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2014 | OriginalPaper | Buchkapitel

2. Basic Mathematical Concepts

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Abstract

Just like in other areas of science and engineering, mathematics also plays an important role in the area of human reliability, error, and human factors. The history of mathematics may be traced back to more than 2,200 years to the development of our day-to-day used number symbols.

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Literatur
1.
Zurück zum Zitat Eves H (1976) An introduction to the history of mathematics. Holt, Rinehart, and Winston, New YorkMATH Eves H (1976) An introduction to the history of mathematics. Holt, Rinehart, and Winston, New YorkMATH
2.
Zurück zum Zitat Owen DB (ed) (1976) On the history of statistics and probability. Marcel Dekker, New YorkMATH Owen DB (ed) (1976) On the history of statistics and probability. Marcel Dekker, New YorkMATH
3.
Zurück zum Zitat Lipschutz S (1964) Set theory and related topics. McGraw Hill Book Company, New YorkMATH Lipschutz S (1964) Set theory and related topics. McGraw Hill Book Company, New YorkMATH
4.
Zurück zum Zitat Lipschutz S (1965) Probability. McGraw Hill Book Company, New York Lipschutz S (1965) Probability. McGraw Hill Book Company, New York
5.
Zurück zum Zitat Fault Tree Handbook (1981) Report No. NUREG-0492, U.S. Nuclear Regulatory Commission, Washington, D.C. Fault Tree Handbook (1981) Report No. NUREG-0492, U.S. Nuclear Regulatory Commission, Washington, D.C.
6.
Zurück zum Zitat Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New YorkMATH Mann NR, Schafer RE, Singpurwalla ND (1974) Methods for statistical analysis of reliability and life data. Wiley, New YorkMATH
7.
Zurück zum Zitat Shooman ML (1968) Probabilistic reliability: an engineering approach. McGraw-Hill Book Company, New York Shooman ML (1968) Probabilistic reliability: an engineering approach. McGraw-Hill Book Company, New York
8.
Zurück zum Zitat Spiegel MR (1965) Laplace transforms. McGraw Hill Book Company, New York Spiegel MR (1965) Laplace transforms. McGraw Hill Book Company, New York
9.
10.
Zurück zum Zitat Patel JK, Kapadia CH, Owen DB (1976) Handbook of statistical distributions. Marcel Dekker, New YorkMATH Patel JK, Kapadia CH, Owen DB (1976) Handbook of statistical distributions. Marcel Dekker, New YorkMATH
11.
Zurück zum Zitat Davis DJ (1952) An analysis of some failure data. J Am Stat Assoc 113–150 Davis DJ (1952) An analysis of some failure data. J Am Stat Assoc 113–150
12.
Zurück zum Zitat Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297MATH Weibull W (1951) A statistical distribution function of wide applicability. J Appl Mech 18:293–297MATH
14.
Zurück zum Zitat Baker AD (1993) A nonparametric estimation of the renewal function. Comput Oper Res 20(2):167–178CrossRefMATH Baker AD (1993) A nonparametric estimation of the renewal function. Comput Oper Res 20(2):167–178CrossRefMATH
15.
Zurück zum Zitat Cabana A, Cabana EM (2005) Goodness-of-fit to the exponential distribution, focused on Weibull alternatives. Commun Stat Simul Comput 34:711–723CrossRefMATHMathSciNet Cabana A, Cabana EM (2005) Goodness-of-fit to the exponential distribution, focused on Weibull alternatives. Commun Stat Simul Comput 34:711–723CrossRefMATHMathSciNet
16.
17.
Zurück zum Zitat Henze N, Meintnis SG (2005) Recent and classical tests for exponentiality: a partial review with comparisons. Metrika 61:29–45CrossRefMATHMathSciNet Henze N, Meintnis SG (2005) Recent and classical tests for exponentiality: a partial review with comparisons. Metrika 61:29–45CrossRefMATHMathSciNet
18.
Zurück zum Zitat Hollander M, Laird G, Song KS (2003) Nonparametric interference for the proportionality function in the random censorship model. Nonparametric Stat 15(2):151–169CrossRefMATHMathSciNet Hollander M, Laird G, Song KS (2003) Nonparametric interference for the proportionality function in the random censorship model. Nonparametric Stat 15(2):151–169CrossRefMATHMathSciNet
19.
Zurück zum Zitat Jammalamadaka SR, Taufer E (2003) Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data. J Nonparametric Stat 15(6):719–729CrossRefMATHMathSciNet Jammalamadaka SR, Taufer E (2003) Testing exponentiality by comparing the empirical distribution function of the normalized spacings with that of the original data. J Nonparametric Stat 15(6):719–729CrossRefMATHMathSciNet
