The failure rate dynamics in heterogeneous populations

Ji Hwan Cha; Maxim Finkelstein

doi:10.1016/j.ress.2012.11.012

The failure rate dynamics in heterogeneous populations

Ji Hwan Cha
, Maxim Finkelstein

Department of Statistics

Research output: Contribution to journal › Article › peer-review

28 Scopus citations

Abstract

Most populations encountered in real world are heterogeneous. In reliability applications, the mixture (observed) failure rate, obviously, can be considered as a measure of 'average' quality in these populations. However, in addition to this average measure, some variability characteristics for failure rates can be very helpful in describing the time-dependent changes in quality of heterogeneous populations. In this paper, we discuss variance and the coefficient of variation of the corresponding random failure rate as variability measures for items in heterogeneous populations. Furthermore, there is often a risk that items of poor quality are selected for important missions. Therefore, along with the 'average quality' of a population, more 'conservative' quality measures should be also defined and studied. For this purpose, we propose the percentile and the tail-mixture of the failure rates as the corresponding conservative measures. Some illustrative examples are given.

Original language	English
Pages (from-to)	120-128
Number of pages	9
Journal	Reliability Engineering and System Safety
Volume	112
DOIs	https://doi.org/10.1016/j.ress.2012.11.012
State	Published - 2013

Bibliographical note

Funding Information:
The authors thank the referees for helpful and constructive comments and suggestions, which have greatly improved the presentation of this paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002.

Keywords

Coefficient of variation
Heterogeneous population
Quality measures
Stochastically ordered subpopulations
Variance

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10.1016/j.ress.2012.11.012

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title = "The failure rate dynamics in heterogeneous populations",

abstract = "Most populations encountered in real world are heterogeneous. In reliability applications, the mixture (observed) failure rate, obviously, can be considered as a measure of 'average' quality in these populations. However, in addition to this average measure, some variability characteristics for failure rates can be very helpful in describing the time-dependent changes in quality of heterogeneous populations. In this paper, we discuss variance and the coefficient of variation of the corresponding random failure rate as variability measures for items in heterogeneous populations. Furthermore, there is often a risk that items of poor quality are selected for important missions. Therefore, along with the 'average quality' of a population, more 'conservative' quality measures should be also defined and studied. For this purpose, we propose the percentile and the tail-mixture of the failure rates as the corresponding conservative measures. Some illustrative examples are given.",

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note = "Funding Information: The authors thank the referees for helpful and constructive comments and suggestions, which have greatly improved the presentation of this paper. The work of the first author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2011-0017338 ). The work of the first author was supported by Priority Research Centers Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education, Science and Technology ( 2009-0093827 ). The work of the second author was supported by the NRF (National Research Foundation of South Africa) grant FA2006040700002.",

year = "2013",

doi = "10.1016/j.ress.2012.11.012",

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N2 - Most populations encountered in real world are heterogeneous. In reliability applications, the mixture (observed) failure rate, obviously, can be considered as a measure of 'average' quality in these populations. However, in addition to this average measure, some variability characteristics for failure rates can be very helpful in describing the time-dependent changes in quality of heterogeneous populations. In this paper, we discuss variance and the coefficient of variation of the corresponding random failure rate as variability measures for items in heterogeneous populations. Furthermore, there is often a risk that items of poor quality are selected for important missions. Therefore, along with the 'average quality' of a population, more 'conservative' quality measures should be also defined and studied. For this purpose, we propose the percentile and the tail-mixture of the failure rates as the corresponding conservative measures. Some illustrative examples are given.

AB - Most populations encountered in real world are heterogeneous. In reliability applications, the mixture (observed) failure rate, obviously, can be considered as a measure of 'average' quality in these populations. However, in addition to this average measure, some variability characteristics for failure rates can be very helpful in describing the time-dependent changes in quality of heterogeneous populations. In this paper, we discuss variance and the coefficient of variation of the corresponding random failure rate as variability measures for items in heterogeneous populations. Furthermore, there is often a risk that items of poor quality are selected for important missions. Therefore, along with the 'average quality' of a population, more 'conservative' quality measures should be also defined and studied. For this purpose, we propose the percentile and the tail-mixture of the failure rates as the corresponding conservative measures. Some illustrative examples are given.

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KW - Stochastically ordered subpopulations

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JO - Reliability Engineering and System Safety

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ER -

The failure rate dynamics in heterogeneous populations

Abstract

Bibliographical note

Keywords

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