| Dedication | p. v |
| Preface | p. xv |
| Acknowledgments | p. xix |
| Reliability and Six Sigma-Introduction | |
| Introduction | p. 1 |
| What Is Six Sigma? | p. 3 |
| What Is New In Six Sigma? | p. 6 |
| Quality and Six Sigma Level | p. 8 |
| Reliability and Six Sigma | p. 9 |
| Reliability and Six Sigma: Probabilistic Models | |
| Introduction | p. 11 |
| Probability Terminology | p. 12 |
| Elementary Theory of Probability | p. 14 |
| Axims of probability | p. 14 |
| Rules of probability | p. 15 |
| Joint event | p. 16 |
| Conditional probability | p. 16 |
| Probability Distribution | p. 17 |
| Random Variable | p. 18 |
| Types of random variables | p. 20 |
| The Probability Distribution of a Random Variable | p. 20 |
| Functional method | p. 21 |
| Parametric method | p. 25 |
| Measures of central tendency | p. 26 |
| Measures of dispersion | p. 27 |
| Variability | p. 29 |
| Discrete Probability Distributions | p. 29 |
| Bernoulli trials | p. 30 |
| Binomial distribution | p. 31 |
| Poisson distribution | p. 33 |
| Continuous Probability Distributions | p. 35 |
| Exponential distribution | p. 36 |
| Memory less property | p. 37 |
| Normal distribution | p. 38 |
| Central limit theorem | p. 42 |
| Lognoral distribution | p. 43 |
| Weibull distribution | p. 44 |
| Stochastic Processes | p. 46 |
| Markov Processes | p. 47 |
| Non-Homogeneous Poisson Process | p. 51 |
| Renewal Process | p. 52 |
| Renewal Function | p. 53 |
| Elementary Renewal Theorem | p. 55 |
| Reliability and Six Sigma Measures | |
| Introduction | p. 57 |
| Six Sigma Measures | p. 57 |
| Yield | p. 58 |
| Defects Per Million Opportunities (DPMO) | p. 59 |
| Sigma Quality Level | p. 60 |
| Conversion of Yield to Sigma Level | p. 60 |
| Conversion of DPMO to Sigma Level | p. 62 |
| Reliability Measures | p. 63 |
| Failure Function | p. 65 |
| Failure function of systems under multiple failure mechanisms | p. 70 |
| Reliability Function | p. 72 |
| Reliability function of items under multiple failure mechanisms | p. 76 |
| Reliability function and Six Sigma | p. 77 |
| Mission Reliability | p. 78 |
| Hazard Function (Instantaneous Failure Rate) | p. 80 |
| Cumulative hazard function | p. 84 |
| Failure rate | p. 88 |
| Mean Time to Failure | p. 89 |
| MTTF and Sigma level | p. 91 |
| Mean Residual Life | p. 93 |
| Mean (Operating) Time Between Failure | p. 95 |
| Maintenance Free Operating Period (MFOP) | p. 98 |
| Maintenance free operating period survivability | p. 99 |
| Case Study: Engineer Tank Engine (Armoured Vehicle Engine) | p. 101 |
| System Reliability | |
| Introduction | p. 105 |
| Reliability Prediction | p. 106 |
| Duty cycle | p. 107 |
| Cyclic exchange rate | p. 107 |
| Reliability Block Diagram | p. 108 |
| Series System | p. 109 |
| Mean time to failure of a series configuration | p. 113 |
| Sigma level and MTTF[subscript s] | p. 114 |
| Hazard rate (function) of a series system | p. 117 |
| Life Exchange Rate Matrix | p. 118 |
| Conditional Probabilities of Survival | p. 120 |
| Parallel Systems | p. 122 |
| Mean time to failure of a parallel configuration | p. 126 |
| Hazard function for a parallel configuration | p. 128 |
| Series-Parallel Combination Configuration | p. 129 |
| K-out-of-N Systems | p. 131 |
| Mean time to failure for a K-out-of-N System | p. 132 |
| Standby Redundancy | p. 133 |
| Cold standby system with perfect switching | p. 134 |
| Cold standby system with imperfect switching | p. 136 |
| Hot standby system | p. 136 |
| Graceful Degradation | p. 137 |
| Case Study - A Sonar System | p. 138 |
| Design for Reliability and Six Sigma | |
| Introduction | p. 143 |
| Quality Function Deployment | p. 144 |
| Building house of quality matrix | p. 145 |
| Reliability Allocation | p. 152 |
| Mathematical formulation | p. 152 |
| Equal apportionment technique | p. 153 |
| Minimum effort algorithm | p. 154 |
| Apportionment for new units | p. 156 |
| Reliability allocation factors | p. 159 |
| Complexity factor | p. 159 |
| Cost | p. 159 |
| State of the Art | p. 160 |
| Redundancy factor | p. 160 |
| Maintainability factor | p. 161 |
| Duty ratio factor | p. 161 |
| Reliability allocation formula | p. 161 |
| Accelerated Testing | p. 165 |
| Environmental Stress Screening (ESS) | p. 166 |
| ESS in the infant mortality period | p. 166 |
| Burn-in | p. 167 |
| ESS Tests | p. 168 |
| Quantitative accelerated life tests | p. 171 |
| Usage rate acceleration | p. 171 |
| Overstress acceleration | p. 171 |
| Highly accelerated life testing (HALT) | p. 173 |
| Safety and Hazard Analysis | p. 174 |
| Fault tree analysis (FTA) | p. 174 |
| Construction of FTA | p. 175 |
| Failure Mode Effects and Criticality Analysis | p. 181 |
| Failure mode effects analysis (FMEA) | p. 182 |
| Criticality analysis | p. 183 |
| Risk analysis through FMEA | p. 185 |
| Functional FMEA and Hardware FMEA | p. 187 |
| Advantages of FMECA | p. 188 |
