially, the plant manager wants no unplanned tool pulls, but sales needs pricing cost reductions. The production scheduler would like a tool regrind schedule that results in minimal inventory. 2. You will soon be meeting with the plant manager and the managers from sales and production scheduling. They are expecting you to have an answer to the question: Given the Plant Manager Strokes before 40,000 Pull need to balance maximizing tool use, minimizing inventory, minimizing production disruption, and minimizing cost, how many strokes should you recommend to run this tool before pulling for a regrind? Create a graph that shows the number of unplanned pulls versus the number of strokes. The graph should com- prise at least six data points. Next, complete the spread- sheet in Figure C8.2.2 showing the costs of each individual's plan. Using the graph and the spreadsheet, prepare a response for the question, how many strokes should the tool be run before pulling it for a regrind? Your analysis should include answers to the following questions: How will this number balance Homework Assignment 6 tool use, cost, inventory, and production disruption? What are the economics of this situation? Plan Manager Strokes before pull Nmuber of pulls Production over life of tool cost of each pull additional cost of an unplanned pull chance of unplanned pulls total additional cost due to unplanned pulls total cost Answer: Reference: Sales Manager 43,000 25 1,075,000 You 40,000 25 1,000,000 Production Scheduler 42,000 25 1,050,000 2,425 4,500 2,425 4,500 2,425 4,500 2,425 4,500 Homework Assignment 6 Summers, D. C. S. (2010). Quality (5th Ed.). New Jersey: Pearson. Homework Assignment 6 Running head: Case Study Questions HOMEWORK ASSIGNMENT 6 Charles V. Nash Allied American University Author Note This paper was prepared for MGT 305: Quality Management, Homework Assignment 6 taught by Dr. Stan Reeley. Homework Assignment 6 Directions: Please complete the following case studies in your textbook. Ensure that your responses are at least one to two pages in length. Please use citations from the textbook when appropriate. Please visit the Academic Resource Center (ARC) for concise APA guidelines. Case Study 8.1 Parts 1, 2, and 3 (p. 299) The registrar's office at a nearby university handles thousands of student class registrations every term. To take care of each student's needs efficiently and correctly, the registrar sees to it that a significant amount of time is spent in training the staff. Each staff member receives one of two types of training: A refresher course is given for current employees, and a general training course is given for new hires. At the end of each of the training courses, a short exam tests the staff member's ability to locate errors on a registration form. A group of 15 registration forms contains 5 forms with errors. During the test, the staff member is asked to randomly select 4 forms and check them for errors. The sampling is to be done without replacement. A major concern of those administering the test is that the forms with errors will not be selected by the staff member who is randomly selecting 4 forms. 1. Find the probability that in a lot of 15 forms, a sample of 4 forms will have no errors. The registrar receives a steady stream of registration forms for the three weeks prior to each term. While the office tries to provide easy-to-comprehend forms with complete instructions, a few forms are completed that are incorrect. Forms are considered incorrectly filled out if any key information is missing. Key information includes the student's local or permanent address, a course number or title, pro- gram or area of study, etc. When incorrect forms are received by the registrar's office they are sent back to the student for correction. This process delays the student's registration. While methods, forms, and instructions have been improving, the registrar feels that 5 percent of the forms are filled out incorrectly. To help continue improv- ing the forms and instructions, he has 10 forms sampled each day to determine the types of errors being made. This information is shared with a quality improvement team whose members are currently working on improving the existing forms. 2. Given that the process has a fraction nonconforming (p) of 5 percent (p = 0.05), what is the probability that in a sample of 10 forms, 3 or fewer will be found with errors? For the three weeks prior to the beginning of every term and for the first two weeks of the term, the registrar's office is very busy. To help determine staffing needs, the registrar decides to study the number of students and/or parents utiliz- ing the office's services during any given minute. From past experience he knows that on average three new customers arrive every minute. Homework Assignment 6 3. Find the probability that in any given minute, five new customers will arrive. What is the probability that more than seven new customers will arrive in a given minute? Case Study 9.1 Parts 1 and 2 (pp. 341-343) Max's B-B-Q Inc. manufactures top-of-the-line barbeque tools. The tools include forks, spatulas, knives, spoons, and shish-kebab skewers. Max's fabricates both the metal parts of the tools and the resin