About the Authors |
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xi | |
Preface |
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xiii | |
Acknowledgments |
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xvii | |
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1 Introduction and Genesis |
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1 | (22) |
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1 | (2) |
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1.2 History and Background of Control Charts |
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3 | (2) |
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1.3 What Is Quality and Quality Improvement? |
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5 | (4) |
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Types of Quality-Related Costs |
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7 | (2) |
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9 | (10) |
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1.4.1 Descriptive Statistics |
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9 | (5) |
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1.4.2 Probability Distributions |
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14 | (1) |
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Continuous Probability Distributions |
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14 | (4) |
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Discrete Probability Distributions |
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18 | (1) |
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1.5 Types of Control Charts |
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19 | (2) |
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1.5.1 Attribute Control Charts |
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19 | (1) |
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1.5.2 Variable Control Charts |
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20 | (1) |
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1.6 Meaning of Process Control |
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21 | (2) |
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22 | (1) |
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2 Shewhart Type Control Charts for Attributes |
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23 | (34) |
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2.1 Proportion and Number of Nonconforming Charts |
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24 | (8) |
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2.1.1 Proportion of Nonconforming Chart (p-Chart) |
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25 | (3) |
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28 | (1) |
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29 | (1) |
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2.1.2 Number of Nonconforming Chart (np-Chart) |
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30 | (1) |
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2.1.3 Performance Evaluation Measures |
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30 | (2) |
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2.2 Number of Nonconformities and Average Nonconformity Charts |
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32 | (8) |
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2.2.1 Number of Nonconformities (c-) Chart |
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33 | (1) |
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2.2.2 Average Nonconformities (u-) Chart |
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34 | (4) |
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2.2.3 The Performance Evaluation Measure |
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38 | (1) |
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Dealing with Low Defect Levels |
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39 | (1) |
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2.3 Control Charts for Over-Dispersed Data |
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40 | (4) |
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2.3.1 Dispersion of Counts Data |
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40 | (1) |
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2.3.2 g-Chart and h-Chart |
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40 | (4) |
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2.4 Generalized and Flexible Control Charts for Dispersed Data |
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44 | (8) |
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2.4.1 The gc- and the gu-Charts |
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45 | (1) |
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2.4.2 Control Chart Based on Generalized Poisson Distribution |
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46 | (1) |
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47 | (1) |
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A Geometric Chart to Monitor Parameter θ |
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48 | (1) |
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2.4.3 The Q- and the T-Charts |
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49 | (3) |
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52 | (1) |
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2.5 Other Recent Developments |
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52 | (5) |
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54 | (3) |
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3 Variable Control Charts |
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57 | (34) |
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57 | (1) |
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58 | (14) |
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3.2.1 Construction of X and R Charts |
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59 | (3) |
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3.2.2 Phase II Control Limits |
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62 | (1) |
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3.2.3 Construction of X Chart for Burr Distribution Under the Repetitive Sampling Scheme |
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63 | (9) |
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72 | (1) |
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3.4 Construction of S-Chart |
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72 | (3) |
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3.4.1 Construction of X Chart |
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74 | (1) |
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3.4.2 Normal and Non-normal Distributions for X and S-Charts |
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75 | (1) |
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75 | (16) |
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3.5.1 Construction of S2-Chart |
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76 | (1) |
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3.5.2 The Construction of Variance Chart for Neutrosophic Statistics |
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77 | (4) |
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3.5.3 The Construction of Variance Chart for Repetitive Sampling |
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81 | (6) |
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87 | (4) |
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4 Control Chart for Multiple Dependent State Sampling |
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91 | (30) |
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91 | (1) |
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4.2 Attribute Charts Using MDS Sampling |
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91 | (7) |
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4.2.1 The np-Control Chart |
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92 | (6) |
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4.3 Conway--Maxwell--Poisson (COM-Poisson) Distribution |
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98 | (8) |
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106 | (1) |
