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Nelson W.B. — Recurrent events data analysis for product repairs, disease recurrences, and other applications
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Название: Recurrent events data analysis for product repairs, disease recurrences, and other applications
Автор: Nelson W.B.
Аннотация: Survival data consist of a single event for each population unit, namely, end of life, which is modeled with a life distribution. In contrast, many applications involve repeated-events data, where a unit may accumulate any number of events over time. Examples include the number and cost of repairs of products, the number and treatment costs of recurrent disease episodes in patients, and the number of childbirths to statisticians. This applied book provides practitioners with basic nonparametric methods for such data, particularly the plot of the estimate of the population mean cumulative function (MCF), which yields most of the information sought.
Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications is the first book to present a simple, unified theory that includes data on costs or other "values" of discrete events, not just the number of events. It surveys computer programs that calculate and plot the MCF estimate with confidence limits, shows their output, and explains how to interpret such plots. Many such calculations can be easily done with a pocket calculator or spreadsheet program. Also, the book introduces basic Poisson and Cox regression models and parametric models, including homogeneous and nonhomogeneous Poisson processes and renewal processes.
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Рубрика: Математика /
Статус предметного указателя: Готов указатель с номерами страниц
ed2k: ed2k stats
Год издания: 2003
Количество страниц: 164
Добавлена в каталог: 21.10.2010
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Предметный указатель
Hypothesis test, difference of two MCFs 112
Increment, MCF 38
Increment, observed 81
Incremental costs, bivariate population 74
Incremental costs, sample 74
Incremental mean number 46
Incremental recurrence cost 69
Increments, integer 24
Increments, negative 24
Independent increments 33 54 74 84 86 133
Independent increments, hypothesis test for 74
Independent increments, nonhomogeneous Poisson process 129
Independent increments, often not valid 128
Infant mortality 29 40
Information sought 28—33
Intensity function 26 see
Interarrival times 2
Interarrival times, Poisson process 124
Internet shopping 32
Interval age data 79—95
Interval age data, common 80
Interval age data, common set 83
Interval age data, differing 80
Interval age data, treated as exact 41
Interval, endpoints 83
Interval, last 86
Issues, practical and theoretical 51—54 107—108
Jackknife 75
JMP 7 40 64 112 132 133
Laplace transformation 131
Least squares 40
Like-new condition 54
Like-old condition 54
Longitudinal analysis 133
Longitudinal data 133
Maintenance 34
maintenance, planning 126
Maintenance, preventative replacement 132
Marked point processes 10
Markov, chains 133
Markov, process 133
MCF estimate 28
MCF estimate at a specified age 40
MCF estimate for a group of events 103—105
MCF estimate for a single type of event 102
MCF estimate for cost 43—46
MCF estimate for number 37—43
MCF estimate for remaining types of events 106
MCF estimate for value 43
MCF estimate with events eliminated 105—107
MCF estimate, all events 100—102
MCF estimate, assumptions 51 70
MCF estimate, assumptions interval data 82
MCF estimate, biased 52 82
MCF estimate, common 115
MCF estimate, comparisons 109 see
MCF estimate, continuous history 49—51
MCF estimate, curve 40 47 81
MCF estimate, design life 5
MCF estimate, difference of two 110
MCF estimate, events combined 103—105
MCF estimate, exact age data 35—58
MCF estimate, formula 69
MCF estimate, gaps 46—49
MCF estimate, interval age data 79—83
MCF estimate, Lawless — Nadeau variance 64
MCF estimate, left censoring 46
MCF estimate, line segments 81 101
MCF estimate, motivation 36
MCF estimate, naive variance estimate 65
MCF estimate, nonparametric 38 40
MCF estimate, not assumed 53
MCF estimate, percentage 100
MCF estimate, plotted points 82
MCF estimate, pooled 91 115
MCF estimate, sampling distribution 70
MCF estimate, staircase 40 47
MCF estimate, steps 38 43 46
MCF estimate, straight line segments 80
MCF estimate, theoretical variance 73
MCF estimate, theory 51
MCF estimate, true naive variance 65
MCF estimate, true variance 60 71
MCF estimate, unbiased 40 53
MCF estimate, variance 70
MCF estimate, variance estimate 60 64 73
MCF estimate, variance for interval data 84
MCF estimate, warranty 95
MCF for a type of event 99
MCF, add types 99
MCF, confidence limits 59—77
MCF, definition 26
MCF, difference of two 110
MCF, finite 53
MCF, K samples 115
MCF, K-variate 99
MCF, linear 42
MCF, mean curve 26
MCF, nonhomogeneous Poisson process 128
MCF, nonparametric 132
MCF, parametric 54
MCF, percentage 46
MCF, Poisson process 122
MCF, power process 129
MCF, sample 38 see
MCF, ultimate 31 80
MCFDIFF 112
MCFLIM 40 64
Mean cost per unit 43
Mean cumulative function see "MCF"
Mean curve 26 51
Mean curve, K-variate 99
Mean number 38
Mean Time Between Failures 56 124
Mean time between recurrences 42
Menopause 81
MIL-HDBK-781 130
Mileage 4 93
Mileage, customer 4
Mileage, test 4
Mileage, versus days 94
Mixture 54
Model with covariates 132—133
