Expectation–maximization algorithm for system-based lifetime data with unknown system structure View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-03

AUTHORS

Yandan Yang, Hon Keung Tony Ng, Narayanaswamy Balakrishnan

ABSTRACT

In science and engineering, we are often interested in learning about the lifetime characteristics of the system as well as those of the components that made up the system. However, in many cases, the system lifetimes can be observed but not the component lifetimes, and so we may not also have any knowledge on the structure of the system. Statistical procedures for estimating the parameters of the component lifetime distribution and for identifying the system structure based on system-level lifetime data are developed here using expectation–maximization (EM) algorithm. Different implementations of the EM algorithm based on system-level or component-level likelihood functions are proposed. A special case that the system is known to be a coherent system with unknown structure is considered. The methodologies are then illustrated by considering the component lifetimes to follow a two-parameter Weibull distribution. A numerical example and a Monte Carlo simulation study are used to evaluate the performance and related merits of the proposed implementations of the EM algorithm. Lognormally distributed component lifetimes and a real data example are used to illustrate how the methodologies can be applied to other lifetime models in addition to the Weibull model. Finally, some recommendations along with concluding remarks are provided. More... »

PAGES

69-98

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s10182-018-0323-x

DOI

http://dx.doi.org/10.1007/s10182-018-0323-x

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1101398175


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0104", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Statistics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Southern Methodist University", 
          "id": "https://www.grid.ac/institutes/grid.263864.d", 
          "name": [
            "Department of Statistical Science, Southern Methodist University, 75275-0332, Dallas, TX, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Yang", 
        "givenName": "Yandan", 
        "id": "sg:person.010760741657.33", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010760741657.33"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Southern Methodist University", 
          "id": "https://www.grid.ac/institutes/grid.263864.d", 
          "name": [
            "Department of Statistical Science, Southern Methodist University, 75275-0332, Dallas, TX, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ng", 
        "givenName": "Hon Keung Tony", 
        "id": "sg:person.013611575357.41", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013611575357.41"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "McMaster University", 
          "id": "https://www.grid.ac/institutes/grid.25073.33", 
          "name": [
            "Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Balakrishnan", 
        "givenName": "Narayanaswamy", 
        "id": "sg:person.0666004356.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0666004356.22"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/s0167-9473(01)00091-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002981483"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00184-010-0331-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009417482", 
          "https://doi.org/10.1007/s00184-010-0331-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/10485252.2011.559547", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011610635"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-71797-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011972383", 
          "https://doi.org/10.1007/978-0-387-71797-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-0-387-71797-5", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011972383", 
          "https://doi.org/10.1007/978-0-387-71797-5"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4684-0192-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017252284", 
          "https://doi.org/10.1007/978-1-4684-0192-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4684-0192-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017252284", 
          "https://doi.org/10.1007/978-1-4684-0192-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/nav.20449", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019829193"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/(sici)1520-6750(199908)46:5<507::aid-nav4>3.0.co;2-d", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032994824"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/nav.20407", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035427414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/nav.20407", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035427414"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.csda.2012.05.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1046906549"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/00949650903292650", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051963230"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03610920600966316", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1058327896"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tr.2002.801853", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061782892"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tr.2011.2134371", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061783536"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1109/tr.2015.2417373", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1061783913"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1177/1748006x13485188", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064073459"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1177/1748006x13485188", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064073459"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1214/aos/1176346060", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064408013"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/9780470191613", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098661620"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1002/9780470191613", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098661620"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2019-03", 
    "datePublishedReg": "2019-03-01", 
    "description": "In science and engineering, we are often interested in learning about the lifetime characteristics of the system as well as those of the components that made up the system. However, in many cases, the system lifetimes can be observed but not the component lifetimes, and so we may not also have any knowledge on the structure of the system. Statistical procedures for estimating the parameters of the component lifetime distribution and for identifying the system structure based on system-level lifetime data are developed here using expectation\u2013maximization (EM) algorithm. Different implementations of the EM algorithm based on system-level or component-level likelihood functions are proposed. A special case that the system is known to be a coherent system with unknown structure is considered. The methodologies are then illustrated by considering the component lifetimes to follow a two-parameter Weibull distribution. A numerical example and a Monte Carlo simulation study are used to evaluate the performance and related merits of the proposed implementations of the EM algorithm. Lognormally distributed component lifetimes and a real data example are used to illustrate how the methodologies can be applied to other lifetime models in addition to the Weibull model. Finally, some recommendations along with concluding remarks are provided.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s10182-018-0323-x", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1312118", 
        "issn": [
          "1863-8171", 
          "1863-818X"
        ], 
        "name": "AStA Advances in Statistical Analysis", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "1", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "103"
      }
    ], 
    "name": "Expectation\u2013maximization algorithm for system-based lifetime data with unknown system structure", 
    "pagination": "69-98", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "740053fd30f35188da0691149926fe97f7b5b9eb1569f57f0cfd230bf0e07730"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s10182-018-0323-x"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1101398175"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s10182-018-0323-x", 
      "https://app.dimensions.ai/details/publication/pub.1101398175"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T13:57", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000371_0000000371/records_130817_00000005.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs10182-018-0323-x"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s10182-018-0323-x'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s10182-018-0323-x'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s10182-018-0323-x'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s10182-018-0323-x'


