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| Barlow R.E., Proschan F. — Mathematical Theory of Reliability |
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| Предметный указатель |
Absolute continuity of an IFR distribution 26
Absorbing Markov chain 125
Absorbing semi-Markov process 135
Absorbing state 123
Age replacement 46 61 67 85
Age replacement, comparison with block replacement 67—72
Age replacement, existence of optimum policy 92
Age replacement, minimax strategy 91—92
AGREE report 3 4
allocation 60 162 163
Allocation of redundancy 50 164
Allocation, complete family of undominated allocations 180—185
ARINC 3
Arrow, K.J. 176 229
Asymptotic relative efficiency 236
Availability 5 7
Availability, limiting availability 85
Barlow, R.E. 7 12 22 40 57 75 81 85 107 108 163 185
Bellman, R. 162
Binomial distribution 17—18
Birnbaum, Z.W. 2 4 5 198
Birth and death process 140 142 154
Black, G. 5
BlackweH's theorem 51 55 59
Blackwell, D. 156
Block replacement 46 67 85 95
Block replacement, comparison with age replacement 67—72
Bounds on density 42
Bounds on DFR distribution 27 28 29 31 32 40 241—242
Bounds on discrete distribution 43
Bounds on IFR distribution 21 28 29 40 41 238—240
Bounds on percentiles 30
Bounds on renewal function 52 53
Bounds on structure failure rate 225—227
Bray, T.A. 185
Brender, D.W. 47 115
Bridge network 206
Buehler, R.J. 4
Burn-in test 10
Campbell, N.R. 2 27
Carhart, R.R. 3
Chebyshev bounds 12
Chebyshev inequality 209
checking see "Inspection"
Chung, K.L. 153
Clark, C.E. 197
Classification of states for a Markov chain 123
Coefficient of variation 237
Coefficient of variation of DFR distribution 33
Coefficient of variation of IFR distribution 33
Coherent structure 199 205
Communicating states 123
Composition of structures 202 203
Control limit rule 152 154 155
Convolution of decreasing failure rate distributions 37
Convolution of increasing failure rate distributions 36—37
Cox, D.R. 16 21 53 139
Cramer, H. 176 195
Cut 205 211
Cyclic rule 160
Daniels, H.E. 2
Dannemiller, M.C. 4
Dantzig, G.B. 158
David, H.A. 180
Davis, D.J. 4 10
Death process 155
Debugging 22
Decreasing failure rate (DFR) 10 11 23 25
Decreasing failure rate (DFR) and replacement 85
Decreasing failure rate (DFR) closed under mixture 37
Decreasing failure rate (DFR) comparison with exponential 26—39
Decreasing failure rate (DFR) definition of 12
Decreasing failure rate (DFR) test of 12
Decreasing failure rate (DFR), bounds on survival probability 12 31 40 41 241—242
Decreasing failure rate distribution absolute continuity of 26
Decreasing failure rate distribution, coefficient of variation of 33
Decreasing failure rate distribution, comparison with exponential distribution 26—35
Decreasing failure rate distribution, convolution of 37
Decreasing failure rate distribution, log convexity of 25
Decreasing failure rate distribution, mixture of 37
Decreasing failure rate distribution, moments of 32 33
Decreasing mean residual life 11 43
Decreasing mean residual life and moments 43
Density, bounds on 45
Derman, C. 86 107 114 152 153 158
Diffusion process 145
Discrete failure distribution 17 18
Discrete failure rate 43
Discrete IFR distribution 24
Discrete time Markov chain 122
Doob, J.L. 55
Down time 79—80 85
Down time, distribution of 79
Drenick, R.F. 8 21 67 152 162
Dual to failure rate 37 38
Duncan, A.J. 2
Dynamic programming 117 162
Early failure 9 10
Effectiveness 5
Efficiency 5 7
Efficiency, limiting 8
Ehrenfest model 145
Elementary renewal theorem 55
Embedded Markov chain 123 144
Epstein, B. 2 3 13 235
Ergodic Markov chain 127
Ergodic states 123
Erlang's formula 148
Erlang, A.K. 1
Esary, J.D. 5 198 204 222
Essential component 212
Essentiality 162
Everett, H. 162
Excess random variable 51
Excess random variable, distribution for 58
Expected gain 5 6 7
Expected number of removals 66
Exponential distribution 1 3 4 5 10 11 15 16 176 194 224
Exponential distribution and Markov process 119
Exponential distribution and redundancy 194—195
Exponential distribution as failure law of complex equipment 18—22
Exponential distribution, comparison with DFR 26—39
Exponential distribution, comparison with IFR 26—39
Exponential distribution, definition of 13
Exponential distribution, failure rate of 13
Exponential distribution, mixture of 37
Exponential distribution, spares for 176—180
Exponential distribution, two parameter 5
Extreme value distribution 2 10 13 16 17 22
Extreme value distribution, definition of 13
Extreme value distribution, failure rate of 13
Fabens, A.J. 136
Fail-safe structure 199 218
Failure distributions 9—45
Failure distributions, discrete 17
Failure rate 4
Failure rate function 10
Failure rate function of discrete distribution 18
Failure rate of binomial distribution 18
Failure rate of convolution 38
Failure rate of exponential distribution 13
Failure rate of extreme value distribution 13
Failure rate of gamma distribution 13 14
Failure rate of geometric distribution 18
Failure rate of log normal distribution 13
