Manufacturing design and six signa assignment

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1. Solve the following problems (show all your work): 1. The number of flaws in a fibre optic cable follows a Poisson distribution. The average number of flaws in 100m of cable is 2.35. a) What is the probability of exactly three flaws in 250m of cable? b) What is the probability of at least two flaws in 150m of cable? c) What is the probability of exactly one flaw in the first 30m of cable and exactly one flaw in the second 50m of cable? 2. It is known that 0.77% of the circuit boards from a production line are defective. If a random sample of 145 circuit boards is taken from this production line, use the Poisson approximation to estimate the probability that the sample contains: a) Exactly 4 defective boards. b) At least 3 defective boards. 3. A company manufacturing oil seals wants to establish Žand R control charts on the process. There are 25 preliminary samples of size 6 on the internal diameter of the seal. The summary data (in mm) are as follows: Σ?5, X-1143.85 and Σ?5, R=14.98 a) Find the control limits that should be used on the X and R control charts. 4. Samples of n = 3 items are taken from a process at regular intervals. A normally distributed quality characteristic is measured and Xand s values are calculated for each sample. After 50 subgroups have been analyzed, we have Σ59, X,-986,65 and Σ79, s82.43 a) Find the control limits that should be used on the X and control charts. 5. A process is being controlled with a fraction nonconforming control chart. The process average has been shown to be 0.033. Three-sigma control limits are used, and the procedure calls for taking daily samples of 340 items. a) Calculate the upper and lower control limits. 6. Webster Chemical's nominal weight for filling tubes of caulk is 10.00 ounces + 0.70 ounces. The target process capability ratio is 1.33. the current distribution of the filling process is centered on 10.0545 ounces with a standard deviation of 0.186 ounces. a) Compute the process capability ratio and process capability index to assess whether the filling process is capable and set properly. Explain your results. 7. Elaborate a flow diagram of a sand casting process. 8. Using the template in CANVAS, Construct the FMEA Chart for the sand casting process. 9. Give detailed explanation of the purpose and goals of the methodology of Six Sigma. 10. Define with your own words lean manufacturing. 11. Define the most important manufacturing systems. 12. Describe in detail each of the design stages of a manufacturing product. 13. What are the types of materials in manufacturing? Give a brief description of each one. 14. What are the main stages of the production of a machined part?
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