1. Chapter 31Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

2. Learning Objectives Chapter 32Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

3. Chapter 33Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Easy to find percentiles of the data; see page 69 Stem-and-Leaf Display 3.1 Describing Variation

4. Chapter 34Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Also called a run chart Plot of Data in Time Order Marginal plot produced by MINITAB

5. Chapter 35Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Group values of the variable into bins, then count the number of observations that fall into each bin Plot frequency (or relative frequency) versus the values of the variable Histograms – Useful for large data sets

6. Chapter 36Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

7. Additional Minitab Graphs Chapter 37Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

8. Chapter 38Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

9. Chapter 39Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Numerical Summary of Data Sample average:

10. Chapter 310Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

11. The Standard Deviation Chapter 311Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

12. Chapter 312Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Box Plot (or Box-and-Whisker Plot)

13. Chapter 313Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Comparative Box Plots

14. Chapter 314Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Probability Distributions

15. Chapter 315Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

16. Chapter 316Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Will see many examples in the text Sometimes called a probability mass function Sometimes called a probability density function

17. Chapter 317Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

18. Chapter 318Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

19. Chapter 319Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The mean is the point at which the distribution exactly “balances”.

20. Chapter 320Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The mean is not necessarily the 50 th percentile of the distribution (that’s the median) The mean is not necessarily the most likely value of the random variable (that’s the mode)

21. Chapter 321Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

22. Chapter 322Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Hypergeometric Distribution 3.2 Important Discrete Distributions

23. Chapter 323Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Discrete distributions are used frequently in designing acceptance sampling plans – see Chapter 15

24. Chapter 324Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

25. Chapter 325Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Basis is in Bernoulli trials The random variable x is the number of successes out of n Bernoulli trials with constant probability of success p on each trial The Binomial Distribution

26. Chapter 326Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

27. Binomial Distributions Chapter 327Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

28. Chapter 328Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

29. Chapter 329Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Frequently used as a model for count data The Poisson Distribution

30. Chapter 330Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

31. Chapter 331Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

32. Chapter 332Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The random variable x is the number of Bernoulli trials upon which the rth success occurs The Negative Binomial Distribution

33. Chapter 333Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The negative binomial distribution is also sometimes called the Pascal distribution When r = 1 the negative binomial distribution is known as the geometric distribution The geometric distribution has many useful applications in SQC

34. Geometric Distribution Chapter 334Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

35. Chapter 335Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Normal Distribution 3.3 Important Continuous Distributions

36. Chapter 336Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

37. Chapter 337Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

38. Chapter 338Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

39. Chapter 339Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

40. Chapter 340Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

41. The Central Limit Theorem Chapter 341Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Practical interpretation – the sum of independent random variables is approximately normally distributed regardless of the distribution of each individual random variable in the sum

42. Chapter 342Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Lognormal Distribution

43. Chapter 343Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

44. Chapter 344Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

45. Chapter 345Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Exponential Distribution

46. Chapter 346Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Relationship between the Poisson and exponential distributions

47. Lack-of-memory property Chapter 347Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

48. Chapter 348Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Gamma Distribution

49. Chapter 349Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

50. Chapter 350Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. When r is an integer, the gamma distribution is the result of summing r independently and identically exponential random variables each with parameter λ. The gamma distribution has many applications in reliability engineering.

51. Chapter 351Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. The Weibull Distribution

52. Chapter 352Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. When β = 1, the Weibull reduces to the exponential

53. An Application of the Weibull Distribution Chapter 353Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

54. Chapter 354Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Determining if a sample of data might reasonably be assumed to come from a specific distribution Probability plots are available for various distributions Easy to construct with computer software (MINITAB) Subjective interpretation 3.4 Probability Plots

55. Normal Probability Plot Chapter 355Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

56. Chapter 356Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

57. The Normal Probability Plot on Standard Graph Paper Chapter 357Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

58. Chapter 358Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Other Probability Plots What is a reasonable choice as a probability model for these data?

59. Chapter 359Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

60. Chapter 360Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. 3.5 Some Useful Approximations

61. Chapter 361Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc.

62. Chapter 362Introduction to Statistical Quality Control, 7th Edition by Douglas C. Montgomery. Copyright (c) 2012 John Wiley & Sons, Inc. Learning Objectives