Software reliability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
Springer
2000
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 339 S. graph. Darst. 1 Diskette (9 cm) |
| ISBN: | 9813083840 |
Staff View
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012759687 | ||
| 003 | DE-604 | ||
| 005 | 20010307 | ||
| 007 | t | ||
| 008 | 990913s2000 d||| |||| 00||| eng d | ||
| 016 | 7 | |a 959290028 |2 DE-101 | |
| 020 | |a 9813083840 |9 981-3083-84-0 | ||
| 035 | |a (OCoLC)247593265 | ||
| 035 | |a (DE-599)BVBBV012759687 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-739 |a DE-29T | ||
| 050 | 0 | |a QA76.76.R44 | |
| 082 | 0 | |a 005.1 |2 21 | |
| 084 | |a ST 230 |0 (DE-625)143617: |2 rvk | ||
| 084 | |a ST 233 |0 (DE-625)143620: |2 rvk | ||
| 100 | 1 | |a Pham, Hoang |d 1960- |e Verfasser |0 (DE-588)122145445 |4 aut | |
| 245 | 1 | 0 | |a Software reliability |c Hoang Pham |
| 264 | 1 | |a Singapore [u.a.] |b Springer |c 2000 | |
| 300 | |a XVIII, 339 S. |b graph. Darst. |e 1 Diskette (9 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 7 | |a Logiciels - Essais (technologie) |2 ram | |
| 650 | 7 | |a Logiciels - Fiabilité |2 ram | |
| 650 | 7 | |a fiabilité logiciel |2 inriac | |
| 650 | 7 | |a génie logiciel |2 inriac | |
| 650 | 7 | |a tolérance panne |2 inriac | |
| 650 | 4 | |a Computer software |x Reliability | |
| 650 | 0 | 7 | |a Zuverlässigkeit |0 (DE-588)4059245-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Software |0 (DE-588)4055382-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Software |0 (DE-588)4055382-6 |D s |
| 689 | 0 | 1 | |a Zuverlässigkeit |0 (DE-588)4059245-5 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-008676165 | |
Record in the Search Index
| _version_ | 1807683328229244928 |
|---|---|
| adam_text |
CONTENTS
PREFACE
.
VII
ACKNOWLEDGMENTS
.
XI
1
INTRODUCTION
.
1
1.1
THE
NEED
FOR
SOFTWARE
RELIABILITY
.
1
1.2
SOFTWARE
RELIABILITY
ENGINEERING
.
4
1.3
WHY
DOES
SOFTWARE
COST
SO
MUCH?
.
5
1.4
BASIC
DEFINITIONS
AND
TERMINOLOGIES
.
7
FURTHER
READING
.
9
PROBLEMS
.
11
REFERENCES
.
11
2
RELIABILITY
ENGINEERING
MEASURES
.
13
2.1
RELIABILITY
DEFINITIONS
.
13
2.2
SYSTEM
MEAN
TIME
TO
FAILURE
.
16
2.3
FAILURE
RATE
FUNCTION
.
18
2.4
RELIABILITY
FUNCTION
FOR
COMMON
DISTRIBUTIONS
.
19
2.4.1
BINOMIAL
DISTRIBUTION
.
19
2.4.2
POISSON
DISTRIBUTION
.
20
2.4.3
EXPONENTIAL
DISTRIBUTION
.
21
2.4.4
NORMAL
DISTRIBUTION
.
22
2.4.5
LOG
NORMAL
DISTRIBUTION
.
24
2.4.6
WEIBULL
DISTRIBUTION
.
26
2.4.7
GAMMA
DISTRIBUTION
.
28
2.4.8
BETA
DISTRIBUTION
.
29
2.4.9
HAZARD
RATE
MODEL
1
.
29
2.4.10
HAZARD
RATE
MODEL
II
.
29
2.5
MAINTAINABILITY
AND
AVAILABILITY
.
30
2.5.1
MAINTAINABILITY
.
30
XIV
CONTENTS
2.5.2
AVAILABILITY
.
32
PROBLEMS
.
33
REFERENCES
.
34
3
SOFTWARE
ENGINEERING
ASSESSMENT
.
37
3.1
INTRODUCTION
.
37
3.2
SOFTWARE
VERSUS
HARDWARE
RELIABILITY
.
38
3.3
SOFTWARE
RELIABILITY
AND
TESTING
CONCEPTS
.
44
3.4
SOFTWARE
LIFECYCLE
.
48
3.4.1
ANALYSIS
PHASE
.
50
3.4.2
DESIGN
PHASE
.
53
3.4.3
CODING
PHASE
.
56
3.4.4
TESTING
PHASE
.
56
3.4.5
OPERATING
PHASE
.
60
3.5
SOFTWARE
DEVELOPMENT
PROCESS
AND
ITS
APPLICATIONS
.