 

This table displays all metadata directly associated to this object as RDF triples.

132 TRIPLES      21 PREDICATES      44 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s10182-018-0323-x schema:about anzsrc-for:01
2 anzsrc-for:0104
3 schema:author Ne39925031d964ddf9b4b9f50afa0f948
4 schema:citation sg:pub.10.1007/978-0-387-71797-5
5 sg:pub.10.1007/978-1-4684-0192-9
6 sg:pub.10.1007/s00184-010-0331-7
7 https://doi.org/10.1002/(sici)1520-6750(199908)46:5<507::aid-nav4>3.0.co;2-d
8 https://doi.org/10.1002/9780470191613
9 https://doi.org/10.1002/nav.20407
10 https://doi.org/10.1002/nav.20449
11 https://doi.org/10.1016/j.csda.2012.05.004
12 https://doi.org/10.1016/s0167-9473(01)00091-3
13 https://doi.org/10.1080/00949650903292650
14 https://doi.org/10.1080/03610920600966316
15 https://doi.org/10.1080/10485252.2011.559547
16 https://doi.org/10.1109/tr.2002.801853
17 https://doi.org/10.1109/tr.2011.2134371
18 https://doi.org/10.1109/tr.2015.2417373
19 https://doi.org/10.1177/1748006x13485188
20 https://doi.org/10.1214/aos/1176346060
21 schema:datePublished 2019-03
22 schema:datePublishedReg 2019-03-01
23 schema:description In science and engineering, we are often interested in learning about the lifetime characteristics of the system as well as those of the components that made up the system. However, in many cases, the system lifetimes can be observed but not the component lifetimes, and so we may not also have any knowledge on the structure of the system. Statistical procedures for estimating the parameters of the component lifetime distribution and for identifying the system structure based on system-level lifetime data are developed here using expectation–maximization (EM) algorithm. Different implementations of the EM algorithm based on system-level or component-level likelihood functions are proposed. A special case that the system is known to be a coherent system with unknown structure is considered. The methodologies are then illustrated by considering the component lifetimes to follow a two-parameter Weibull distribution. A numerical example and a Monte Carlo simulation study are used to evaluate the performance and related merits of the proposed implementations of the EM algorithm. Lognormally distributed component lifetimes and a real data example are used to illustrate how the methodologies can be applied to other lifetime models in addition to the Weibull model. Finally, some recommendations along with concluding remarks are provided.
24 schema:genre research_article
25 schema:inLanguage en
26 schema:isAccessibleForFree false
27 schema:isPartOf N39a906a36e5242ebab0b977a6141a70a
28 Nc4d03d260b49400a957e9b06e08d7e65
29 sg:journal.1312118
30 schema:name Expectation–maximization algorithm for system-based lifetime data with unknown system structure
31 schema:pagination 69-98
32 schema:productId N4af2cbc40c65439692b4e195985846f9
33 N5429cbb3335f4734a07b64cf857979a8
34 Nb952af1f88e547dcb00c39e219afdf17
35 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101398175
36 https://doi.org/10.1007/s10182-018-0323-x
37 schema:sdDatePublished 2019-04-11T13:57
38 schema:sdLicense https://scigraph.springernature.com/explorer/license/
39 schema:sdPublisher N54629de974534c9090831cf1da01889a
40 schema:url https://link.springer.com/10.1007%2Fs10182-018-0323-x
41 sgo:license sg:explorer/license/
42 sgo:sdDataset articles
43 rdf:type schema:ScholarlyArticle
44 N39a906a36e5242ebab0b977a6141a70a schema:issueNumber 1
45 rdf:type schema:PublicationIssue
46 N4af2cbc40c65439692b4e195985846f9 schema:name readcube_id
47 schema:value 740053fd30f35188da0691149926fe97f7b5b9eb1569f57f0cfd230bf0e07730
48 rdf:type schema:PropertyValue
49 N5429cbb3335f4734a07b64cf857979a8 schema:name dimensions_id
50 schema:value pub.1101398175
51 rdf:type schema:PropertyValue
52 N54629de974534c9090831cf1da01889a schema:name Springer Nature - SN SciGraph project
53 rdf:type schema:Organization
54 Nb952af1f88e547dcb00c39e219afdf17 schema:name doi
55 schema:value 10.1007/s10182-018-0323-x
56 rdf:type schema:PropertyValue
57 Nbcabc14b3ff94f7288e082a2e584c736 rdf:first sg:person.013611575357.41
58 rdf:rest Ne0ed7ebf98664c6ab62b542c8417640a
59 Nc4d03d260b49400a957e9b06e08d7e65 schema:volumeNumber 103
60 rdf:type schema:PublicationVolume