handles. These are then riveted together to create the tools (Figure C8.2.1). Recently, Max's hired you as a process engineer. Your first assignment is to study routine tool wear on the company's stamping ma- chine. In particular, you will be studying tool-wear patterns for the tools used to create knife blades. In the stamping process, the tooling wears slightly during each stroke of the press as the punch shears through the material. As the tool wears, the part features become smaller. The knife has specifications of 10 mm; 0.025 mm; under- sized parts must be scrapped. The tool can be re-sharpened to bring the parts produced back into specification. To reduce manufacturing costs and simplify machine scheduling, it is critical to pull the tool and perform maintenance only when absolutely necessary. It is very important for scheduling, costing, and quality purposes that the average number of strokes, or tool run length, be determined. Knowing the average number of strokes that can be performed by a tool enables routine maintenance to be scheduled. It is the plant manager's philosophy that tool maintenance be scheduled proactively. When a tool is pulled unexpectedly, the tool maintenance area may not have time to work on it immediately. Presses without tools don't run, and if they are not running, they are not making money. As the process engineer studying tool wear, you must develop a prediction for when the tool should be pulled and re-sharpened. The following information is available from the tool maintenance department. The average number of strokes for a tool is 45,000. The standard deviation is 2,500 strokes. A punch has a total of 25 mm that can be ground off be- fore it is no longer useful. Each regrind to sharpen a punch removes 1 mm of punch life. The cost to regrind is 2 hours of press downtime to remove and reinsert tool, at $300 per hour 5 hours of tool maintenance time, at $65 per hour 5 hours of downtime while press is not being used, at $300 per hour The average wait time for unplanned tool regrind is 15 hours at $300 per hour. Because of the large number of strokes per tool regrind, this is considered to be a continuous distribution. The normal curve probability distribution is applicable. Question 1: One percent of the tools wear out very early in their expected productive life. Early tool wear out and, thus, an unplanned tool pull can be caused by a variety of factors, including changes in the hardness of the material being punched, lack of lubrication, the hardness of the tool steel, and the width of the gap between the punch and the die. Key part dimensions are monitored using X and R charts. These charts reveal when the tool needs to be reground in order to preserve part quality. Use the normal probability Homework Assignment 6 distribution and the information provided to calculate the number of strokes that would result in an early wear out percentage of 1 percent or fewer. If the plant manager wants the tool to be pulled for a regrind at 40,000 strokes, what is the chance that there will be an early tool wear out failure before the tool reaches 40,000 strokes? Now that you have been at Max's B-B-Q Inc. for a while, the plant manager asks you to assist the production scheduling department with pricing data on a high volume job requiring knife blades for the company's best customer. As you know, it is the plant manager's philosophy to be proactive when scheduling tool maintenance (regrinds) rather than have to unexpectedly pull the tool. However, pricing will be a very important factor in selling this job to the customer. Essentially, the plant manager wants no unplanned tool pulls, but sales needs pricing cost reductions. The production scheduler would like a tool regrind schedule that results in minimal inventory. Question 2: You will soon be meeting with the plant manager and the managers from sales and production scheduling. They are expecting you to have an answer to the question: Given the Plant Manager Strokes before 40,000 Pull need to balance maximizing tool use, minimizing inventory, minimizing production disruption, and minimizing cost, how many strokes should you recommend to run this tool before pulling for a regrind? Create a graph that shows the number of unplanned pulls versus the number of strokes. The graph should com- prise at least six data points. Next, complete the spread- sheet in Figure C8.2.2 showing the costs of each individual's plan. Using the graph and the spreadsheet, prepare a response for the question, how many strokes should the tool be run before pulling it for a regrind? Your analysis should include answers to the following questions: How will this number balance tool use, cost, inventory, and production disruption? What are the economics of this situation? Plan Manager Strokes before pull Nmuber of pulls Production over life of tool cost of each pull additional cost of an unplanned pull chance of unplanned pulls total additional cost due to unplanned pulls total cost Sales Manager 43,000 25 1,075,000 You 40,000 25 1,000,000 Production Scheduler 42,000 25 1,050,000 2,425 4,500 2,425 4,500 2,425 4,500 2,425 4,500 Homework Assignment 6 Reference: Summers, D. C. S. (2010). Quality (5th Ed.). New Jersey: Pearson