62
3.5.1
ANALYTIC
HIERARCHY
PROCESS
.
62
3.5.2
EVALUATION
OF
SOFTWARE
DEVELOPMENT
PROCESS
.
63
3.6
SOFTWARE
VERIFICATION
AND
VALIDATION
.
67
3.7
DATA
COLLECTION
AND
ANALYSIS
.
69
FURTHER
READING
.
71
PROBLEMS
.
71
REFERENCES
.
71
4
SOFTWARE
RELIABILITY
MODELING
.
73
4.1
INTRODUCTION
.
73
4.2
HALSTEAD
'
S
SOFTWARE
METRIC
.
74
4.3
MCCABE
'
S
CYCLOMATIC
COMPLEXITY
METRIC
.
78
4.4
ERROR
SEEDING
MODELS
.
81
4.4.1
MILLS
'
ERROR
SEEDING
MODEL
.
81
4.4.2
CAI
'
S
MODEL
.
83
4.4.3
HYPERGEOMETRIC
DISTRIBUTION
MODEL
.
.
85
4.5
FAILURE
RATE
MODELS
.
87
4.5.1
JELINSKI
-MORANDA
MODEL
.
87
4.5.2
SCHICK-WOLVERTON
MODEL
.
90
4.5.3
JELINSKI-MORANDA
GEOMETRIC
MODEL
.
92
4.5.4
MORANDA
GEOMETRIC
POISSON
MODEL
.
92
4.5.5
NEGATIVE-BINOMIAL
POISSON
MODEL
.
93
4.5.6
MODIFIED
SCHICK
-WOLVERTON
MODEL
.
93
4.5.7
GOEL-OKUMOTO
DEBUGGING
MODEL
.
93
CONTENTS
XV
4.6
CURVE
FITTING
MODELS
.
94
4.6.1
ESTIMATION
OF
ERRORS
MODEL
.
94
4.6.2
ESTIMATION
OF
COMPLEXITY
MODEL
.
95
4.6.3
ESTIMATION
OF
FAILURE
RATE
MODEL
.
95
4.7
RELIABILITY
GROWTH
MODELS
.
95
4.7.1
COUTINHO
MODEL
.
96
4.7.2
WALL
AND
FERGUSON
MODEL
.
96
4.8
NON-HOMOGENEOUS
POISSON
PROCESS
MODELS.
96
4.9
MARKOV
STRUCTURE
MODELS
.
97
4.9.1
MARKOV
MODEL
WITH
IMPERFECT
DEBUGGING
.
98
4.9.2
LITTLEWOOD
MARKOV
MODEL
.
98
4.9.3
SOFTWARE
SAFETY
MODEL
.
99
PROBLEMS
.
100
REFERENCES
.
102
5
NHPP
SOFTWARE
RELIABILITY
MODELS
.
105
5.1
INTRODUCTION
.
105
5.2
PARAMETER
ESTIMATION
.
106
5.3
NHPP
MODELS
.
108
5.3.1
NHPP
EXPONENTIAL
MODEL
.
108
5.3.2
NHPP
S-SHAPED
MODEL
.
115
5.3.3
NHPP
IMPERFECT
DEBUGGING
MODEL
.
120
5.3.4
NHPP
IMPERFECT
DEBUGGING
S-SHAPED
MODEL
.
.
.
128
5.4
APPLICATIONS
.
134
5.5
IMPERFECT
DEBUGGING
VERSUS
PERFECT
DEBUGGING
.
145
5.6
A
GENERALIZED
NHPP
SOFTWARE
RELIABILITY
MODEL
.
148
5.7
MEAN
TIME
BETWEEN
FAILURES
FOR
NHPP
.
152
PROBLEMS
.
155
REFERENCES
.
157
6
SOFTWARE
COST
MODELS
.
159
6.1
INTRODUCTION
.
159
6.2
A
SOFTWARE
COST
MODEL
WITH
RISK
FACTOR
.
162
6.3
A
GENERALIZED
SOFTWARE
COST
MODEL
.
165
6.4
A
COST
MODEL
WITH
MULTIPLE
FAILURE
ERRORS
.
169
6.4.1
COST
SUBJECT
TO
RELIABILITY
CONSTRAINT
.
171
6.4.2
COST
SUBJECT
TO
THE
NUMBER
OF
REMAINING
ERRORS
CONSTRAINT
.
172
6.4.3
SOFTWARE
RELIABILITY
SUBJECT
TO
COST
CONSTRAINT.
.
173
XVI
CONTENTS
6.5
APPLICATIONS
.
173
PROBLEMS
.
176
REFERENCES
.
177
7
FAULT-TOLERANT
SOFTWARE
.
179
7.1
INTRODUCTION
.
