Repairable systems reliability: modeling, inference, misconceptions and their causes
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1984
|
| Series: | Lecture notes in statistics
7 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 223 S. graph. Darst. |
| ISBN: | 0824772768 |
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| adam_text | Contents
PREFACE v
1. SCOPE 1
2. TERMINOLOGY, NOTATION AND BASIC MODELS 7
A. Definitions 7
B. Notation 8
C. Acronyms 10
D. Basic Models for Parts 10
(1) Force of mortality (FOM) and probability
density function (PDF) of a part 10
(2) Mean time to failure (MTTF) 11
(3) Partwearout 11
(4) Part burn in 14
(5) Statistical analysis of times to failure of parts 14
E. Basic Concepts for Stochastic Point Processes 17
(1) Arrival and interarrival times and rate
of occurrence of failures 17
(2) Independent increments 20
(3) Stationary increments 20
(4) Synchronous and asynchronous sampling 20
(5) Stationary sequence of interarrival times 21
(6) Stationarity of a point process 21
(7) Transient and nonstationary point processes 21
(8) Rate of occurrence of failures for stationary, transient
and nonstationary point processes 22
(9) Intensity function of a stochastic point process 23
(10) Time between failures, mean time between failures and
reliability function of a stochastic point process 23
(11) Improvement and deterioration properties of a
stochastic point process 25
(12) Interarrival times vs spacings between order statistics 26
(13) Chronological or spatial ordering of part failure times 27
(14) Statistical analysis of part and system failure data 29
ix
x Contents
F. Basic Models Applicable to Repairable Systems 29
(1) Homogeneous Poisson Process (HPP) 29
(2) Nonhomogeneous Poisson Process (NHPP) 30
(3) Renewal Process 33
(4) Superimposed Renewal Process (SRP) 34
(5) Branching Poisson Process (BPP) 36
G. Discussion of Improvement/Deterioration Properties of a
Stochastic Point Process 37
(1) Introduction 37
(2) Jewell s results 38
(3) Two interpretations of one functional form
of a ROCOF 41
(4) An example where failure rate increases and
simultaneously decreases 43
(5) Summary 45
H. Overview of Survey of Repairable Systems Reliability 46
3. PROBABILISTIC MODELING OF REPAIRABLE SYSTEMS 47
A. Superimposed Renewal Process (SRP) 47
B. Nonhomogeneous Poisson Process (NHPP) 51
C. Branching Poisson Process (BPP) 52
D. Catastrophic Models 52
E. Application of Software Reliability Models 53
F. Models Which Include Repair Times 53
G. Event Altered Rate Models 55
H. Failure Processes Subjected to Random Deletions 55
I. Imperfect Repair Models 55
J. Steady State Reliability Models 56
K. Stochastic FOM s 57
L. Negative Binomial Process 58
M. Renewal Process 59
N. Systems Which Suffer Only a Finite Number
of Failures 61
4. SHORTCOMINGS OF PROBABILISTIC MODELING
OF REPAIRABLE SYSTEMS RELIABILITY 63
A. Real World Factors 63
B. Importance of Real World Factors 65
C. Where Do We Go From Here? 68
5. STATISTICAL ANALYSIS OF REPAIRABLE
SYSTEMS FAILURE DATA 70
A. Overview of Sections B F 71
B. Trend Testing 73 j
Contents x/.
