Probability and Statistics in Engineering and Management Science

by Hines, William W.; Montgomery, Douglas C.

• ISBN13: 9780471600909
• ISBN10: 0471600903
• Edition: 3rd
• Format: Hardcover
• Copyright: 1990-01-01
• Publisher: John Wiley & Sons Inc

Summary

* End-of-chapter summaries reinforce the main topics and goals of the chapter.

Table of Contents

Introduction and Data Description	1	(27)
The Field of Probability and Statistics	1	(3)
Graphical Presentation of Data	4	(4)
Measurement Data: the Frequency Distribution and Histogram	4	(3)
Count Data: the Pareto Chart	7	(1)
Numerical Description of Data	8	(10)
Measures of Central Tendency	9	(2)
Measures of Dispersion	11	(4)
Grouped Data	15	(3)
Exploratory Data Analysis	18	(3)
The Stem and Leaf Plot	18	(2)
The Box Plot	20	(1)
Summary	21	(1)
Exercises	22	(6)
An Introduction to Probability	28	(35)
Introduction	28	(1)
A Review of Sets	29	(4)
Experiments and Sample Spaces	33	(3)
Events	36	(1)
Probability Definitions and Assignment	37	(5)
Finite Sample Spaces and Enumeration	42	(5)
Tree Diagram	43	(1)
Multiplication Principle	43	(1)
Permutations	44	(1)
Combinations	45	(2)
Permutations of Like Objects	47	(1)
Conditional Probability	47	(7)
Partitions, Total Probability, and Bayes' Theorem	54	(2)
Summary	56	(1)
Exercises	57	(6)
One-Dimension Random Variables	63	(23)
Introduction	63	(4)
The Distribution Function	67	(2)
Discrete Random Variables	69	(4)
Continuous Random Variables	73	(2)
Some Characteristics of Distributions	75	(5)
Chebyshev's Inequality	80	(2)
Summary	82	(1)
Exercises	82	(4)
Functions of One Random Variable and Expectation	86	(22)
Introduction	86	(1)
Equivalent Events	86	(2)
Functions of a Discrete Random Variable	88	(2)
Continuous Functions of a Continuous Random Variable	90	(3)
Expectation	93	(4)
Approximations to E(H(X)) and V(H(X))	97	(2)
The Moment-Generating Function	99	(3)
Summary	102	(1)
Exercises	103	(5)
Joint Probability Distributions	108	(43)
Introduction	108	(1)
Joint Distributions for Two-Dimensional Random Variables	109	(4)
Marginal Distributions	113	(5)
Conditional Distributions	118	(5)
Conditional Expectation	123	(2)
Regression of the Mean	125	(2)
Independence of Random Variables	127	(1)
Covariance and Correlation	128	(3)
The Distribution Function for Two-Dimensional Random Variables	131	(2)
Functions of Two Random Variables	133	(3)
Joint Distributions of Dimension n > 2	136	(2)
Linear Combinations	138	(4)
Moment Generating Functions and Linear Combinations	142	(1)
The Law of Large Numbers	142	(2)
Summary	144	(1)
Exercises	145	(6)
Some Important Discrete Distributions	151	(25)
Introduction	151	(1)
Bernoulli Trials and the Bernoulli Distribution	151	(3)
The Binomial Distribution	154	(5)
Mean and Variance of the Binomial Distribution	154	(2)
The Cumulative Binomial Distribution	156	(1)
An Application of the Binomial Distribution	156	(3)
The Geometric Distribution	159	(2)
Mean and Variance of the Geometric Distribution	159	(2)
The Pascal Distribution	161	(1)
Mean and Variance of the Pascal Distribution	162	(1)
The Multinomial Distribution	162	(1)
The Hypergeometric Distribution	163	(2)
Mean and Variance of the Hypergeometric Distribution	164	(1)
The Poisson Distribution	165	(4)
Development from a Poisson Process	165	(1)
Development of the Poisson Distribution from the Binomial	166	(1)
Mean and Variance of the Poisson Distribution	167	(2)
Some Approximations	169	(1)
Generation of Realizations	170	(1)
Summary	170	(2)
Exercises	172	(4)
Some Important Continuous Distributions	176	(18)
Introduction	176	(1)