179
7.2
BASIC
FAULT-TOLERANT
SOFTWARE
TECHNIQUES
.
181
7.2.1
RECOVERY
BLOCK
SCHEME
.
182
7.2.2
A-VERSION
PROGRAMMING
.
182
7.2.3
OTHER
ADVANCED
TECHNIQUES
.
183
7.3
SELF-CHECKING
DUPLEX
SCHEME
.
184
7.4
RELIABILITY
MODELING
.
186
7.4.1
RECOVERY
BLOCK
.
187
7.4.2
AT-VERSION
PROGRAMMING
.
187
7.4.3
HYBRID
FAULT-TOLERANT
SCHEME
.
189
7.5
REDUCTION
OF
COMMON-CAUSE
FAILURES
.
192
7.6
SUMMARY
.
193
PROBLEMS
.
194
REFERENCES
.
195
8
SOFTWARE
RELIABILITY
MODELS
WITH
ENVIRONMENTAL
FACTORS
.
199
8.1
INTRODUCTION
.
199
8.2
DEFINITION
OF
ENVIRONMENTAL
FACTORS
.
199
8.3
ENVIRONMENTAL
FACTORS
ANALYSIS
.
205
8.4
A
GENERALIZED
MODEL
WITH
ENVIRONMENTAL
FACTORS
.
210
8.4.1
ENVIRONMENTAL
FACTORS
ESTIMATION
USING
MAXIMUM
LIKELIHOOD
ESTIMATION
.
211
8.4.2
ENVIRONMENTAL
FACTORS
ESTIMATION
USING
MAXIMUM
PARTIAL
LIKELIHOOD
APPROACH
.
212
8.5
ENHANCED
PROPORTIONAL
HAZARD
JELINSKI-MORANDA
(EPJM)
MODEL.
213
8.6
AN
APPLICATION
WITH
ENVIRONMENTAL
FACTORS
.
216
PROBLEMS
.
219
REFERENCES
.
220
APPENDIX
A
THEORY
OF
ESTIMATION
.
221
A.L
POINT
ESTIMATION
.
221
A.1.1
MAXIMUM
LIKELIHOOD
ESTIMATION
METHOD
.
223
A.1.2
METHOD
OF
MOMENTS
.
230
CONTENTS
XVII
A.2
GOODNESS
OF
FIT
TECHNIQUES
.
230
A.2.1
CHI-SQUARED
TEST
.
231
A.2.
2
KOLMOGOROV-SMIRNOV
D
TEST
.
232
A.2.3
LEAST
SQUARED
ESTIMATION
.
233
A.3
INTERVAL
ESTIMATION
.
235
A.3.1
CONFIDENCE
INTERVALS
FOR
THE
NORMAL
PARAMETERS
.
235
A.3.2
CONFIDENCE
INTERVALS
FOR
THE
EXPONENTIAL
PARAMETERS
.
238
A.3.3
CONFIDENCE
INTERVALS
FOR
THE
BINOMIAL
PARAMETERS
.
240
A.3.4
CONFIDENCE
INTERVALS
FOR
THE
POISSON
PARAMETERS
.
241
A.4
TOLERANCE
LIMITS
.
242
A.4.1
TOLERANCE
LIMITS
FOR
NORMAL
POPULATIONS
.
242
A.4.
2
TOLERANCE
LIMITS
FOR
EXPONENTIAL
POPULATIONS
.
243
A.5
NON-PARAMETRIC
TOLERANCE
LIMITS
.
244
A.6
SEQUENTIAL
SAMPLING
.
245
A.7
BAYESIAN
METHODS
.
253
PROBLEMS
.
;
.
.
.
259
REFERENCES
.
260
APPENDIX
B
STOCHASTIC
PROCESSES
.
261
B.L
INTRODUCTION
.
261
B.2
MARKOV
PROCESSES
.
262
B.2.1
SYSTEM
MEAN
TIME
BETWEEN
FHILURES
.
271
B.3
POISSON
PROCESSES
.
282
B.4
RENEWAL
PROCESSES
.
284
B.5
QUASI-RENEWAL
PROCESSES
.
287
B.6
NON-HOMOGENEOUS
POISSON
PROCESSES
.
290
FURTHER
READING
.
292
PROBLEMS
.
293
REFERENCE
.
293
LAPLACE
TRANSFORM
.
293
APPENDIX
C
SURVEY
OF
FACTORS
THAT
AFFECT
SOFTWARE
RELIABILITY
.
297
XVIII
CONTENTS
APPENDIX
D
DISTRIBUTION
TABLES
.
301
SOLUTIONS
TO
SELECTED
PROBLEMS
.
325
INDEX
.
