Quality and Reliability Methods - SAS

More documents

Recommendations

Info

348 Reliability Growth Chapter 18 References For example, consider the cumulative events function. The cumulative number of events at time t since testing initiation is given by Nt () = λt β . It follows that log(N(t)) = log(λ) +βlog(t). The parameters λ and β in log(N(t)) are replaced by their MLEs to estimate log(N(t)). The delta method is applied to this expression to obtain an estimate of its variance. This estimate is used to construct a 95% Wald-based confidence interval. The resulting confidence limits are then transformed using the exponential function to give confidence limits for the estimated cumulative number of events at time t. Statistical Details for the Piecewise Weibull NHPP Change Point Detection Report The change point is estimated as follows: • Using consecutive event times, disjoint intervals are defined. • Each point within such an interval can be considered to be a change point defining a piecewise Weibull NHPP model with two phases. So long as the two phases defined by that point each consist of at least two events, the algorithm can compute MLEs for the parameters of that model. The loglikelihood for that model can also be computed. • Within each of the disjoint intervals, a constrained optimization routine is used to find a local optimum for the loglikelihood function. • These local optima are compared, and the point corresponding to the largest is chosen as the estimated change point. Note that this procedure differs from the grid-based approach described in Guo et al, 2010. References Crow, L. H., (1975), “Reliability Analysis for Complex, Repairable Systems,” AMSAA Technical Report No. 138, Dec. 1975, U.S. Army Materiel Systems Analysis Activity, Aberdeen Proving Ground, MD. Crow, L. H., (1982), “Confidence Interval Procedures for the Weibull Process with Applications to Reliability Growth,” Technometrics, Feb. 1982, 24:1, 67-72. Guo, H., Mettas, A., Sarakakis, G., and Niu, P. (2010), “Piecewise NHPP Models with Maximum Likelihood Estimation for Repairable Systems,” Reliability and Maintainability Symposium (RAMS), 25-28 Jan. 2010 Proceedings, San Jose, CA. Lee, L. and Lee S. K., (1978), “Some Results on Inference for the Weibull Process,” Technometrics, Feb. 1978, 20:1, 41-45. Meeker, W. Q. and Escobar, L. A., (1998), Statistical Methods for Reliability Data, John Wiley & Sons. MIL-HDBK-00189 (1981), Military Handbook: Reliability Growth Management, U.S. Department of Defense, Washington DC. Rigdon, S. E. and Basu, A. P., (2000), Statistical Methods for the Reliability of Repairable Systems, John Wiley & Sons.
Chapter 19 Reliability and Survival Analysis Univariate Survival Survival data contain duration times until the occurrence of a specific event and are sometimes referred to as event-time response data. The event is usually failure, such as the failure of an engine or death of a patient. If the event does not occur before the end of a study for an observation, the observation is said to be censored. The Reliability and Survival menu includes several types of survival analysis. This chapter focuses on univariate survival, the Survival item on the Reliability and Survival menu. Survival calculates estimates of survival functions using the product-limit (Kaplan-Meier) method for one or more groups of either right-censored or complete data. (Complete data have no censored values.) This platform gives an overlay plot of the estimated survival function for each group and for the whole sample. JMP also computes the log rank and Wilcoxon statistics to test homogeneity between groups. Diagnostic plots and fitting options are available for exponential, Weibull, and lognormal survival distributions. An analysis of competing causes for the Weibull model is also available. Interval censoring is supported by Turnbull estimates. Life Distribution, Fit Life by X, and Recurrence Analysis are discussed in the following chapters: “Lifetime Distribution” on page 207, the “Lifetime Distribution II” on page 237, and “Recurrence Analysis” on page 261. The “Reliability and Survival Analysis II” chapter on page 371 gives details of both Fit Parametric Survival and Fit Proportional Hazards.
Page 1 and 2:
Version 10 Quality and Reliability
Page 3:
INDIRECT OR CONSEQUENTIAL DAMAGES O
Page 6 and 7:
6 Nelson Rules . . . . . . . . . .
Page 8 and 9:
8 8 Assess Measurement Systems The
Page 10 and 11:
10 Other Menu Options . . . . . . .
Page 12 and 13:
12 Reliability Forecast Platform Op
Page 15 and 16:
Chapter 1 Learn about JMP Documenta
Page 17 and 18:
Chapter 1 Learn about JMP 17 Book C
Page 19 and 20:
Chapter 1 Learn about JMP 19 Book C
Page 21 and 22:
Chapter 1 Learn about JMP 21 Additi
Page 23 and 24:
Chapter 1 Learn about JMP 23 Additi
Page 25 and 26:
Chapter 2 Statistical Control Chart
