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| Barlow R.E., Proschan F. — Mathematical Theory of Reliability |
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| Предметный указатель |
Mission survival probability 8
Molina, E.C. 96 177
Moment inequalities 33 43
Moments of increasing failure rate distribution 32 33
Moments of increasing failure rate distribution and decreasing mean residual life 43
Monotone failure rate 22—35 229 231
Monotone failure rate, preservation of 35—39
Monotonic structure 199 204—228
Mood, A.M. 218
Moore — Shannon inequality 201 213 215 218
Moore, E.I. 4 163 198 213
Morrison, D.F. 180
Morse, P.M. 86
Moskowitz, F. 162
Multicomponent structure 198—227
Negative binomial distribution 17
Negative binomial distribution, definition of 17
Negative binomial distribution, failure rate of 18
Nonperiodic Markov chain 123 129
Normal distribution 2 11 16
Normal distribution, failure rate of 13 15
Normal distribution, inspection schedule for 113
Normal distribution, truncated 13 88
Normal distribution, truncated, definition of 13
Open-circuit failure 163 188 199
Operating characteristics of maintenance policy 46—83
Operating time 80 81
Opportunistic replacement 117
Optimum inspection schedule 107
Order statistics 38 223
Order statistics of increasing failure rate distribution 36 38
Ososkov, G.A. 1 20
Palm, C. 1
Parallel redundancy 162 164—165 170—175
Parallel system 28 33 39 63 65
Parallel-series 188
Parzen, E. 49 57 127
Pascal distribution 17
Path 205 211
Path and cut bounds on structure reliability 208—211
Pearson, K. 96
percentile 27
Period of state 123
Periodic replacement 84 85 96
Periodic replacement with minimal repair 96—98
Planned replacement 85
Pointwise availability 7
Poisson distribution 1 17 49
Poisson distribution, definition of 17
Poisson distribution, failure rate of 18
Poisson process 10 11 15 19 20 51 56 57
Poisson process, expected number of renewals in 51
Polya frequency density of order two 60 61
Polya frequency density of order two and inspection schedule 110—111
Polya frequency function of order two 24 110 230 231
Polya frequency sequence of order two 230
Pooled samples 37
Preparedness models 84 107
Prokhorov, Yu.V. 53
Proschan, F. 5 12 22 37 48 57 61 85 107 163 169 176 185 199 204 222 227 234
Pyke, R. 131 234
Quality control 2
Queueing 139
Quorum function 201 220
Radner, R. 107
Random age replacement 46 72—74 85—95
Random walk 144
Randomized stable rule 156 157 160
Redundancy 139
Redundancy allocations, complete family of 166
Redundancy allocations, procedure 1 166 173
Redundancy allocations, procedure 2 169 174
Redundancy for exponential failure distribution 194—195
Redundancy for uniform failure distribution 195—196
Redundancy, allocation of 164
Redundancy, optimization 162—197
Redundancy, parallel 162 164—165 170—175
Redundancy, standby 162 165 175—180
Redundancy, two types of failure 185—197
Redundancy, undominated allocation 164—166
Redundant structures, replacement of 63
Relay network 163 188 198 199—204 211
Reliability 211
Reliability function of structure 206
Reliability, bounds on structure 208
Reliability, definitions of 5 6 7
Reliability, function 207
Reliability, maximizing system 188
Removals 61
Removals, expected number of 66
Removals, time between 66
Renewal counting process 48 53
Renewal density 50
Renewal density for gamma density 57
Renewal density theorem 60
Renewal density, bounds on 59
Renewal function for shifted exponential 57
Renewal function for truncated exponential 57
Renewal function, bounds on 53 54 68 69 71 72
Renewal function, definition of 50
Renewal process 8 19
Renewal process, definition of 48
Renewal process, underlying IFR distribution 49
Renewal quantity, generalized 135
Renewal random variable 48
Renewal random variable, bounds on moments of 54
Renewal random variable, distribution for gamma density 56
Renewal random variable, positivity properties of 60
Renewal theory 2 4 48
