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Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair
We introduce a general transformation of hazard rates and discuss the corresponding change of a life length distribution. Minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes, and in particular...
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| Published in: | Mathematics of operations research 1989-05, Vol.14 (2), p.355-361 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c284t-d0d985937e14294e671325889749089f2ca3588c47a8f6da09db0774a1d18eff3 |
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| container_end_page | 361 |
| container_issue | 2 |
| container_start_page | 355 |
| container_title | Mathematics of operations research |
| container_volume | 14 |
| creator | Arjas, E Norros, I |
| description | We introduce a general transformation of hazard rates and discuss the corresponding change of a life length distribution. Minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes, and in particular on the Girsanov theorem for point processes. We then study the role of the available information and the consequent definition of "state" in the change of distributions. By using the general notion of F -minimal repair, where F stands for the information which identifies the state of the considered device, we show that the "black box"-minimal repair modeling leads to a stochastically longer total life length than the more realistic one based on internal state information. Thus the former forms a potential source of bias in minimal repair modeling. |
| doi_str_mv | 10.1287/moor.14.2.355 |
| format | article |
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Minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes, and in particular on the Girsanov theorem for point processes. We then study the role of the available information and the consequent definition of "state" in the change of distributions. By using the general notion of F -minimal repair, where F stands for the information which identifies the state of the considered device, we show that the "black box"-minimal repair modeling leads to a stochastically longer total life length than the more realistic one based on internal state information. 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Thus the former forms a potential source of bias in minimal repair modeling.</description><subject>Climacteric</subject><subject>compensator</subject><subject>Girsanov's theorem</subject><subject>imperfect repair</subject><subject>Martingales</subject><subject>Mathematical inequalities</subject><subject>Mathematical models</subject><subject>Mathematical transformations</subject><subject>Operations research</subject><subject>Probability</subject><subject>Reliability</subject><subject>stochastic comparison</subject><subject>Stochastic models</subject><issn>0364-765X</issn><issn>1526-5471</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1989</creationdate><recordtype>article</recordtype><recordid>eNqFkM1LwzAYh4MoOD-O3jwEL17szJumTettzI8NJoJM8RayNlkztqZLOmT-9WbWgTdP4c3veT94ELoA0gea8duVta4PrE_7cZIcoB4kNI0SxuEQ9UicsoinyccxOvF-QQgkHFgPmWEl67nCVuOJ0QrfG986M9u0xtb43Ugs8Uh-SVfiqZO119at5C67w4Maj2u13silabf407QVHjTN0hQ_OW4tfja1WcklflWNNO4MHWm59Or89z1Fb48P0-Eomrw8jYeDSVTQjLVRSco8S_KYK2A0ZyrlENMky3LOcpLlmhYyDmXBuMx0WkqSlzPCOZNQQqa0jk_RVTe3cXa9Ub4VC7txdVgpKNAUOAANUNRBhbPeO6VF48KtbiuAiJ1MsZMpgAkqgszAX3b8wrfhfw_HabgL4hDfdLGpd4b8v9OuO7wy8-rTOCX2fUFu9Zf8BgH9jhI</recordid><startdate>19890501</startdate><enddate>19890501</enddate><creator>Arjas, E</creator><creator>Norros, I</creator><general>INFORMS</general><general>The Institute of Management Sciences and the Operations Research Society of America</general><general>Institute for Operations Research and the Management Sciences</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>19890501</creationdate><title>Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair</title><author>Arjas, E ; Norros, I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c284t-d0d985937e14294e671325889749089f2ca3588c47a8f6da09db0774a1d18eff3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1989</creationdate><topic>Climacteric</topic><topic>compensator</topic><topic>Girsanov's theorem</topic><topic>imperfect repair</topic><topic>Martingales</topic><topic>Mathematical inequalities</topic><topic>Mathematical models</topic><topic>Mathematical transformations</topic><topic>Operations research</topic><topic>Probability</topic><topic>Reliability</topic><topic>stochastic comparison</topic><topic>Stochastic models</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Arjas, E</creatorcontrib><creatorcontrib>Norros, I</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Mathematics of operations research</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Arjas, E</au><au>Norros, I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair</atitle><jtitle>Mathematics of operations research</jtitle><date>1989-05-01</date><risdate>1989</risdate><volume>14</volume><issue>2</issue><spage>355</spage><epage>361</epage><pages>355-361</pages><issn>0364-765X</issn><eissn>1526-5471</eissn><coden>MOREDQ</coden><abstract>We introduce a general transformation of hazard rates and discuss the corresponding change of a life length distribution. Minimal repair transformations are shown to be special cases of this framework which builds on general results concerning likelihood ratios for point processes, and in particular on the Girsanov theorem for point processes. We then study the role of the available information and the consequent definition of "state" in the change of distributions. By using the general notion of F -minimal repair, where F stands for the information which identifies the state of the considered device, we show that the "black box"-minimal repair modeling leads to a stochastically longer total life length than the more realistic one based on internal state information. Thus the former forms a potential source of bias in minimal repair modeling.</abstract><cop>Linthicum</cop><pub>INFORMS</pub><doi>10.1287/moor.14.2.355</doi><tpages>7</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0364-765X |
| ispartof | Mathematics of operations research, 1989-05, Vol.14 (2), p.355-361 |
| issn | 0364-765X 1526-5471 |
| language | eng |
| recordid | cdi_proquest_journals_212617112 |
| source | JSTOR Archival Journals and Primary Sources Collection; BSC - Ebsco (Business Source Ultimate) |
| subjects | Climacteric compensator Girsanov's theorem imperfect repair Martingales Mathematical inequalities Mathematical models Mathematical transformations Operations research Probability Reliability stochastic comparison Stochastic models |
| title | Change of Life Distribution Via a Hazard Transformation: An Inequality with Application to Minimal Repair |
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