QM456 HW5 fall 2010
1) Tea is sold in 2000 milliliter (ml) bottles. The process has a standard deviation of 15 ml and has a business rule that requires l% or less probability of overfilling. Overfilling is defined at more than 1990 ml. What is their target mean?
Other than selling in what should be a 2000 ml bottle and the SD, the following has little to do with the preceding. For instance, the business rule target and process mean is 2000 ml for the rest of this problem.
You believe that employee training in SPC and process improvement that would cost $500,000.00 will enable you and your employees you are in charge of to reduce the standard deviation to between 3 and 6 millimeters (uniform distribution), each millimeter of product costs $.001, there is a fine of $1.00 per bottle if the fill is below 1990 ml and it costs $.25 per overfilled bottle (they can hold 2005 mililiters), accrue monthly, produce 3 million bottles per month, 2.5 years life of project, and discount using 14% APR. You have to come up with a convincing argument to convince your employer. Your employer is not in the habit of spending money on something like training where the return is hard to quantify, and sees no difference between a process with a mean of 2000 SD of 15 and a process with a mean of 2000 SD 3.3333. In addition, the manager is reluctant to spend money on any idea that raises the amount of material over 1990 ml which happens as the SD goes down. Develop that argument quantitatively by showing what the NPV is by reducing the variability to 3.3333 ml standard deviations and explain why the cost of just overfilling over 1990 goes up. Can you come up with an even more cost effective policy regarding the mean?
2) 7th edition, Ch11P 8 & 9; 8th edition P7 & 8 in CH10
3) Ch11P 15-18 7th edition; same questions in CH10 8th edition
4) A company has done a systems analysis and found the following
Currently your firm’s product has a market price $5 dollars below competition with a warranty of 4000 hours and you are losing market share. You have been delegated to resurrect this products market share and profit.
Competitor information: substitute product has a replacement warranty if the product fails before or at 5000 hours and a price of $35.00 per unit. All other features are equal to the product of the firm for which you work for.
Customers are somewhat insensitive to price change but are very sensitive to warranties (actually the other way around in most markets) and are otherwise indifferent to your firm’s product or the competitors. To show this point to your supervisor you conducted a survey that showed that 99% of the population agreed with the statement that warranty was more important than price (as long as within 6 dollars) and other product features. To make your point you sampled enough people to have a 99.74% confidence interval with a margin of error of 1%. How big was your sample?
Assume you work in a TQM environment where management is willing to provide you resources and allows you to manage/lead as you see fit.
You have found the following.
1) Your firms product life averages 8000 hours with a standard deviation of 1000 hours
2) Current replacement cost = $20.00 per unit
3) Variable cost of production = $15.00 per unit
4) Total fixed costs including G&A and sales allocated to this product is $20 million per year
5) Current market share is one million units per year
6) Market share will go up 50% if you drop the price another 3 dollars per unit.
7) Within the price bounds you found, market share will go up 80% if your guarantee is 30% greater than your competition.
8) A process improvement is available that reduces the standard deviation of product life by 50%, will last 5 years before competition catches up with you, and costs $5 million to put in place.
9) The firm has level production (produces the same amount monthly) and uses a discount rate of 14% APR.
Decide what to do. Support conceptually and quantitatively.
5) You are in charge of a production line located in the Midwest and the customer service representative from the company you are working for is asking what is up with your line. He has been getting many complaints from Wal-Mart about your product. Wal-Mart says that although your product is lasting as long as your company’s literature says it will for most of their customers, there are certain stores whose customers are bringing the product back because the product did not function as long as it was supposed to. Wal-Mart feels that you are shipping your worst product to these stores because the stores have many more warranty claims against your product than other stores. You ask for the names of the stores that are having problems and note that they are all in hot dry climates. You also know that what product goes to what stores is completely random. Explain to me what you think is going on here. Suggest several ways to take care of the problem.
6) Assuming a 95% confidence interval, how many people would Gallop have had to poll to say that the President’s positive rating for his current fiscal policy is 15% with a .5% margin of error. Even if Gallop asked the number of people you recommend from your calculation, what else would you want to know to determine if the finding by Gallop is representative of you and your peers?
7) You are buying a machine with 7 moving parts in it, 3 of which can do the same task and are there for redundancy. The salesperson tells you that the machine has a reliability of .99. Because you took QM456 at U of I, you know that you need to determine how long of time 99% of the product will last. Since the salesman did not tell you, you are suspicious and decide to do a little research. You need an R10,000. The research shows that the individual reliability for each of the 4 parts in series is .9980 for 11,000 hours. You found that the 3 parts in parallel were made by 3 different manufactures and had the following reliabilities. R9,000 = .85, R10,000 = .84 R12,000 = .85. What is the machine’s true reliability for 10,000 hours? Would you buy the machine?
8) You currently have a business that is just breaking even and a board that says that if things do not improve soon, they will shut the plant down. Raising the price of the product is not possible. You have what was a 3.5 sigma process whose mean has drifted 1 standard deviation to the left of the desired norm, which is 30 with a tolerance of +/- 3.5. The process-mean seems to be staying where it is, as is the standard deviation. The one customer of the company demands that you have a process of a Cp of 2 and a Cpk of 1.5, because they do not want to perform acceptance sampling and you do not want them to because they charge you the exorbitant amount of $10 for a unit if it measures 33.5 or 26.5. Currently the Takt time of production is .10 minutes and you have to produce 24/7 all year (365 days) to meet demand. The accountants for the company accrue every month and they have told you the discount rate for the company is 15% APR. The product you are producing will have a 5 year life. As COO you have determined the cause of the drift and what it will take to fix the drift and make the process between a 5.5 and 6 sigma process. Furthermore, you have determined the onetime cost of the process change will be $3 million. You also are a firm believer in Taguchi’s loss function. It will cost $1.5 million to close the company. Currently it costs you a total of $5000/month to determine the measurement of a unit of product and $5 to adjust it to the specification norm, and to keep the business you are currently performing adjustments on units that make sense to adjust. Assume that if the new process shows that 4 times the new standard deviation falls between the specification norm and the measure of the unit where it made sense to start fixing product, you will not measure or fix any product. Convince me to make the change or close the company. Also, determine the greatest number of units possible that could be out of compliance over the 5 years, given a constant six-sigma process.