Renyi, A. 235
Repair time distribution 17
Repairman problems 121 139—151
replacement 2 5
Replacement for truncated normal 88—91
Replacement of redundant structures 63—65
| Replacement rate 8
Replacement rule 153 154
Replacement, age 61—66 85
Replacement, age, for finite time span 92—95
Replacement, age, for infinite time span 86—92
Replacement, and DFR distributions 85
Replacement, block 85
Replacement, bound on time to failure 62
Replacement, existence of optimum age policy 86
Replacement, expected number of failures 66
Replacement, exponential bounds on operating characteristics 65 66
Replacement, finite time span 85
Replacement, infinite time span 85
Replacement, mean time to failure 61
Replacement, minimax strategy for age 91 92
Replacement, opportunistic 117
Replacement, optimum age 85—95
Replacement, optimum block 95—96
Replacement, optimum block, for gamma 95—96
Replacement, periodic 84 85 96
Replacement, periodic, with minimal repair 96—98
Replacement, planned 85
Replacement, random age 72—74 86
Replacement, sequential 84 85 98—107
Replacement, sequential, for gamma distribution 104—107
Replacement, underlying IFR failure distribution 62
Reverse regular function 230
Roeloffs, R. 114
Rosenblatt, J.R. 4
Rubin, H. 25 229
Rustagi, J.S. 34
S-shapedness property 198 199 211—218
Sacks, J. 86
Saunders, S.C. 2 198
Savage, I.R. 95 107
Scarf, H. 176 229
Schoenberg, I.J. 230 231
Semi-Markov process 4 121 131—139
Semi-Markov process, absorbing 135
Semi-Markov process, limit theorems 135—137
Sequential replacement 84 85 98—107
Sequential replacement for gamma distribution 104—107
Series system 28 33 39 63 162 225
Series system of IFR (DFR) components 33—34
Series-parallel 186
Servicing reliability 83
Sevastjanov, B.A. 148
Shannon, C.E. 4 163 198
Sheffer stroke organ 198
Short-circuit failure 163 188 199
Shortage 162
Shortage random variable 51 58
Shortage random variable, distribution for 58
Sign reverse regular 230
Single unit, exponential failure and constant repair 78—79
Single unit, exponential failure and repair 77—78 80
Single unit, failure and repair 74—77
Size of path (cut) 206
Smith, W.L. 4 21 48 56 60 136 139
Snell, J. 122
Sobel, M. 3 4 5 235
Spare parts problem 49
spares 36 38 49 139 162 165
Spares for exponential failure distribution 176—180
Spares for gamma failure distribution 180
Standby redundancy 162 165 175—180
States, absorbing 123
States, communicating 123
States, ergodic 123
States, period of 123
Stationary Markov process 122
Steck, G.P. 4
Steffenson, J.F. 10
Strategic reliability 8
Structure failure rate, and component failure rates 221—228
Structure failure rate, and component failure rates, bounds on 225
Structure function 204
Superposition of renewal processes 19
Survival probability, under age replacement 61
System survival probability, bounds for 28
Szegoe, G. 230
Tables of bounds for IFR (DFR) distributions 238—242
Takacs, L. 47 59 75 79 139 147 150
Tate, R.F. 5
Telephone trunking 1 11 148 149
Test for increasing failure rate 234—237
Time between removals 66
Time homogeneous Markov chain 131
Tischendorf, J.A. 5
Total positivity 5 229—233
Total positivity, definition of 229
Totally positive functions 25
Tradeoff between redundancy and replacement 64
Transient state 123
Truelove, A.J. 8
Two parameter exponential distribution 5
Two-terminal network 205 210
Unbiased test 232
Undominated redundancy allocation 164—166
Uniform distribution 113 195
Uniform distribution, inspection schedule for 113
Uniform distribution, redundancy 195—196
Unimodality 232
Variation diminishing property 230 231
von Neumann, J. 4 198
Weibull distribution 2 4 5 9 11 13 14 16 98 196 236
Weibull distribution, definition of 13
Weibull distribution, failure rate of 13 14
Weibull, W. 2 16
Weiss, G. 4 47 62 75 90
Welker, E.L. 7 67
Widder, D.V. 229
Williams, G.T. 197
Work hardening 10
Zahl, S. 162
Zelen, M. 4 16
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