The Desk Reference of Statistical Quality Methods

by Crossley, Mark L.

• ISBN13: 9780873894722
• ISBN10: 0873894723
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: Asq Pr

Summary

This reference guide illustrates how to execute forty essential statistical improvement methods frequently used in the quality sciences, such as acceptance sampling for attributes, discrete distributions, multivariate charts, and Weibull analysis. Arranged alphabetically, each entry provides computational steps, application comments, and a brief presentation on how to use the tool or technique. An appendix contains distribution and value tables.

Author Biography

Mark L. Crossley holds a BS in Chemistry and Mathematics from the University of North Carolina and a MS in Quality Assurance from California State University. He is the president of Quality Management Associates, Inc., a consulting firm in Salisbury, North Carolina, specializing in the use of statistical methods for quality improvement, and he is a nationally recognized instructor for the American Society for Quality.

Table of Contents

Acceptance Control Chart	1	(7)
Modified Control Limits	1	(3)
Acceptance Control Charts	4	(1)
Bibliography	5	(2)
Acceptance Sampling for Attributes	7	(18)
Operating Characteristic (OC) Curve	8	(3)
MIL-STD-105E (ANSI/ASZC Z1.4)	11	(1)
Format for Use and Discussion	12	(3)
Continuous Sampling Plans (CSPs)	15	(1)
CSP-1 Plan	16	(5)
CSP-2 Plan	21	(3)
A Method for Selecting the AQL	24	(1)
Bibliography	24	(1)
Acceptance Sampling for Variables	25	(8)
Sampling Plans Based on Specified AQL, RQL, α Risk, and β Risk	27	(2)
Sampling Plans Based on Range R	29	(2)
Bibliography	31	(2)
Average/Range Control Chart	33	(8)
Bibliography	40	(1)
Average/Standard Deviation Control Chart	41	(6)
Bibliography	45	(2)
Chart Resolution	47	(12)
Variable Control Charts: Individuals	47	(4)
Variables Control Charts: Averages	51	(2)
Attribute Chart: P Charts	53	(1)
For P ≤ 0.10, Poisson Distribution	54	(1)
For P ≥ 0.10, Normal Distribution	55	(2)
Bibliography	57	(2)
Chi-Square Contingency and Goodness-of-Fit	59	(8)
Chi-Square Contigency Tables	59	(3)
Goodness-of-Fit	62	(1)
Goodness-of-Fit to Poisson Distribution	62	(3)
Goodness-of-Fit to Uniform Distribution	65	(1)
Goodness-of-Fit to Specified Distribution	65	(1)
Bibliography	66	(1)
Chi-Square Control Chart	67	(8)
Bibliography	74	(1)
Confidence Interval for the Average	75	(6)
Confidence Interval, n ≤ 30	76	(1)
Confidence Interval, n > 30	77	(1)
Confidence Limit, n > 30, Single-Sided Limit	78	(1)
Confidence Limit, n ≤ 30, Single-Sided Limit	79	(1)
Bibliography	80	(1)
Confidence Interval for Proportions	81	(10)
Bibliography	89	(2)
Confidence Interval for Standard Deviation	91	(4)
Testing Homogeneity of Variances	93	(1)
Bibliography	94	(1)
Defects/Unit Control Charts	95	(8)
Case Study	97	(5)
Bibliography	102	(1)
Demerit/Unit Chart	103	(8)
Bibliography	110	(1)
Descriptive Statistics	111	(6)
Bibliography	115	(2)
Designed Experiments	117	(38)
Normal Probability Plot	124	(2)
Visualization of Two-Factor Interactions	126	(5)
Fractional Factorial Experiments	131	(10)
Calculation of Main Effects	135	(2)
Two-Factor Interactions	137	(3)
Statistical Significance Based on t Test	140	(1)
Variation Reduction	141	(3)
Response Modeling	144	(3)
An Alternative Method for Evaluating Effects Based on Standard Deviation	147	(2)
Plackett-Burman Screening Designs	149	(5)
Achieving tghe Final Objective	154	(1)
Bibliography	154	(1)
Discrete Distributions	155	(10)
Hypergeometric Distribution	155	(1)
Binomial Distribution	156	(2)
Poisson Distribution	158	(2)
The Normal Distribution as an Approximation of the Binomial	160	(2)
Pascal Distribution	162	(1)
Cumulative Distribution Tables	163	(1)
Bibliography	164	(1)
Evolutionary Operation, EVOP	165	(8)
Bibliography	171	(2)
Exponentially Weighted Moving Average, EWMA	173	(8)
Bibliography	179	(2)
F-Test	181	(4)
Single-Sided vs. Double-Sided Tests	182	(3)
Histograms	185	(6)
Example of a Frequency Histogram	185	(5)
Bibliography	190	(1)
Hypothesis Testing	191	(16)
Formulation of the Hypothesis	191	(1)
Conclusions and Consequences for a Hypothesis Test	192	(1)
Selecting a Test Statistic and Rejection Criteria	193	(13)
Hypothesis about the Variance	205	(1)
Bibliography	206	(1)
Individual-Median/Range Chart	207	(8)
Bibliography	214	(1)
Individual/Moving Range Chart	215	(8)
