EXERCISES
2.7. Explain the importance of tollgates in the DMAIC process.

At a tollgate, a project team presents its work to managers and “owners” of the process. In a six-sigma organization, the tollgate participants also would include the project champion, master black belts, and other black belts not working directly on the project. Tollgates are where the project is reviewed to ensure that it is on track and they provide a continuing opportunity to evaluate whether the team can successfully complete the project on schedule. Tollgates also present an opportunity to provide guidance regarding the use of specific technical tools and other information about the problem. Organization problems and other barriers to success—and strategies for dealing with them—also often are identified during tollgate reviews. Tollgates are critical to the overall problem-solving process; It is important that these reviews be conducted very soon after the team completes each step. 2.11. Suppose that your business is operating at the three-sigma quality level. If projects have an average improvement rate of 50% annually, how many years will it take to achieve Six Sigma quality?
3.4  66,810 1  0.5  3.4 / 66,810  0.5 x ln  3.4 / 66,810   x ln 0.5 x ln  3.4 / 66,810  ln 0.5  14.26 years  14 years, 3 months x Page 51

2.12. Suppose that your business is operating at the 5-sigma quality level. If projects have an average improvement rate of 50% annually, how many years will it take to achieve Six Sigma quality? 5 sigma quality is approximately 233 ppm defective, assuming the customary 1.5 shift in mean (Figure 1.2(b)).
3.4  233 1  0.5  3.4 / 233  0.5 x ln  3.4 / 233  x ln 0.5 x ln  3.4 / 233 ln 0.5  6.2 years  6 years, 1 month x Page 51

CHAPTER 2 THE DMAIC PROCESS 2-3 2.13. Explain why it is important to separate sources of variability into