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4.5 Control Charts for Non-normal Distributions |
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107 | (2) |
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4.6 Control Charts for Exponential Distribution |
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109 | (2) |
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4.7 Control Charts for Gamma Distribution |
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111 | (10) |
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118 | (3) |
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5 EWMA Control Charts Using Repetitive Group Sampling Scheme |
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121 | (40) |
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5.1 Concept of Exponentially Weighted Moving Average (EWMA) Methodology |
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121 | (5) |
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5.2 Attraction of EWMA Methodology in Manufacturing Scenario |
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126 | (1) |
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5.3 Development of EWMA Control Chart for Monitoring Averages |
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127 | (1) |
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5.4 Development of EWMA Control Chart for Repetitive Sampling Scheme |
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127 | (1) |
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5.5 EWMA Control Chart for Repetitive Sampling Using Mean Deviation |
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128 | (11) |
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5.6 EWMA Control Chart for Sign Statistic Using the Repetitive Sampling Scheme |
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139 | (8) |
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5.7 Designing of a Hybrid EWMA (HEWMA) Control Chart Using Repetitive Sampling |
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147 | (14) |
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154 | (7) |
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6 Sampling Schemes for Developing Control Charts |
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161 | (30) |
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6.1 Single Sampling Scheme |
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161 | (1) |
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6.2 Double Sampling Scheme |
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162 | (3) |
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6.3 Repetitive Sampling Scheme |
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165 | (11) |
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6.3.1 When a Shift of μ1 = μ + kσ Occurs in the Process |
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169 | (7) |
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6.4 Mixed Sampling Scheme |
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176 | (4) |
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6.4.1 Mixed Control Chart Using Exponentially Weighted Moving Average (EWMA) Statistics |
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179 | (1) |
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6.5 Mixed Control Chart Using Process Capability Index |
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180 | (11) |
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6.5.1 Analysis Through Simulation Approach |
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187 | (1) |
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187 | (4) |
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7 Memory-Type Control Charts for Attributes |
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191 | (40) |
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7.1 Exponentially Weighted Moving Average (EWMA) Control Charts for Attributes |
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191 | (18) |
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7.1.1 Binomial EWMA Charts |
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192 | (2) |
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7.1.2 Poisson EWMA (PEWMA) Chart |
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194 | (2) |
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Performance Evaluation Measure |
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196 | (1) |
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Calculation of ARLs Using the Markov Chain Approach |
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196 | (6) |
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202 | (1) |
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202 | (2) |
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Conway--Maxwell--Poisson (COM--Poisson) EWMA Chart |
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204 | (5) |
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7.2 CUSUM Control Charts for Attributes |
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209 | (11) |
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7.2.1 Binomial CUSUM Chart |
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210 | (5) |
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7.2.2 Poisson CUSUM Chart |
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215 | (2) |
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7.2.3 Geometric CUSUM Chart |
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217 | (2) |
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7.2.4 COM--Poisson CUSUM Chart |
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219 | (1) |
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219 | (1) |
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7.3 Moving Average (MA) Control Charts for Attributes |
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220 | (11) |
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221 | (2) |
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223 | (2) |
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225 | (1) |
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226 | (5) |
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8 Multivariate Control Charts for Attributes |
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231 | (20) |
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8.1 Multivariate Shewhart-Type Charts |
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231 | (12) |
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8.1.1 Multivariate Binomial Chart |
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231 | (2) |
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233 | (1) |
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8.1.2 Multivariate Poisson (MP) Chart |
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234 | (5) |
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8.1.3 Multivariate Conway--Maxwell--Poisson (COM--Poisson) Chart |
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239 | (4) |
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8.2 Multivariate Memory-Type Control Charts |
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243 | (3) |
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8.2.1 Multivariate EWMA Charts for Binomial Process |
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243 | (1) |
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244 | (1) |
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8.2.2 Multivariate EWMA Charts for Poisson Process |
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245 | (1) |
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8.3 Multivariate Cumulative Sum (CUSUM) Schemes |
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246 | (5) |
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8.3.1 Multivariate CUSUM Chart for Poisson Data |
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247 | (1) |
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248 | (3) |
Appendix A Areas of the Cumulative Standard Normal Distribution |
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251 | (2) |
Appendix B Factors for Constructing Variable Control Charts |
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253 | (2) |
Index |
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255 | |