The Uniform Distribution	176	(3)
Mean and Variance of the Uniform Distribution	177	(2)
The Exponential Distribution	179	(4)
The Relationship of the Exponential Distribution to the Poisson Distribution	179	(1)
Mean and Variance of the Exponential Distribution	180	(3)
Memoryless Property of the Exponential Distribution	183	(1)
The Gamma Distribution	183	(4)
The Gamma Function	183	(1)
Definition of the Gamma Distribution	184	(1)
Relationship Between the Gamma Distribution and the Exponential Distribution	184	(1)
Mean and Variance of the Gamma Distribution	185	(2)
The Weibull Distribution	187	(1)
Mean and Variance of the Weibull Distribution	187	(1)
Generation of Realizations	188	(1)
Summary	189	(2)
Exercises	191	(3)
The Normal Distribution	194	(34)
Introduction	194	(1)
The Normal Distribution	194	(8)
Properties of the Normal Distribution	195	(1)
Mean and Variance of the Normal Distribution	196	(1)
The Cumulative Normal Distribution	197	(1)
The Standard Normal Distribution	197	(1)
Problem-Solving Procedure	198	(4)
The Reproductive Property of the Normal Distribution	202	(3)
The Central Limit Theorem	205	(4)
The Normal Approximation to the Binomial Distribution	209	(3)
The Lognormal Distribution	212	(4)
Density Function	212	(1)
Mean and Variance of the Lognormal Distribution	213	(1)
Other Moments	214	(1)
Properties of the Lognormal Distribution	214	(2)
The Bivariate Normal Distribution	216	(5)
Generations of Normal Realizations	221	(1)
Summary	222	(1)
Exercises	222	(6)
Random Samples and Sampling Distributions	228	(16)
Random Samples	228	(1)
Statistics and Sampling Distributions	229	(2)
The Chi-Square Distribution	231	(3)
The t Distribution	234	(4)
The F Distribution	238	(3)
Summary	241	(1)
Exercises	241	(3)
Parameter Estimation	244	(44)
Point Estimation	244	(11)
Properties of Estimators	245	(5)
The Method of Maximum Likelihood	250	(3)
The Method of Moments	253	(1)
Precision of Estimation: the Standard Error	254	(1)
Confidence Interval Estimation	255	(23)
Confidence Interval on the Mean, Variance Known	257	(3)
Confidence Interval on the Difference in Two Means, Variance Known	260	(2)
Confidence Interval on the Mean of a Normal Distribution, Variance Unknown	262	(3)
Confidence Interval on the Difference in Means of Two Normal Distributions, Variances Unknown	265	(3)
Confidence Interval on 1-2 for Paired Observations	268	(1)
Confidence Interval on the Variance of a Normal Distribution	269	(2)
Confidence Interval on the Ratio of Variances of Two Normal Distributions	271	(2)
Confidence Interval on a Proportion	273	(2)
Confidence Interval on the Difference in Two Proportions	275	(1)
Approximate Confidence Intervals in Maximum Likelihood Estimation	276	(1)
Simultaneous Confidence Intervals	277	(1)
Summary	278	(3)
Exercises	281	(7)
Tests of Hypotheses	288	(65)
Introduction	288	(6)
Statistical Hypotheses	288	(1)
Type I and Type II Errors	289	(3)
One-Sided and Two-Sided Hypotheses	292	(2)
Tests of Hypotheses on the Mean, Variance Known	294	(7)
Statistical Analysis	294	(2)
Choice of Sample Size	296	(4)
The Relationship Between Tests of Hypotheses and Confidence	300	(1)
Large Sample Test with Unknown Variance	300	(1)
P-Values	300	(1)
Tests of Hypotheses on the Equality of Two Means, Variances Known	301	(3)
Statistical Analysis	301	(2)
Choice of Sample Size	303	(1)
Tests of Hypotheses on the Mean of a Normal Distribution, Variance Unknown	304	(4)
Statistical Analysis	305	(1)
Choice of Sample Size	306	(2)
Tests of Hypotheses on the Means of Two Normal Distributions, Variances Unknown	308	(4)
Case 1: σ21 = σ22	308	(2)