Model, choice of 121
Model, counting process 121
Model, Cox 132
Model, Crow-AMSAA 129
Model, growth 134
Model, Markov 133
Model, mix of events 98—100
Model, nonparametric 25
Model, other 133—134
Model, parametric 35 121 133
Model, Poisson process 122—124
Model, population 25—28
Model, series-system 108
Model, single unit 133
MTBF 124
Naive confidence limits 64—68
Naive confidence limits for cost 65
Naive confidence limits for number 64
Naive confidence limits, calculation 67
Naive confidence limits, limitations 64
Naive confidence limits, not for cost 64
Naive confidence limits, steps 67
Nonhomogeneous Poisson process 65 86 127—130
Nonhomogeneous Poisson process, definition 128
Nonhomogeneous Poisson process, depicted 128
Nonhomogeneous Poisson process, estimate 128
Nonhomogeneous Poisson process, MCF 128
Nonhomogeneous Poisson process, naive confidence limits 128
Nonhomogeneous Poisson process, parametric MCF 128
Nonhomogeneous Poisson process, recurrence rate 128
Nonhomogeneous Poisson process, variance 129
Number at risk 38 43 46
Number at risk, approximate 81
Number entering 81
Overhaul 33
Parametric models 54
Patient losses 53
Permutation tests 115
Placebo treatment 5 55
plot 110
Plot, accuracy 42
Plot, advantages 35
Plot, combined 105
Plot, comparison 110 112
Plot, disadvantages 35
Plot, Duane 130
Plot, enhanced 101
Plot, hazard 38
Plot, linear grid 47
Plot, log-log 43 47 87 95 129 130
Plot, point per interval 82
Plot, point per recurrence 82
Plot, reliability growth 130
Poisson distribution 122
Poisson distribution, analysis 124—126
Poisson distribution, confidence limits for A 125
Poisson distribution, cumulative distribution function (cdf) 124
Poisson distribution, density function 122
Poisson distribution, estimate common 126
Poisson distribution, mean 122
Poisson distribution, multisample analyses 126—127
Poisson distribution, normal approximation 124
Poisson distribution, pooled estimate 126
Poisson distribution, pooled rate variance 127
Poisson distribution, prediction for a count 125
Poisson distribution, prediction limits 126
Poisson distribution, probability density 122
Poisson distribution, regression fitting 132
Poisson distribution, regression model 132
Poisson distribution, standard deviation 124
Poisson distribution, statistically independent counts 126
Poisson distribution, variance 124
Poisson process 54 121—127
Poisson process, confidence limits 125
Poisson process, definition 122
Poisson process, estimate 124
Poisson process, homogeneous 128
Poisson process, interarrival times 124
Poisson process, MCF 122
Poisson process, mixture 33 75
Poisson process, model 122—124
Poisson process, pooled estimate 125
Poisson process, Proschan data 33
Poisson process, recurrence rate 122 123
Poisson process, recurrence rate, estimate 124
Poisson process, renewal 131
Poisson process, sample recurrence rate 124
Poisson process, single-sample analyses 124—126
Poisson process, sum of counts 124
Population 19
Population, bivariate 73
Population, cumulative history function 23—25
Population, finite 53
Population, infinite 71
Population, mixture 75
Population, model 23—34
Population, stratified 76
Population, target 19 26 70
Power law 129
Power process, definition 129
Power process, MCF 129
Power process, Poisson process is a special case 129
Power process, recurrence rate 129
Power relationship 129
Practical issues 18—21
Prediction 31 54 125
Prediction limits 54 91
Prediction limits, approximate 126
Prediction limits, Poisson 126
Prediction, error 125
Prediction, variance 125
probability density 28
Process, counting 2 128
Process, independent increments 86
Proschan data see "Application Proschan"
R/100 5
Random sampling, simple 70
Recurrence rate for group of events 99
Recurrence rate for types of events 99
Recurrence rate, add types 99
Recurrence rate, bathtub 29
Recurrence rate, behavior 28 40
Recurrence rate, constant 27 42 83 132
Recurrence rate, decreasing 27
Recurrence rate, definition 26
Recurrence rate, estimate 40
Recurrence rate, increasing 27
Recurrence rate, nonhomogeneous Poisson process 128
Recurrence rate, Poisson process 122
Recurrence rate, power process 129
Recurrences see "Events"
references 137—142
Regression, Cox 132
Regression, parametric 132
Regression, Poisson 132
Related topics 121—135
Relationship, log-linear 132
Reliability, demonstration 97
Reliability, growth 129 130
Reliability, growth confidence limits 130
Reliability, growth prediction 130
Reliability, growth prediction limits 130
Reliability, growth rate 130
Reliability, growth, ReliaSoft 130
Reliability, growth, WinSMITH 130
Reliability, improvement 129
Reliability, Procedure 86
ReliaSoft 40 64 86 112 130
Renewal process 48 54 130—132
Renewal process, cdf estimate 131
Renewal process, definition 130
Renewal process, equation 131
Renewal process, function 130
Renewal process, MCF properties 131
Renewal process, Poisson 131
Renewal process, recurrence rate 131
Renewal process, Weibull 131
Repair, definition 19
replacement 19
Replacement rates 87
Replacement, optimum age 132
Replacement, preventive 132
Reporting delays 53 91
Resampling 75
Resampling limits 75
Retirement 32
Retirement, optimum age 32
S-Plus 40 64 112 133
Sample 36
Sample MCF 38 see
Sample of units 133
Sample size 35
Sample, biased 21 52
Sample, nonrandom 19 90
Sample, random 19 51
Sample, self-selected 52 90
Sample, simple random 51 71
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