| 1. |
- Basu, A.P, et al.
(author)
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Multivariate harmonic new better than used in expectation distributions
- 1983
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In: Scandinavian Journal of Statistics. - 0303-6898 .- 1467-9469. ; 10:1, s. 19-25
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Journal article (peer-reviewed)abstract
- Various definitions of multivariate harmonic new better than used in expectation (MHNBUE) life distributions are introduced and their interrelationships are studied. The definitions are multivariate generalizations of the univariate aging property HNBUE which is weaker than the new better than used in expectation (NBUE) property. Various closure properties of the different MHNBUE classes are proved. Some examples are also given to illustrate the relationships between our MHNBUE properties and the MNBUE properties presented by Buchanan and Singpurwalla (1977). We also study the dual multivariate harmonic new worse than used in expectation (MHNWUE) classes
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| 2. |
- Bergman, Bo, et al.
(author)
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A family of test statistics for detecting monotone mean residual life
- 1989
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In: Journal of Statistical Planning and Inference. - : Elsevier BV. - 0378-3758 .- 1873-1171. ; 21:2, s. 161-178
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Journal article (peer-reviewed)abstract
- The mean residual life of a life distribution F with survival function F̄=1-F is defined as e(x)=(sh{phonetic}∞xF̄(t)dt)/F̄(x) if F̄(x)>0 (e(x)=0 if F̄(x)=0). The function e(x) has proved to be of great interest in many different areas such as biometry, reliability and social sciences. The class DMRL (IMRL) consists of those life distributions which have decreasing (increasing) mean residual life; i.e. e(x) is a decreasing (increasing) function of x. In this paper we present and study a family of test statistics intended for testing exponentiality against DMRL (IMRL). The family includes the test statistics proposed for the same purpose by Hollander and Proschan (1975) for complete samples and later generalized by Chen et al. (1983a) to accomodate randomly right censored samples. We compare the efficiency for different members in the family of test statistics when testing against some different alternatives. Furthermore, we study the efficiency loss due to different amount of exponential censoring. The asymptotical normal distribution of the test statistics are presented and the quality of the normal approximation is also discussed
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| 3. |
- Bergman, Bo, et al.
(author)
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A graphical method applicable to age-replacement problems
- 1982
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In: IEEE Transactions on Reliability. - 0018-9529 .- 1558-1721. ; R-31:5, s. 478-481
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Journal article (peer-reviewed)abstract
- The Total Time on Test (TTT) concept has proven to be a very useful tool in several reliability contexts. The objective of this note is to illustrate how a generalization of the TTT-concept, the TTT-transform, defined as a certain function of the survivor function, can be used when analyzing different types of age-replacement problems. (14 refs.)
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| 4. |
- Bergman, Bo, et al.
(author)
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A note on some test statistics against HNBUE
- 1987
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In: Annals of the Institute of Statistical Mathematics. - 0020-3157 .- 1572-9052. ; 39:3, s. 483-488
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Journal article (peer-reviewed)abstract
- Some comments and extensions are given to the paper on statistics for testing exponentiality against the HNBUEE property (i.e. {Mathematical expression} ≦μ exp(-t/μ), t≧0) by Basu and Ebrahimi
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| 5. |
- Bergman, Bo, et al.
(author)
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Letter to the editors
- 1988
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In: Reliability Engineering & System Safety. - : Elsevier BV. - 0951-8320 .- 1879-0836. ; 21:2, s. 155-160
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Journal article (other academic/artistic)
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| 6. |
- Bergman, Bo, et al.
(author)
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Testing against HNBUE with randomly censored data
- 1985
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In: Contributions to probability and statistics in honour of Gunnar Blom. - Lund : Lund University. Department of Mathematical Statistics. ; , s. 49-72
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Book chapter (other academic/artistic)abstract
- The "harmonic new better than used in expectation" (HNBUE) class of life distributions contains all the more familiar classes from reliability theory such as the "increasing failure rate" (IFR) and "new better than used" (NBU), while still allowing one to formulate interesting inequalities comparing such distributions with the memoryless exponential distribution. In this paper test statistics based on the product-limit estimator are derived for testing the hypothesis of HNBUE versus exponentiality given a sample of censored observations from the life distribution of interest. A study of the asymptotic relative efficiency focusses on the loss of information due to censoring.
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| 7. |
- Bergman, Bo, et al.
(author)
-
The total time on test concept and its use in reliability theory
- 1984
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In: Operations Research. - : Institute for Operations Research and the Management Sciences (INFORMS). - 0030-364X .- 1526-5463. ; 32:3, s. 596-606
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Journal article (peer-reviewed)abstract
- More than 30 years ago, Epstein and Sobel introduced the Total Time on Test (TTT-) concept. During the last 10 years different generalizations of this concept have been defined and studied, e.g. the TTT-transform and the TTT-plot; a basic paper was presented by Barlow and Campo in 1975. Many of these generalizations have proven to be very useful in different areas of reliability, both from a theoretical and a practical point of view. The purpose of this expository paper is to present some of these generalizations and illustrate their value.
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| 8. |
- Bergman, Bo, et al.
(author)
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TTT-concept and replacements to extend system life
- 1987
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In: European Journal of Operational Research. - 0377-2217 .- 1872-6860. ; 28:3, s. 302-307
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Journal article (peer-reviewed)abstract
- In a number of papers the current authors have illustrated how the Total Time on Test (TTT) concept can be used when analysing the ordinary age replacement problem and different generalization thereof. In this paper we show that the TTT-concept is very useful also when analysing another replacement problem discussed by C. Derman et al. in which the replacements of a vital component, for which there are n space units, are made with the goal of maximizing the expected system life. (12 refs.)
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| 9. |
- Bergman, Bo, et al.
(author)
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TTT transforms and age replacements with discounted costs
- 1983
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In: Naval Research Logistics Quarterly. - : Wiley. - 0028-1441 .- 1931-9193. ; 30:4, s. 631-639
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Journal article (peer-reviewed)abstract
- The ordinary age replacement problem consists of finding an optimal age at which a unit, needed in a continuous production process, should be replaced in order to minimize the average long-run cost per unit time. Bergman introduced a graphical procedure based on the total-time-on-test (TTT) concept for the analysis of the age replacement problem. In this article, that idea is generalized to the situation of discounted costs. We also study a more general age replacement problem in which we have a form of imperfect repair.
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| 10. |
- Klefsjö, Bengt
(author)
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A useful ageing property based on the Laplace transform
- 1983
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In: Journal of Applied Probability. - : Cambridge University Press (CUP). - 0021-9002 .- 1475-6072. ; 20:3, s. 615-626
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Journal article (peer-reviewed)abstract
- The class of life distributions for which , where , and , is studied. We prove that this class is larger than the HNBUE (HNWUE) class (consisting of those life distributions for which for x ≧ 0) and present results concerning closure properties under some usual reliability operations. We also study some shock models and a certain cumulative damage model. The class of discrete life distributions for which for 0 ≦ p ≦ 1, where , is also studied.
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