Assignment:
1) An electronic component at Eltcomp has a specification of 250.0 ± 7.5 ohms. Scrapping a defective component results in a $135 loss.
a) Determine the Taguchi loss function.
b) If the process is centered at 248.6 ohms with a standard deviation of 1.7 ohms, what is the expected loss per unit?
2) At Elektroparts Manufacturers' integrated circuit business, it was found that any output voltage that exceeds 255.0 ± 0.5 volts was unacceptable to the customer. Exceeding these limits results in an estimated loss of $30.
a) Determine the Taguchi loss function.
b) The voltage of the integrated circuit can be corrected in the plant by changing a resistor that costs $2.00. At what tolerance should the integrated circuit be manufactured?
3) Ten transformers were each tested for 720 hours, four of which failed; at 297, 401, 422, and 457 hours. Once a transformer fails, it cannot be restarted.
a) What is the failure rate for these transformers?
b) What is the MTTF?
4) A particular type of light bulb has a mean life of only 40 hours. Use the exponential distribution to answer the following questions.
a) What percentage of light bulbs will fail within 50 hours?
b) When is it expected that 50% of the light bulbs will have failed?
c) When is it expected that 95% of the light bulbs will have failed?
5) In a complex manufacturing process, three operations are performed in series. Because of the nature of the process, machines frequently fall out of adjustment and must be repaired. To keep the system going, two identical machines are used at each stage; thus, if one fails, the other can be used while the first is repaired (see accompanying figure).
The reliabilities of the machines are as follows:
Machine Reliability
A 0.975
B 0.999
C 0.825
a) What is the system reliability, assuming only one machine at each stage?
b) What is the system reliability when there are two machines at each stage?