Case 2: σ21 = σ22	310	(1)
Choice of Sample Size	311	(1)
The Paired t-Test	312	(3)
Tests of Hypotheses on the Variance	315	(3)
Test Procedures for a Normal Population	315	(1)
Choice of Sample Size	316	(1)
A Large-Sample Test Procedure	317	(1)
Tests for the Equality of Two Variances	318	(3)
Test Procedure for Normal Populations	318	(2)
Choice of Sample Size	320	(1)
A Large-Sample Test Procedure	320	(1)
Tests of Hypotheses on a Proportion	321	(2)
Statistical Analysis	321	(1)
Choice of Sample Size	322	(1)
Tests of Hypotheses on Two Proportions	323	(4)
A Large-Sample Test for H0: p1 = p2	323	(1)
Choice of Sample Size	324	(1)
A Small Sample Test for H0: p1 = p2	325	(2)
Testing for Goodness of Fit	327	(8)
The Chi-Square Goodness-of-Fit Test	327	(4)
Probability Plotting	331	(2)
Selecting the Form of a Distribution	333	(2)
Contingency Table Tests	335	(5)
Summary	340	(1)
Exercises	340	(13)
Design and Analysis of Single-Factor Experiments: the Analysis of Variance	353	(37)
The Completely Randomized Single-Factor Experiment	353	(13)
An Example	353	(1)
The Analysis of Variance	354	(7)
Estimation of the Model Parameters	361	(2)
Residual Analysis and Model Checking	363	(2)
An Unbalanced Design	365	(1)
Tests on Individual Treatment Means	366	(5)
Orthogonal Contrasts	366	(3)
Duncan's Multiple Range Test	369	(2)
The Random Effects Model	371	(4)
The Randomized Block Design	375	(7)
Design and Statistical Analysis	375	(4)
Tests on Individual Treatment Means	379	(1)
Residual Analysis and Model Checking	380	(2)
Determining Sample Size in Single-Factor Experiments	382	(3)
Summary	385	(1)
Exercises	385	(5)
Design of Experiments with Several Factors	390	(65)
Examples of Experiment Design Applications	390	(3)
Factorial Experiments	393	(4)
Two-Factor Factorial Experiments	397	(12)
Statistical Analysis of the Fixed Effects Model	398	(5)
Model Adequacy Checking	403	(2)
One Observation per Cell	405	(1)
The Random Effects Model	405	(3)
The Mixed Model	408	(1)
General Factorial Experiments	409	(4)
The 2k Factorial Design	413	(20)
The 22 Design	414	(7)
The 2k Design for k > 2 Factors	421	(7)
A Single Replicate of the 2k Design	428	(5)
Confounding in the 2k Design	433	(5)
Fractional Replication of the 2k Design	438	(9)
The One-Half Fraction of the 2k	438	(6)
Smaller Fractions: the 2k-p Fractional Factorial	444	(3)
Summary	447	(1)
Exercises	448	(7)
Simple Linear Regression and Correlation	455	(32)
Simple Linear Regression	456	(5)
Hypothesis Testing in Simple Linear Regression	461	(4)
Interval Estimation in Simple Linear Regression	465	(2)
Prediction of New Observations	467	(2)
Measuring the Adequacy of the Regression Model	469	(6)
Residual Analysis	469	(1)
The Lack-of-Fit Test	470	(4)
The Coefficient of Determination	474	(1)
Transformation to a Straight Line	475	(1)
Correlation	476	(4)
Summary	480	(1)
Exercises	480	(7)
Multiple Regression	487	(72)
Multiple Regression Models	487	(1)
Estimation of the Parameters	488	(8)
Confidence Intervals in Multiple Linear Regression	496	(2)
Prediction of New Observations	498	(1)
Hypothesis Testing in Multiple Linear Regression	499	(6)
Test for Significance of Regression	499	(3)
Tests on Individual Regression Coefficients	502	(3)
Measures of Model Adequacy	505	(6)
The Coefficient of Multiple Determination	505	(1)
Residual Analysis	506	(2)
Testing Lack of Fit Using Near Neighbors	508	(3)
Polynomial Regression	511	(3)
Indicator Variables	514	(3)
The Correlation Matrix	517	(4)
Problems in Multiple Regression	521	(11)
Multicollinearity	521	(6)
Influential Observations in Regression	527	(2)