| FMECA and FTA in Design | p. 188 |
| Hazard Analysis | p. 188 |
| Hazard analysis methodology | p. 189 |
| Failure Reporting Analysis and Corrective Action System (FRACAS) | p. 192 |
| Case Study - Aircraft Emergency Stopping System | p. 194 |
| Functional FMEA | p. 195 |
| Hardware FMEA | p. 196 |
| In-Service Reliability | |
| Introduction | p. 207 |
| Definition of Inservice Reliability | p. 209 |
| Inservice Reliability Data | p. 211 |
| Inservice Mtbf | p. 217 |
| Parts Life Tracking | p. 223 |
| Safety Critical Parts | p. 226 |
| Usage Monitoring | p. 228 |
| Time to Failure Analysis | p. 233 |
| Estimating Mttf from the Test Sample | p. 234 |
| Aggregated Cumulative Hazard (ACH) | p. 236 |
| Prognostics | p. 237 |
| Relevant Condition Parameters RCP | p. 238 |
| Relevant Condition Indicators RCI | p. 243 |
| Case Study: Aircraft Engine Components | p. 244 |
| The data | p. 245 |
| Analysis of failures generating unscheduled maintenance | p. 247 |
| No fault found (NFF) | p. 249 |
| Reliability and Six Sigma Estimation | |
| Introduction | p. 253 |
| Reliability Estimation and Failure Data | p. 254 |
| Estimation of Parameters: Empirical Approach | p. 255 |
| Estimation of parameters: Complete Ungrouped Data | p. 255 |
| Confidence Interval | p. 256 |
| Analysis of grouped data | p. 260 |
| Analysis of censored data | p. 263 |
| Regression | p. 264 |
| Correlation co-efficient | p. 267 |
| Linear regression for exponential distribution | p. 267 |
| Linear regression for Weibull distribution | p. 269 |
| Linear regression for normal distribution | p. 271 |
| Maximum Likelihood Estimation (MLE) | p. 272 |
| Complete and uncensored data | p. 273 |
| Maximum likelihood estimator of exponential distribution | p. 274 |
| Maximum likelihood estimator for Weibull distribution | p. 276 |
| Maximum likelihood estimator for normal distribution | p. 279 |
| Case Study: Engineer Tank | p. 281 |
| Software Reliability | |
| Introduction | p. 289 |
| Software Reliability Metrics | p. 291 |
| Requirement reliability metrics | p. 291 |
| Design and Code reliability metrics | p. 292 |
| Testing reliability metrics | p. 293 |
| Software Reliability Models | p. 293 |
| Software Reliability Prediction Models | p. 295 |
| In-house historical data collection model | p. 295 |
| Musa's execution time model | p. 295 |
| Putnam's model | p. 297 |
| Software Reliability Estimation Model | p. 299 |
| Exponential model | p. 299 |
| Generalized exponential model | p. 300 |
| Goel-Okumoto Model | p. 301 |
| Jelinski-Moranda Model | p. 302 |
| Software Testing | p. 303 |
| Software Risk Analysis Using Fmea | p. 305 |
| Fault Tolerant Software | p. 307 |
| Recovery blocks | p. 307 |
| N-version programming | p. 309 |
| Case Study: Ariane 5 | p. 309 |
| Availability and Six Sigma | |
| Introduction | p. 313 |
| Point Availability | p. 314 |
| Markov model for point availability | p. 314 |
| Average availability | p. 317 |
| Inherent availability | p. 317 |
| Availability, DPMO and Sigma level | p. 318 |
| System Availability | p. 320 |
| Achieved Availability | p. 323 |
| Operational Availability | p. 325 |
| Reliability and Six Sigma Management | |
| Introduction | p. 329 |
| Reliability Management | p. 330 |
| Reliability demonstration | p. 330 |
| Two-Sided Reliability Demonstration Test | p. 331 |
| Demonstration of constant failure rate or MTBF | p. 333 |
| Reliability Growth Program | p. 334 |
| Duane Model | p. 335 |
| Life Cycle Cost and Total Cost of Ownership | p. 338 |
| Total Cost of Ownership Model | p. 339 |
| Mathematical models for estimation of total cost of ownership | p. 340 |
| Estimation of operating cost | p. 340 |
| Estimation of Maintenance Cost | p. 342 |
| Estimation of logistic support cost | p. 343 |
| Total cost of ownership | p. 343 |
| Total Cost of Ownership - Case Study on Freight Cars on an Asian Railway System | p. 344 |
| Reliability and maintainability of freight car | p. 344 |
| Operational availability of freight car | p. 346 |
| Operating cost of freight car | p. 346 |
| Maintenance cost for freight car | p. 347 |
| Logistic support cost | p. 348 |
| Total cost of ownership of freight car | p. 348 |
| Impact of Sigma Level on Total Cost of Ownership | p. 349 |
| Six Sigma Project Management | p. 350 |
| Analytic hierarchy process (AHP) for Six Sigma project selection | p. 351 |
| Dmaic Cycle | p. 355 |
| Define phase | p. 356 |
| Measure Phase | p. 357 |
| Analyze Phase | p. 358 |
| Improve phase | p. 359 |
| Control phase | p. 359 |
| Case Study: Dmaic Methodology | p. 360 |
| PowerPlus battery manufacturing company | p. 360 |
| Define stage | p. 361 |
| Measure | p. 361 |
| Analyze | p. 361 |
| Improve Stage | p. 363 |
| Control | p. 363 |
| Design for Six Sigma (DFSS) | p. 363 |
| Six Sigma Black Belt and Green Belt | p. 364 |
| Appendix | p. 365 |
| References | p. 371 |
| Index | p. 381 |
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