(1) Graphical techniques 74
(a) Plotting cumulative failures versus cumulative time
on linear paper 74
(b) Estimating average ROCOF in successive
time periods 76
(c) Duane plots 77
(2) Summary of Ascher and Feingold (1978b) 78
(a) Category H M 78
(b) Category H N 79
(c) Category R M 80
(d) Category R N 82
(e) Category S M 82
(f) Pooling of test results 82
(3) Jewell s results and their implications 83
C. Fitting of Nonstationary Models 83
(1) NHPP models 83
(2) Sequences of independent but not identically
distributed RV s 86
(a) Models assuming specific distributions 86
(b) Distribution free models 88
D. Testing for Independence of Successive X; s 88
E. Fitting the BPP to Repairable System Failure Data 89
F. Analysis of IID Data 91
(1) Distribution free methods 91
(2) Methods based on partial distributional knowledge 92
(3) Asymptotic properties versus the real world 93
(4) Estimation of FOM and PDF 93
(5) Fitting a Weibull distribution to IID data 95
G. Regression Analysis of Multivariate Data 96
6. RELIABILITY GROWTH 100
A. Overview 100
B. Point Process Models 101
(1) NHPP reliability growth models 101
(a) Power law model 101
(b) Cox Lewis (Cozzolino) model; log linear model 103
(c) Cozzolino s Initial Defects model
(generalized version) 104
(d) Extended Cox Lewis model 104
(2) Alternative reliability growth models 104
(a) McWilliams model 104
(b) Braun Paine model 105
xii Contents
(c) Singpurwalla model 106
(d) Cozzolino s other models 107
C. Differential Equation Reliability Growth Models 107
(1) IBM model 108
(2) Exponential single term power series model 108
(3) Lloyd Lipow model 109
(4) Aroef model 109
(5) Simple exponential model 109
D. Parochialism of the Reliability Growth Literature 110
E. Discussion Ill
7. REPAIRABLE SYSTEMS COST MODELS 113
A. Overview 113
B. Deteriorating Repairable Systems 115
(1) Age dependent replacement policies — Type 1 policies 115
(2) Modified Type 1 policies 116
(3) Minimal repair policies based on planned
replacement intervals 118
(a) Type 2 policy 118
(b) Type 3 and Type 4 policies 120
(c) Type 2 and Type 3 policies 120
(d) Relationship between modified Type 1 policies
and minimal repair policies 121
(4) Minimal repair policies based on repair cost limits 124
(5) Cost models based on independent, but not identically
distributed, interarrival times 125
C. Repairable Systems under Reliability Improvement 126
(1) System redesign during development 126
(2) System debugging during production 126
D. Adaptive Cost Policies 128
E. Discussion 129
8. MISCONCEPTIONS/RELIABILITY TERMINOLOGY 133
A. Misconceptions 133
(1) There are two bathtub curves 136
(2) Repairable system bathtub curve vs.
Drenick s theorem 139
(3) A linear plot on linear paper does no? imply an HPP 140
(4) Unjustified reordering by magnitude 142
(5) Overhauls do not necessarily renew a system 144
(6) Survival to x stated for FOM but then disregarded 146
(7) A sequence of exponential distributions is not ,
necessarily an HPP 147 |
Contents xm
(8) Independence of successive Z, s is not guaranteed 149
(9) Availability is not necessarily equal to
MTBF/(MTBF + MTTR) 150
(10) Strict DFOM of pooled data does not indicate
improvement, nor necessarily even burn in 151
(11) Discussing models for parts and claiming that results
hold for systems 151
(12) Reliability with repair ^repairable system 151
(13) Summary: not everything is IID, much less
IID exponential 152
B. Misconceptions Due to Terminology/Notation 152
(1) Failure rate 153
(2) Operating times of parts versus operating
times of systems 157
(3) Times between failures 157
(4) Wearout versus deterioration 159
(5) Burn in versus improvement 159
(6) Weibull distribution versus Weibull process 160
(7) Order statistics 161
(8) Summary 161
C. Other Reasons for Misconceptions 162
(1) There is considerable connection between a point
process and a distribution 162
(2) There is excessive emphasis on parts and hence,
on the IID assumption 162
(3) Most nonstationary stochastic processes are
mathematically difficult/intractable 162
(4) IFR, IFRA, ... , NBUE, DFR, DFRA, ... , NWUE 163
(5) Time to first failure, or next failure, is often important 164
(6) Statistical analyses often ignore time ordering 164
(7) Varying number of systems at risk 164
D. Summary 168
9. FUTURE WORK 169
A. Research Topics 169
(1) Definitions of system improvement
and deterioration 169
(2) Multivariate regression models 171
(a) Choice of appropriate time scales 171
(b) Procedures for choosing relevent
explanatory factors 171
(c) Methods for aggregating explanatory factors 171
(d) Procedures for handling high stress periods 172
(e) Heterogeneity of systems 172
xiv Contents
(3) Superposition of point processes other than
HPP s and NHPP s 173
(4) Conditions under which superposed renewal processes
approach an HPP for finite t 173
(5) Competing risks problems 174
(6) Switchover from ensemble average to point
process approach 174
(7) Alternatives to the NHPP for reliability
growth modeling 175
(8) Probabilistic modeling of repairable systems 176
(9) Locating breakpoints on repairable system
bathtub curve 177
(10) Criteria for adequacy of representation of