61 Ne0ed7ebf98664c6ab62b542c8417640a rdf:first sg:person.0666004356.22
62 rdf:rest rdf:nil
63 Ne39925031d964ddf9b4b9f50afa0f948 rdf:first sg:person.010760741657.33
64 rdf:rest Nbcabc14b3ff94f7288e082a2e584c736
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:0104 schema:inDefinedTermSet anzsrc-for:
69 schema:name Statistics
70 rdf:type schema:DefinedTerm
71 sg:journal.1312118 schema:issn 1863-8171
72 1863-818X
73 schema:name AStA Advances in Statistical Analysis
74 rdf:type schema:Periodical
75 sg:person.010760741657.33 schema:affiliation https://www.grid.ac/institutes/grid.263864.d
76 schema:familyName Yang
77 schema:givenName Yandan
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.010760741657.33
79 rdf:type schema:Person
80 sg:person.013611575357.41 schema:affiliation https://www.grid.ac/institutes/grid.263864.d
81 schema:familyName Ng
82 schema:givenName Hon Keung Tony
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013611575357.41
84 rdf:type schema:Person
85 sg:person.0666004356.22 schema:affiliation https://www.grid.ac/institutes/grid.25073.33
86 schema:familyName Balakrishnan
87 schema:givenName Narayanaswamy
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0666004356.22
89 rdf:type schema:Person
90 sg:pub.10.1007/978-0-387-71797-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011972383
91 https://doi.org/10.1007/978-0-387-71797-5
92 rdf:type schema:CreativeWork
93 sg:pub.10.1007/978-1-4684-0192-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017252284
94 https://doi.org/10.1007/978-1-4684-0192-9
95 rdf:type schema:CreativeWork
96 sg:pub.10.1007/s00184-010-0331-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009417482
97 https://doi.org/10.1007/s00184-010-0331-7
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1002/(sici)1520-6750(199908)46:5<507::aid-nav4>3.0.co;2-d schema:sameAs https://app.dimensions.ai/details/publication/pub.1032994824
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1002/9780470191613 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098661620
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1002/nav.20407 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035427414
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1002/nav.20449 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019829193
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/j.csda.2012.05.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1046906549
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1016/s0167-9473(01)00091-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002981483
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1080/00949650903292650 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051963230
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1080/03610920600966316 schema:sameAs https://app.dimensions.ai/details/publication/pub.1058327896
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1080/10485252.2011.559547 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011610635
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1109/tr.2002.801853 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061782892
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1109/tr.2011.2134371 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061783536
120 rdf:type schema:CreativeWork
121 https://doi.org/10.1109/tr.2015.2417373 schema:sameAs https://app.dimensions.ai/details/publication/pub.1061783913
122 rdf:type schema:CreativeWork
123 https://doi.org/10.1177/1748006x13485188 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064073459
124 rdf:type schema:CreativeWork
125 https://doi.org/10.1214/aos/1176346060 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064408013
126 rdf:type schema:CreativeWork
127 https://www.grid.ac/institutes/grid.25073.33 schema:alternateName McMaster University
128 schema:name Department of Mathematics and Statistics, McMaster University, L8S 4K1, Hamilton, ON, Canada
129 rdf:type schema:Organization
130 https://www.grid.ac/institutes/grid.263864.d schema:alternateName Southern Methodist University
131 schema:name Department of Statistical Science, Southern Methodist University, 75275-0332, Dallas, TX, USA
132 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...