Page 27 and 28:
Page 29 and 30:
Page 31 and 32:
Page 33 and 34:
Page 35 and 36:
Page 37 and 38:
Page 39 and 40:
Page 41 and 42:
Page 43 and 44:
Page 45 and 46:
Page 47 and 48:
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
Chapter 3 Introduction to Control C
Page 55 and 56:
Page 57 and 58:
Page 59 and 60:
Chapter 4 Interactive Control Chart
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Chapter 5 Shewhart Control Charts V
Page 71 and 72:
Chapter 5 Shewhart Control Charts 7
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
Page 79 and 80:
Page 81 and 82:
Page 83 and 84:
Page 85 and 86:
Page 87 and 88:
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Chapter 6 Cumulative Sum Control Ch
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Chapter 7 Multivariate Control Char
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
Page 115 and 116:
Page 117 and 118:
Page 119 and 120:
Page 121 and 122:
Chapter 8 Assess Measurement System
Page 123 and 124:
Page 125 and 126:
Page 127 and 128:
Page 129 and 130:
Page 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
Page 141 and 142:
Chapter 9 Capability Analyses The C
Page 143 and 144:
Chapter 9 Capability Analyses 143 L
Page 145 and 146:
Chapter 9 Capability Analyses 145 C
Page 147 and 148:
Page 149 and 150:
Page 151 and 152:
Chapter 10 Variability Charts Varia
Page 153 and 154:
Chapter 10 Variability Charts 153 V
Page 155 and 156:
Page 157 and 158:
Page 159 and 160:
Page 161 and 162:
Page 163 and 164:
Chapter 10 Variability Charts 163 R
Page 165 and 166:
Page 167 and 168:
Page 169 and 170:
Chapter 10 Variability Charts 169 D
Page 171 and 172:
Chapter 10 Variability Charts 171 A
Page 173 and 174:
Page 175 and 176:
Page 177 and 178:
Page 179 and 180:
Chapter 11 Pareto Plots The Pareto
Page 181 and 182:
Chapter 11 Pareto Plots 181 Pareto
Page 183 and 184:
Page 185 and 186:
Page 187 and 188:
Chapter 11 Pareto Plots 187 Launch
Page 189 and 190:
Chapter 11 Pareto Plots 189 One-Way
Page 191 and 192:
Chapter 11 Pareto Plots 191 Two-Way
Page 193 and 194:
Chapter 11 Pareto Plots 193 Defect
Page 195 and 196:
Chapter 11 Pareto Plots 195 Defect
Page 197 and 198:
Chapter 12 Ishikawa Diagrams The Di
Page 199 and 200:
Chapter 12 Ishikawa Diagrams 199 Pr
Page 201 and 202:
Chapter 12 Ishikawa Diagrams 201 Bu
Page 203 and 204:
Page 205 and 206:
Page 207 and 208:
Chapter 13 Lifetime Distribution Us
Page 209 and 210:
Chapter 13 Lifetime Distribution 20
Page 211 and 212:
Page 213 and 214:
Page 215 and 216:
Page 217 and 218:
Page 219 and 220:
Page 221 and 222:
Page 223 and 224:
Page 225 and 226:
Page 227 and 228:
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
Page 235 and 236:
Page 237 and 238:
Chapter 14 Lifetime Distribution II
Page 239 and 240:
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
Page 261 and 262:
Chapter 15 Recurrence Analysis The
Page 263 and 264:
Chapter 15 Recurrence Analysis 263
Page 265 and 266:
Page 267 and 268:
Page 269 and 270:
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
Page 277 and 278:
Chapter 16 Degradation Using the De
Page 279 and 280:
Chapter 16 Degradation 279 Overview
Page 281 and 282:
Chapter 16 Degradation 281 The Degr
Page 283 and 284:
Chapter 16 Degradation 283 Model Sp
Page 285 and 286:
Page 287 and 288:
Page 289 and 290:
Page 291 and 292:
Chapter 16 Degradation 291 Inverse
Page 293 and 294:
Chapter 16 Degradation 293 Platform
Page 295 and 296:
Chapter 16 Degradation 295 Platform
Page 297 and 298: Chapter 16 Degradation 297 Model Re
Page 299 and 300: Chapter 16 Degradation 299 Destruct
Page 301 and 302: Chapter 16 Degradation 301 Stabilit
Page 303 and 304: Chapter 17 Forecasting Product Reli
Page 317 and 318: Chapter 18 Reliability Growth Using
Page 319 and 320: Chapter 18 Reliability Growth 319 O
Page 321 and 322: Chapter 18 Reliability Growth 321 E
Page 327 and 328: Chapter 18 Reliability Growth 327 T
Page 329 and 330: Chapter 18 Reliability Growth 329 F
Page 343 and 344: Chapter 18 Reliability Growth 343 A
Page 345 and 346: Chapter 18 Reliability Growth 345 A
Page 347: Chapter 18 Reliability Growth 347 S
Page 351 and 352: Chapter 19 Reliability and Survival
Page 399 and 400:
Chapter 20 Reliability and Survival
Page 401 and 402:
Page 403 and 404:
Page 405 and 406:
References Abernethy, Robert B. (19
Page 407 and 408:
References 407 Carroll, R.J., Ruppe
Page 409 and 410:
References 409 Haaland, P.D. (1989)
Page 411 and 412:
References 411 Lawless, J.F. (1982)
Page 413 and 414:
References 413 Nelson, W.B. (2003),
Page 415 and 416:
References 415 Snee, R.D. and Marqu
Page 417 and 418:
Index JMP Quality and Reliability M
Page 419 and 420:
Index 419 Fit SEV 242 Fit Weibull 2
Page 421 and 422:
Index 421 Q Quantiles table 356 R R
Page 423 and 424:
Index 423 Weibull Plot 360 Westgard
show all

Quality and Reliability Methods - SAS

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?