R12000 in dollars

Sheet1
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.