20.
Zurück zum Zitat Jammalamadaka SR, Taufer E (2006) Use of mean residual life in testing departures from exponentiality. J Nonparametric Stat 18(3):277–292CrossRefMATHMathSciNet Jammalamadaka SR, Taufer E (2006) Use of mean residual life in testing departures from exponentiality. J Nonparametric Stat 18(3):277–292CrossRefMATHMathSciNet
21.
Zurück zum Zitat Kunitz H (1989) A new class of bathtub-shaped hazard rates and its application in comparison of two test-statistics. IEEE Trans Reliab 38(3):351–354CrossRefMATH Kunitz H (1989) A new class of bathtub-shaped hazard rates and its application in comparison of two test-statistics. IEEE Trans Reliab 38(3):351–354CrossRefMATH
23.
Zurück zum Zitat Meintanis SG (2009) A class of tests for exponentiality based on a continuum of moment conditions. Kybernetika 45(6):946–959MATHMathSciNet Meintanis SG (2009) A class of tests for exponentiality based on a continuum of moment conditions. Kybernetika 45(6):946–959MATHMathSciNet
24.
Zurück zum Zitat Morris K, Szynal D (2008) Some U-statistics in goodness-of-fit tests derived from characterizations via record values. Int J Pure Appl Math 46(4):339–414MathSciNet Morris K, Szynal D (2008) Some U-statistics in goodness-of-fit tests derived from characterizations via record values. Int J Pure Appl Math 46(4):339–414MathSciNet
25.
Zurück zum Zitat Morris K, Szynal D (2007) Goodness-of-fit tests based on characterizations involving moments of order statistics. Int J Pure Appl Math 38(1):83–121MATHMathSciNet Morris K, Szynal D (2007) Goodness-of-fit tests based on characterizations involving moments of order statistics. Int J Pure Appl Math 38(1):83–121MATHMathSciNet
26.
Zurück zum Zitat Na MH (1999) Spline hazard rate estimation using censored data. J KSIAM 3(2):99–106 Na MH (1999) Spline hazard rate estimation using censored data. J KSIAM 3(2):99–106
27.
Zurück zum Zitat Nam KH, Chang SJ (2006) Approximation of the renewal function for Hjorth model and Dhillon model. J Korean Soc Qual Manage 34(1):34–39 Nam KH, Chang SJ (2006) Approximation of the renewal function for Hjorth model and Dhillon model. J Korean Soc Qual Manage 34(1):34–39
28.
Zurück zum Zitat Nam KH, Park DH (1997) Failure rate for Dhillon model. In: Proceedings of the spring conference of the Korean society, pp 114–118 Nam KH, Park DH (1997) Failure rate for Dhillon model. In: Proceedings of the spring conference of the Korean society, pp 114–118
29.
Zurück zum Zitat Nimoto N, Zitikis R (2008) The Atkinson index, the moran statistic, and testing exponentiality. J Jpn Stat Soc 38(2):187–205CrossRef Nimoto N, Zitikis R (2008) The Atkinson index, the moran statistic, and testing exponentiality. J Jpn Stat Soc 38(2):187–205CrossRef
30.
Zurück zum Zitat Noughabi HA, Arghami NR (2011) Testing exponentiality based on characterizations of the exponential distribution. J Stat Comput Simul i First:1–11 Noughabi HA, Arghami NR (2011) Testing exponentiality based on characterizations of the exponential distribution. J Stat Comput Simul i First:1–11
31.
Zurück zum Zitat Szynal D (2010) Goodness-of-fit tests derived from characterizations of continuous distributions, stability in probability, Banach Center Publications, vol 90. Institute of Mathematics, Polish Academy of Sciences, Warszawa, pp 203–223 Szynal D (2010) Goodness-of-fit tests derived from characterizations of continuous distributions, stability in probability, Banach Center Publications, vol 90. Institute of Mathematics, Polish Academy of Sciences, Warszawa, pp 203–223
32.
Zurück zum Zitat Szynal D, Wolynski W (2012) Goodness-of-fit tests for exponentiality and Rayleigh distribution. Int J Pure Appl Math 78(5):751–772 Szynal D, Wolynski W (2012) Goodness-of-fit tests for exponentiality and Rayleigh distribution. Int J Pure Appl Math 78(5):751–772
33.
Zurück zum Zitat Na MH, Lee HW, Kim JJ (1997) A smooth estimation of failure rate function. J Korean Soc Qual Manage 25(3):51–61 Na MH, Lee HW, Kim JJ (1997) A smooth estimation of failure rate function. J Korean Soc Qual Manage 25(3):51–61
Metadaten
Titel
Basic Mathematical Concepts
verfasst von
B. S. Dhillon
Copyright-Jahr
2014
DOI
https://doi.org/10.1007/978-3-319-04019-6_2

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