337 |
| any_adam_object | 1 |
| author | Pham, Hoang 1960- |
| author_GND | (DE-588)122145445 |
| author_facet | Pham, Hoang 1960- |
| author_role | aut |
| author_sort | Pham, Hoang 1960- |
| author_variant | h p hp |
| building | Verbundindex |
| bvnumber | BV012759687 |
| callnumber-first | Q - Science |
| callnumber-label | QA76 |
| callnumber-raw | QA76.76.R44 |
| callnumber-search | QA76.76.R44 |
| callnumber-sort | QA 276.76 R44 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | ST 230 ST 233 |
| ctrlnum | (OCoLC)247593265 (DE-599)BVBBV012759687 |
| dewey-full | 005.1 |
| dewey-hundreds | 000 - Computer science, information, general works |
| dewey-ones | 005 - Computer programming, programs, data, security |
| dewey-raw | 005.1 |
| dewey-search | 005.1 |
| dewey-sort | 15.1 |
| dewey-tens | 000 - Computer science, information, general works |
| discipline | Informatik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>00000nam a2200000 c 4500</leader><controlfield tag="001">BV012759687</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20010307</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">990913s2000 d||| |||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">959290028</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9813083840</subfield><subfield code="9">981-3083-84-0</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)247593265</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012759687</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-739</subfield><subfield code="a">DE-29T</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA76.76.R44</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">005.1</subfield><subfield code="2">21</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 230</subfield><subfield code="0">(DE-625)143617:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 233</subfield><subfield code="0">(DE-625)143620:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Pham, Hoang</subfield><subfield code="d">1960-</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)122145445</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Software reliability</subfield><subfield code="c">Hoang Pham</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2000</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XVIII, 339 S.</subfield><subfield code="b">graph. Darst.</subfield><subfield code="e">1 Diskette (9 cm)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Logiciels - Essais (technologie)</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Logiciels - Fiabilité</subfield><subfield code="2">ram</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">fiabilité logiciel</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">génie logiciel</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">tolérance panne</subfield><subfield code="2">inriac</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Computer software</subfield><subfield code="x">Reliability</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Zuverlässigkeit</subfield><subfield code="0">(DE-588)4059245-5</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Software</subfield><subfield code="0">(DE-588)4055382-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Software</subfield><subfield code="0">(DE-588)4055382-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Zuverlässigkeit</subfield><subfield code="0">(DE-588)4059245-5</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="943" ind1="1" ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008676165</subfield></datafield></record></collection> |
| id | DE-604.BV012759687 |
| illustrated | Illustrated |
| indexdate | 2024-08-18T00:32:40Z |
| institution | BVB |
| isbn | 9813083840 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008676165 |
| oclc_num | 247593265 |
| open_access_boolean | |
| owner | DE-739 DE-29T |
| owner_facet | DE-739 DE-29T |
| physical | XVIII, 339 S. graph. Darst. 1 Diskette (9 cm) |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| spelling | Pham, Hoang 1960- Verfasser (DE-588)122145445 aut Software reliability Hoang Pham Singapore [u.a.] Springer 2000 XVIII, 339 S. graph. Darst. 1 Diskette (9 cm) txt rdacontent n rdamedia nc rdacarrier Logiciels - Essais (technologie) ram Logiciels - Fiabilité ram fiabilité logiciel inriac génie logiciel inriac tolérance panne inriac Computer software Reliability Zuverlässigkeit (DE-588)4059245-5 gnd rswk-swf Software (DE-588)4055382-6 gnd rswk-swf Software (DE-588)4055382-6 s Zuverlässigkeit (DE-588)4059245-5 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pham, Hoang 1960- Software reliability Logiciels - Essais (technologie) ram Logiciels - Fiabilité ram fiabilité logiciel inriac génie logiciel inriac tolérance panne inriac Computer software Reliability Zuverlässigkeit (DE-588)4059245-5 gnd Software (DE-588)4055382-6 gnd |
| subject_GND | (DE-588)4059245-5 (DE-588)4055382-6 |
| title | Software reliability |
| title_auth | Software reliability |
| title_exact_search | Software reliability |
| title_full | Software reliability Hoang Pham |
| title_fullStr | Software reliability Hoang Pham |
| title_full_unstemmed | Software reliability Hoang Pham |
| title_short | Software reliability |
| title_sort | software reliability |
| topic | Logiciels - Essais (technologie) ram Logiciels - Fiabilité ram fiabilité logiciel inriac génie logiciel inriac tolérance panne inriac Computer software Reliability Zuverlässigkeit (DE-588)4059245-5 gnd Software (DE-588)4055382-6 gnd |
| topic_facet | Logiciels - Essais (technologie) Logiciels - Fiabilité fiabilité logiciel génie logiciel tolérance panne Computer software Reliability Zuverlässigkeit Software |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008676165&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT phamhoang softwarereliability |