| |
| Problem 1, 10 points |
| The failure rate for a product is | 0.0000005395 | units per hour and the design engineers believe that it |
| is steady from 100 hours to 80,600 hours of product life. If you only wanted to replace | 0.0223539132 | proportion |
| of the product due to warranty claims: 1) how long would your warranty period be, 2) what would you do |
| about the fact that the rate of failure is not steady until after 100 hours of operation, and 3) briefly, (one or two |
| short sentences) discuss what else you would put in the warranty relative to reliability? |
| Problem 2, 15 points |
| step 1 | step 2 | step 3 | step 4 |
| 0.9617868549 | 0.9725931267 | 0.96248938 | 0.9642791018 |
| R10000 | R11000 | R12000 | R10000 |
| 0.9758152675 |
| R9000 |
| 0.9635922685 |
| R10000 |
| What is the R10000 reliability of the above system? A signal travels from left to right and, in step two, can go through any of the three |
| units working in parallel. |
| Problem 3, 38 points | 0.3015302977 |
| Design engineers have set product specifications at 60 mm/sec +/-.8 mm/sec. You know that product which measures |
| +/- .8 mm/sec from the mean costs the company an extra $ | 33.02 | per unit. You also know that it will cost you $ | 9.9 | per unit to adjust |
| a product to 60 mm/sec. You also know that your process is a 3 sigma process and the mean is | 0.45 | SD less | than |
| the target. The firm accepts Taguchi's loss function as a viable means of modeling costs. How much is your |
| process 1) currently costing you if you do nothing, 2) if you fix those that make sense to fix? Would you spend | 8.2061211909 | million |
| dollars to create a centered process with a Cp ranging from 1.5 to 2? If you did have such a process, would you adjust or not adjust |
| (support using Taguchi's cost function)? Production is | 108092 | units per month (accrue monthly), costs $5000 per month to |
| inspect each unit, productive life cycle of the product is projected to be | 4.9045908932 | years, and the discount rate is expected to range from |
| 9% to 15%APR. Support your answer both quantitatively (95% CL, n = 50) and qualitatively (six stake holder consideration). |
| Problem 4 (3 points)) What decision do you make relative to control charts when you know the costs of Type I and Type II errors? |
| |
| Problem 5 (2 points) What is the purpose of step 18 in the process of creating a QCP? |
| Problem 6, 38 points | takt time is | 2.6031 | minutes, work 24/7/365 | 30.4166666667 | days in a month |
| Specifications are .5". +/- .001 inches, it costs | 450.77 | dollars when product is below the lower tolerance and | 65.08 | dollars |
| labor and $100 per .001 inch to bring those above the upper tolerance to 1 SD below tolerance. The SD of the process is | 0.0002895995 | . |
| I can also change the system to a 5 to 6 sigma process for | 2.6030605954 | million dollars. The organization accrues monthly, has a discount |
| rate that varies between 10 and 15% APR, looks only 3 years into the future on any project, is spending an additional $7000/month to inspect the |
| product, if put in the new system will spend only $2000 to control the process, currently the machine is set to produce a mean that is on target. |
| Is there a business rule you could change currently to save money with the system as is, and what should that rule be if there is one? Should |
| you alter the system to reduce the SD, show your answer as a 95% confidence interval using a sample of 50. Do not forget to judge your decision |
| from the perspectives of all stakeholders. |
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