repairable systems models 178
(11) Trend testing 179
(12) Adaptation of time series techniques 180
B. Military Standards and Handbooks 180
(1) Military handbook on repairable systems 180
(2) Updating of MIL STD 757 181
(3) Updating of MIL STD 721 181
(4) Updating of MIL STD 781 181
(5) Updating of MIL HDBK 217 182
ENVOI 184
REFERENCES 185
AUTHOR INDEX 205
SUBJECT INDEX 209
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| id | DE-604.BV003649586 |
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| indexdate | 2024-07-09T16:03:19Z |
| institution | BVB |
| isbn | 0824772768 |
| language | English |
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| publishDate | 1984 |
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| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Ascher, Harold Verfasser aut Repairable systems reliability modeling, inference, misconceptions and their causes Harold Ascher ; Harry Feingold New York [u.a.] Dekker 1984 XIV, 223 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 7 Fiabilité - Méthodes statistiques Fiabilité - Méthodes statistiques ram Maintenabilité - Méthodes statistiques Maintenabilité - Méthodes statistiques ram SYSTEME REPARABLE inriac SYSTME STOCHASTIQUE inriac fiabilité système inriac Maintainability (Engineering) Statistical methods Reliability (Engineering) Statistical methods Methode (DE-588)4038971-6 gnd rswk-swf Reliabilität (DE-588)4213628-3 gnd rswk-swf Zuverlässigkeit (DE-588)4059245-5 gnd rswk-swf Korrektur (DE-588)4205358-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Technik (DE-588)4059205-4 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Reliabilität (DE-588)4213628-3 s Methode (DE-588)4038971-6 s DE-604 Zuverlässigkeit (DE-588)4059245-5 s Technik (DE-588)4059205-4 s Statistik (DE-588)4056995-0 s Stochastischer Prozess (DE-588)4057630-9 s Korrektur (DE-588)4205358-4 s Feingold, Harry Verfasser aut Lecture notes in statistics 7 (DE-604)BV009541824 7 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002324616&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ascher, Harold Feingold, Harry Repairable systems reliability modeling, inference, misconceptions and their causes Lecture notes in statistics Fiabilité - Méthodes statistiques Fiabilité - Méthodes statistiques ram Maintenabilité - Méthodes statistiques Maintenabilité - Méthodes statistiques ram SYSTEME REPARABLE inriac SYSTME STOCHASTIQUE inriac fiabilité système inriac Maintainability (Engineering) Statistical methods Reliability (Engineering) Statistical methods Methode (DE-588)4038971-6 gnd Reliabilität (DE-588)4213628-3 gnd Zuverlässigkeit (DE-588)4059245-5 gnd Korrektur (DE-588)4205358-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Technik (DE-588)4059205-4 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4038971-6 (DE-588)4213628-3 (DE-588)4059245-5 (DE-588)4205358-4 (DE-588)4057630-9 (DE-588)4059205-4 (DE-588)4056995-0 |
| title | Repairable systems reliability modeling, inference, misconceptions and their causes |
| title_auth | Repairable systems reliability modeling, inference, misconceptions and their causes |
| title_exact_search | Repairable systems reliability modeling, inference, misconceptions and their causes |
| title_full | Repairable systems reliability modeling, inference, misconceptions and their causes Harold Ascher ; Harry Feingold |
| title_fullStr | Repairable systems reliability modeling, inference, misconceptions and their causes Harold Ascher ; Harry Feingold |
| title_full_unstemmed | Repairable systems reliability modeling, inference, misconceptions and their causes Harold Ascher ; Harry Feingold |
| title_short | Repairable systems reliability |
| title_sort | repairable systems reliability modeling inference misconceptions and their causes |
| title_sub | modeling, inference, misconceptions and their causes |
| topic | Fiabilité - Méthodes statistiques Fiabilité - Méthodes statistiques ram Maintenabilité - Méthodes statistiques Maintenabilité - Méthodes statistiques ram SYSTEME REPARABLE inriac SYSTME STOCHASTIQUE inriac fiabilité système inriac Maintainability (Engineering) Statistical methods Reliability (Engineering) Statistical methods Methode (DE-588)4038971-6 gnd Reliabilität (DE-588)4213628-3 gnd Zuverlässigkeit (DE-588)4059245-5 gnd Korrektur (DE-588)4205358-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd Technik (DE-588)4059205-4 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Fiabilité - Méthodes statistiques Maintenabilité - Méthodes statistiques SYSTEME REPARABLE SYSTME STOCHASTIQUE fiabilité système Maintainability (Engineering) Statistical methods Reliability (Engineering) Statistical methods Methode Reliabilität Zuverlässigkeit Korrektur Stochastischer Prozess Technik Statistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002324616&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV009541824 |
| work_keys_str_mv | AT ascherharold repairablesystemsreliabilitymodelinginferencemisconceptionsandtheircauses AT feingoldharry repairablesystemsreliabilitymodelinginferencemisconceptionsandtheircauses |