Bibliography	221	(2)
Measurement Error Assessment	223	(14)
Variables Measurements Error	223	(11)
Terms and Concepts	223	(5)
Combined (Gage) Repeatability and Reproducibility Error (GR & R)	228	(1)
Consequences of Measurement Error	228	(1)
Confidence Interval for Repeatability, Reproducibility and Combined R&R	229	(1)
Confidence Interval for Repeatability, EV	230	(2)
Confidence Interval for Reproducibility, AV	232	(1)
Confidence Interval for Combined Repeatability and Reproducibility, R&R	233	(1)
Attribute and Visual Inspection Error	234	(2)
Bibliography	236	(1)
Multivariate Charts	237	(18)
T2 Charts	237	(11)
The T2 Equation	240	(1)
Calculation of Individual and Average Covariance	241	(1)
Calculation of Individual T2 Values	242	(2)
Calculation of the Control Limits	244	(4)
Standardized Euclidean Distance, DE	248	(6)
Plotting Statistic	248	(1)
Control Limits and Center Line	249	(5)
Bibliography	254	(1)
Nonnormal Distribution Cpk	255	(14)
Cpk Adjusted for SK and KU Using Normal Probability Plots	266	(1)
Bibliography	267	(2)
Nonparametric Statistics	269	(6)
Comparing Two Averages: Wilcoxon-Mann-Whitney Test	269	(3)
Comparing More Than Two Averages: The Kruskall-Wallis Rank Sum Test	272	(1)
Bibliography	273	(2)
Normal Distribution	275	(8)
Central Limit Theorem	280	(3)
Pareto Analysis	283	(6)
Bibliography	287	(2)
Pre-Control	289	(6)
Description	289	(2)
A Comparison of Pre-Control and SPC	291	(3)
Bibliography	294	(1)
Process Capability Indices	295	(12)
Cpk	295	(2)
Confidence Interval for Cpk	297	(3)
Cr and Cp Indices	300	(1)
Confidence INterval for Cp and Cr	301	(1)
Cpm Index	302	(5)
Bibliography	306	(1)
p Chart	307	(18)
Exponential Model	318	(3)
Data Transformation	321	(2)
Bibliography	323	(2)
Regression and Correlation	325	(8)
Linear Least Square Fit	325	(1)
Confidence for the Estimated Expected Value	326	(1)
Assessing the Model: Drawing Inferences about β1	327	(4)
Testing β1	328	(1)
Measuring the Strength of the Linear Relationship	329	(1)
Testing the Coefficient of Correlation	329	(2)
Bibliography	331	(2)
Reliability	333	(18)
Exponential Distribution	337	(12)
Determination of Failure Rate, λ	337	(3)
Confidence Internal for λ from Time-Censored (Type I) Data	340	(1)
Confidence Interval for λ from Failure-Censored (Type II) Data	341	(2)
Success Run Theorum	343	(1)
Reliability Modeling	344	(1)
Series Systems	344	(1)
Parallel Systems	345	(1)
Complex Systems	346	(1)
Shared-Load Parallel Systems	347	(1)
Standby Parallel Systems	348	(1)
Bibliography	349	(2)
Sequential Simplex Optimization	351	(10)
Theoretical Optimum	351	(1)
Strategies for Optimization	351	(9)
Shotgun Approach	352	(1)
Approach of a Single Factor at a Time	352	(1)
Basic Simplex Algorithm	353	(1)
Simplex Calculations	354	(6)
Bibliography	360	(1)
Short-Run Attribute Charts	361	(8)
Short-Run p Chart	366	(2)
Bibliography	368	(1)
Short-Run Average/Range Chart	369	(12)
For the Short-Run Average Chart	369	(1)
For the Short-Run Range Chart	370	(1)
For X	371	(1)
For R	372	(8)
Bibliography	380	(1)
Short-Run Individual/Moving Range Chart	381	(10)
Derivation of the Plotting Characteristic for the Location Statistic	381	(1)
Derivation of the Plotting Characteristic for the Variation Statistic	381	(2)
Selecting a Value for XT and MRT	383	(6)
Bibliography	389	(2)
SPC Chart Interpretation	391	(6)
Bibliography	396	(1)
Taguchi Loss Function	397	(6)
Losses with Nonsymmetric Specifications	401	(1)
Bibliography	402	(1)
Testing for a Normal Distribution	403	(14)
Normal Probability Plot	403	(8)
Normal Probability Plots Using Transformed Data	409	(2)
Chi-Square Goodness-of-Fit Test	411	(2)
Skewness and Kurtosis	413	(3)
Bibliography	416	(1)
Weibull Analysis	417	(8)
Probability Plotting	418	(3)
Plotting Data Using Weibull Paper	421	(3)
Estimation of Minimum Life Characteristic	423	(1)
Bibliography	424	(1)
Zone Charts	425	(10)
Construction of Zone Charts	426	(7)
Collect Historical Data	428	(5)
Bibliography	433	(2)
Appendix A: Tables	435	(10)
Standard Normal Distribution	435	(1)
Poisson Unity Values, Pa	436	(1)
Poisson Unity Values, RQL/AQL	437	(1)
t-Distribution	438	(1)
Chi-Square Distribution	439	(1)
Control Chart Factors I	440	(1)
Control Chart Factors II	440	(1)
Critical Values of Smaller Rank Sum for Wilcoxon-Mann-Whitney Test	441	(1)
Values of i and f for CSP-1 Plans	442	(1)
Cumulative Poisson Distribution	443	(2)
F-table	445