## Quality Engineering StatisticsThis book is a compendium of many of the statistical tools and tests used by quality and engineering professionals. it is a practical handbook that lists significant statistical methods, outlines assumptions for testing, and provides formulas and completed examples. the book is ideal for engineers who know what type of test to perform but need an easy-to-use reference to help complete the task. Readers should have an understanding of basic statistics. a bibliography contains references to texts that can provide the necessary theory and mathematical foundations. |

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### Contents

i | |

v | |

vii | |

ix | |

x | |

11 | |

12 | |

25 Small Sample Size Confidence Intervals | 13 |

72 Poisson Distribution | 53 |

73 Hypergeometric Distribution | 55 |

74 Geometric Distribution | 56 |

75 Uniform Distribution | 57 |

76 Negative Binomial Distribution | 58 |

GoodnessofFit Tests | 61 |

82 Test of Normality Using Skewness and Kurtosis | 63 |

Sample Size Determination for Tests of Hypotheses | 67 |

26 Confidence Interval for Poisson Distributed Data | 14 |

Testing for Differences in Means | 17 |

32 OneSided Test 𝜎 Known | 18 |

33 Testing a Sample Mean Versus a Hypothesized Mean When 𝜎 Is Estimated From the Sample Data One Sample t Test | 19 |

34 Testing for a Difference in Two Population Means Standard Deviations Known Two Sample Z Test | 20 |

35 Testing for a Difference in Two Population Means Standard Deviations Not Known But Assumed Equal Two Sample t Test | 21 |

36 Testing for a Difference in Two population Means Standard Deviations Not Known and Not Assumed Equal AspinWelch Test | 22 |

37 Testing for Differences in Means of Paired Samples Paired Sample t Test | 23 |

38 Testing for a Difference in Two Proportions | 25 |

39 Testing for Difference in Count Data | 26 |

310 Hypothesis Testing for Differences in Means Confidence Interval Approach | 27 |

Testing for Differences in Variances | 31 |

42 Testing an Observed Variance to a Hypothesized Variance Large Samples | 32 |

43 Testing for a Difference in Two Observed Variances Using Sample Data F Test | 33 |

44 Testing for a Difference in Two Observed Variances Using Large Samples | 34 |

45 Testing for Differences in Several Observed Variances Bartletts Test | 35 |

Decision Errors and Risks in Hypothesis Testing | 39 |

52 Alpha 𝛼 and Beta 𝛽 Risks | 40 |

Continuous Probability Distributions | 43 |

62 Predictions Using the Normal Distribution | 44 |

63 Central Limit Theorem | 45 |

65 Lognormal Distribution | 49 |

Discrete Probability Distributions | 51 |

91 Sample Size Required to Test an Observed Mean Versus a Hypothesized Mean When 𝜎 Is Known One Sample Z Test | 68 |

92 Sample Size Required to Test an Observed Mean Versus a Hypothesized Mean When 𝜎 Is Estimated From Observed Values One Sample t Test | 69 |

93 Sample Size Required to Test for Differences in Two Observed Means When Each Population Is Known Two Sample Z Test | 70 |

94 Sample Size Required to Test for Differences in Two Observed Means When 𝜎 Is Estimated From the Observed Data Two Sample t Tests | 71 |

96 Sample Size Required for ChiSquare Test of Observed Variance to a Hypothesized Variance | 73 |

97 Sample Size Required for F Test of Two Observed Variances | 74 |

Analysis of Variance | 77 |

102 OneWay ANOVA Fixed Effects Model | 78 |

103 TwoWay ANOVA Fixed Effects Model Single Replicate | 80 |

104 TwoWay ANOVA Fixed Effects Model With Replication | 84 |

105 Random effects Model | 88 |

Tables | 91 |

Normal Distribution | 92 |

t Distribution | 95 |

ChiSquare | 96 |

F Distribution 𝛼 005 | 97 |

F Distribution 𝛼 001 | 99 |

Median Rank Values | 101 |

Gamma Function | 104 |

107 | |

109 | |

### Common terms and phrases

183 minutes alternative hypothesis ANOVA table appear in table Bartlett's test binomial distribution calculate the probability calculate the sample calculate the value calculated value chi-square test confidence interval confidence level critical value degrees of freedom expected number expected value F test F value factor FIXED EFFECTS MODEL fraction nonconforming HYPOTHESIZED MEAN hypothesized variance kurtosis large sample level of risk mean of process Median Rank nonconformances per unit nonconforming item normal distribution null hypothesis H0 number of nonconformances number of occurrences OBSERVED VARIANCES one-tail test paired samples point estimate Poisson distribution population mean population variance random effects model reject the null REQUIRED TO TEST result sample data sample drawn sample of 25 SAMPLE SIZE REQUIRED Sample t Test section 3.5 shape parameter SSAxB sum of squares tail Testing for Differences treatment levels trial TWO-TAIL TEST Two-Way ANOVA variance calculated VERSUS A HYPOTHESIZED Weibull distribution