Failure rate of negative binomial distribution 18
Failure rate of normal distribution 13 15
Failure rate of Poisson distribution 18
Failure rate of system 38
Failure rate of Weibull distribution 13 14
| Failure rate, bounds on 45
Failure rate, definition of 22
Failure rate, general 41—45
Failure rate, instantaneous 23
Failure rate, monotone 22—35
Fan, K. 35
Fatigue in materials 2
Feller, W. 2 15 51 139
Finite time span replacement 85
Finite time span replacement, age replacement 92—93
First-passage time 130 132—134 142
Flehinger, B.J. 47 67 74 152
Force of mortality 10
Frechet, M. 129
Freudenthal, A.M. 11
Fundamental renewal equation 50
Fundamental renewal theorem 59
Gamma distribution 2 5 9 11 13 14 16 236
Gamma distribution and spares 180
Gamma distribution, failure rate of 13 14
Gantmacher, F. 229
Geisler, M.A. 162
Generalized renewal quantity 135
Geometric distribution 17
Geometric distribution, definition of 17
Geometric distribution, failure rate of 18
Gordon, R. 163
Gourary, M.H. 162
Green, A.W. 11
Guarantee time 13
Gumbel, E.J. 2 10 16
Gupta, S. 5
Hanne, J.R. 163
Hardy, G.H. 209
Harris, T.E. 144
Hazard rate 10 23
Herd, G.R. 23 47
Hirschmann, I.I. 229
Horne, R.C. 7 11
Hosford, J.E. 7
Howard, R.A. 156
Hunter, L.C. 7 47 75 88 107 108 112 163 185
IFR Markov chain 121 154
Increasing failure rate (IFR) 11 23 25 216 217 221 224
Increasing failure rate (IFR) and convolution 36
Increasing failure rate (IFR), bounds on survival probability 12 28 29 41 238—240
Increasing failure rate (IFR), closed under convolution 36
Increasing failure rate (IFR), comparison with exponential 26—39
Increasing failure rate (IFR), definition of 12 23
Increasing failure rate (IFR), test for 12 234—237
Increasing failure rate distribution and absolute continuity 26
Increasing failure rate distribution, bounds on mean 30
Increasing failure rate distribution, bounds on percentile 30
Increasing failure rate distribution, coefficient of variation of 33
Increasing failure rate distribution, comparison with exponential distribution 26—35
Increasing failure rate distribution, definition of discrete IFR distribution 24
Increasing failure rate distribution, log concavity of 25
Increasing failure rate distribution, mixture 37
Increasing failure rate distribution, moments of 32 33
Increasing failure rate distribution, order statistics of 36 38
Increasing failure rate distribution, tables of bounds 238—242
Infinite time span replacement 85
Infinite time span replacement, age replacement 86—92
Inspection policies 107—117
Inspection policies for normal distribution 113
Inspection policies for Polya frequency function 110—111
Inspection policies for uniform distribution 113
Inspection policies with renewal 114—117
Inspection policies, minimax 107 114
Inspection policies, optimum 107
Instantaneous failure rate 23
Intensity function 10
Interval availability 5
Interval availability, limiting 7 8
Interval reliability 8 74 82
Interval reliability, limiting 74
Irreducible Markov chain 160
Jensen's inequality 27
Jewell, W.S. 156
Johnson, N.L. 53
Jordan, C. 54
Jorgenson, D. 107 117
k-out-of-n structures 36 199 215 218—221 223 224 226
Kao, J.H.K. 4 16
Karlin, S. 25 34 61 87 117 140 142 145 154 176 227 229 231 232 237
Karr, H.W. 162
Kemeny, J. 122
Kendall, M.G. 235
Kettelle's algorithm 172 173 180—185
Kettetle, J.D. 162 170
Khintchine, A.Ya. 1 20
Klein, M. 119
Kolmogorov, B.V. 53
Krein, M. 229
Lieblein, J. 16 196
Life testing 2 3 5 30
Likelihood ratio test 236
Limiting efficiency 8
Limiting interval availability 7 8
Linear programming 121 153 156 158 161
Littlewood, J.E. 209
Log normal distribution 9 11 13 17
Logistic problems 5
Lorentz, G.G. 35
Lotka, A.J. 2 47
Lusser, R. 3
Madansky, A. 4
Maintainability 4
Maintenance policies 1
Maintenance policies, operating characteristics of 46—83
Maintenance policies, opportunistic 107 117—118
Maintenance policies, optimum 84
Maintenance ratio 8
Mann, H.B. 235
Manne, A.S. 156
Marginal checking 121 151—156
Marginal checking intervals 155
Marginal states 152 155
Markov bound 238
Markov chain 121—131 152 157
Markov chain, absorbing 125
Markov chain, classification of states 123
Markov chain, discrete time 122
Markov chain, embedded 123 144
Markov chain, ergodtc 123
Markov chain, IFR Markov chain 121 154
Markov chain, irreducible 160
Markov chain, time homogeneous 131
Markov chain, transition matrix 122
Markov process 119
Markov process and exponential distribution 119
Markov process, definition of 121
Markov process, stationary 122
Markov renewal process 131 156
Markovian deterioration 156—161
Marshall, A.W. 12 22 40 45 48
McGregor, J. 140 142 145 154 229
McLean, J.B. 162
Mean residual life 11 47 53
Mean residual life and replacement policy 47
Mean time to failure with replacement 61
Mean time to in-service failure bounds on 62
Median 31 63
Mendenhall, W. 5
Mihoc 129
Mill's ratio 10
Mine, H. 162
Minimax checking 114
Minimax inspection schedule 107 114
Mission success ratio 8
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