Autocorrelation	529	(3)
Selection of Variables in Multiple Regression	532	(11)
The Model-Building Problem	532	(1)
Computational Procedures for Variable Selection	532	(11)
Sample Computer Output	543	(9)
Summary	552	(1)
Exercises	552	(7)
Nonparametric Statistics	559	(20)
Introduction	559	(1)
The Sign Test	560	(5)
A Description of the Sign Test	560	(3)
The Sign Test for Paired Samples	563	(1)
Type II Error (β) for the Sign Test	563	(2)
Comparison of the Sign Test and the t-Test	565	(1)
The Wilcoxon Signed Rank Test	565	(4)
A Description of the Test	566	(1)
A Large-Sample Approximation	567	(1)
Paired Observations	567	(1)
Comparison with the t-Test	568	(1)
The Wilcoxon Rank-Sum Test	569	(2)
Description of the Test	569	(2)
A Large-Sample Approximation	571	(1)
Comparison with the t-Test	571	(1)
Nonparametric Methods in the Analysis of Variables	571	(4)
The Kruskal-Wallis Test	571	(3)
The Rank Transformation	574	(1)
Summary	575	(1)
Exercises	575	(4)
Statistical Quality Control and Reliability Engineering	579	(51)
Quality Improvement and Statistics	579	(1)
Statistical Quality Control	580	(1)
Statistical Process Control	581	(21)
Introduction to Control Charts	582	(1)
Control Charts for Measurements	583	(9)
Control Charts for Attributes	592	(6)
Other SPC Problem Solving Tools	598	(3)
Implementing SPC	601	(1)
Statistically-Based Sampling Plans	602	(5)
Tolerance Limits	607	(1)
Reliability Engineering	608	(15)
Basic Reliability Definitions	608	(3)
The Exponential Time to Failure Model	611	(2)
Simple Serial Systems	613	(2)
Simple Active Redundancy	615	(2)
Standby Redundancy	617	(2)
Life Testing	619	(1)
Reliability Estimation with a Known Time to Failure Distribution	620	(1)
Estimation with the Exponential Time to Failure Distribution	620	(3)
Demonstration and Acceptance Testing	623	(1)
Summary	623	(1)
Exercises	623	(7)
Stochastic Processes and Queueing	630	(24)
Introduction	630	(1)
Discrete-Time Markov Chains	630	(3)
Classification of States and Chains	633	(3)
Continuous-Time Markov Chains	636	(4)
The Birth-Death Process in Queueing	640	(3)
Considerations in Queueing Models	643	(1)
Basic Single Server Model with Constant Rates	644	(3)
Single Server with Limited Queue Length	647	(1)
Multiple Servers with an Unlimited Queue	648	(2)
Other Queueing Models	650	(1)
Summary	650	(1)
Exercises	651	(3)
Statistical Decision Theory	654	(17)
The Structure and Concept of Decisions	654	(6)
Bayesian Inference	660	(2)
Applications to Estimation	662	(4)
Applications to Hypothesis Testing	666	(2)
Summary	668	(1)
Exercises	668	(3)
Appendix	671	(41)
Table I Cumulative Poisson Distribution	672	(3)
Table II Cumulative Standard Normal Distribution	675	(2)
Table III Percentage Points of the X2 Distribution	677	(2)
Table IV Percentage Points of the t Distribution	679	(1)
Table V Percentage Points of the F Distribution	680	(5)
Chart VI Operating Characteristic Curves	685	(9)
Chart VII Operating Characteristic Curves for the Fixed Effects Model Analysis of Variance	694	(4)
Chart VIII Operating Characteristic Curves for the Random Effects Model Analysis of Variance	698	(4)
Table IX Critical Values for the Wilcoxon Two-sample Test	702	(2)
Table X Critical Values for the Sign Test	704	(1)
Table XI Critical Values for the Wilcoxon Signed-rank Test	705	(1)
Table XII Significant Ranges for Duncan's Multiple Range Test	706	(2)
Table XIII Factors for Quality Control Charts	708	(1)
Table XIV Factors for Two-sided Tolerance Limits	709	(2)
Table XV Random Numbers	711	(1)
References	712	(3)
Answers to Selected Exercises	715	(12)
Index	727