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Stress-strength based on m -generalized order statistics and concomitant for dependent families

Filippo Domma, Abbas Eftekharian, Mostafa Razmkhah (2019)

Applications of Mathematics

The stress-strength model is proposed based on the m -generalized order statistics and the corresponding concomitant. For the dependency between m -generalized order statistics and its concomitant, a bivariate copula expansion is considered and the stress-strength model is obtained for two special cases of order statistics and upper record values. In the particular case of copula function, the generalized Farlie-Gumbel-Morgenstern bivariate distribution function is considered with proportional reversed...

Suavización no paramétrica en fiabilidad.

M.ª Angeles Fernández Sotelo, Wenceslao González Manteiga (1986)

Trabajos de Estadística

En este trabajo consideramos estimaciones no paramétricas de las funciones de razón de fallo y supervivencia en fiabilidad haciendo uso de suavizaciones no paramétricas de la función de distribución empírica (datos no censurados) y de la distribución de Kaplan-Meier (datos censurados). Se obtienen sesgos, varianzas y distribuciones asintóticas de los estimadores aquí propuestos probándose mediante técnicas de expansiones de segundo orden la eficiencia de éstos respecto de otras estimaciones introducidas...

Symmetric models for lifetimes: the role of exchangeable equivalence relations

Anna Gerardi, Barbara Torti (2003)

Bollettino dell'Unione Matematica Italiana

A model of a heterogeneous population partitioned into a finite number of classes according an exchangeable equivalence relation is studied. With this motivation the properties of exchangeable equivalence relations are investigated and, in particular, the structure of its equivalence classes is characterized.

Tail orderings and the total time on test transform

Jarosław Bartoszewicz (1996)

Applicationes Mathematicae

The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.

Test for exponentiality against Weibull and gamma decreasing hazard rate alternatives

Simos G. Meintanis (2007)

Kybernetika

A sub-exponential Weibull random variable may be expressed as a quotient of a unit exponential to an independent strictly positive stable random variable. Based on this property, we propose a test for exponentiality which is consistent against Weibull and Gamma distributions with shape parameter less than unity. A comparison with other procedures is also included.

Testing a homogeneity of stochastic processes

Jaromír Antoch, Daniela Jarušková (2007)

Kybernetika

The paper concentrates on modeling the data that can be described by a homogeneous or non-homogeneous Poisson process. The goal is to decide whether the intensity of the process is constant or not. In technical practice, e.g., it means to decide whether the reliability of the system remains the same or if it is improving or deteriorating. We assume two situations. First, when only the counts of events are known and, second, when the times between the events are available. Several statistical tests...

The Lorenz transform approach to the optimal repair-cost limit replacement policy with imperfect repair

T. Dohi, F. S. Othman, N. Kaio, Sunji Osaki (2001)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties...

The Lorenz Transform approach to the Optimal Repair-Cost limit remplacement Policy with Imperfect Repair

T. Dohi, F. S. Othman, N. Kaio, Sunji Osaki (2010)

RAIRO - Operations Research

In this paper, we consider a repair-cost limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair-cost limit which minimizes the expected cost per unit time in the steady-state, using the Lorenz transform of the underlying repair-cost distribution function. The method proposed can be applied to an estimation problem of the optimal repair-cost limit from empirical repair-cost data. Numerical examples are devoted to examine asymptotic properties...

The optimal control chart procedure

Jaroslav Skřivánek (2004)

Kybernetika

The moving average (MA) chart, the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart are the most popular schemes for detecting shifts in a relevant process parameter. Any control chart system of span k is specified by a partition of the space ℝ k into three disjoint parts. We call this partition as the control chart frame of span k . A shift in the process parameter is signalled at time t by having the vector of the last k sample characteristics fall out of the...

Theoretical aspects of total time on test transform of weighted variables and applications

Mojtaba Esfahani, Gholam Reza Mohtashami-Borzadaran, Mohammad Amini (2023)

Kybernetika

Although the total time on test (TTT) transform is not a newly discovered concept, it has many applications in various fields. On the other hand, weighted distributions are extensively developed by the statisticians to tackle the insufficiency of the standard statistical distributions in modeling the arising data from real-world problems in the contexts like medicine, ecology, and reliability engineering. This paper develops the TTT transform for the weighted random variables and investigates the...

Una medida matricial para la comparación de experimentos censurados.

Agustín Turrero Nogués (1988)

Qüestiió

En este trabajo se desarrolla un método de comparación de experimentos con datos censurados. Dicho método se basa en la evaluación de la pérdida de información que se produce en estudios de supervivencia y fiabilidad cuando los tiempos de vida se censuran aleatoriamente por la derecha. Se supone que la distribución del tiempo de vida depende de un parámetro k-variante desconocido θ; y se usa la matriz de Fisher como medida de información apropiada acerca de θ. Se propone una medida matricial de...

Unbiased estimation for two-parameter exponential distribution under time censored sampling

S. Sengupta (2009)

Applicationes Mathematicae

The problem considered is that of unbiased estimation for a two-parameter exponential distribution under time censored sampling. We obtain a necessary form of an unbiasedly estimable parametric function and prove that there does not exist any unbiased estimator of the parameters and the mean of the distribution. For reliability estimation at a specified time point, we give a necessary and sufficient condition for the existence of an unbiased estimator and suggest an unbiased estimator based on a...

Unbiased estimation of reliability for two-parameter exponential distribution under time censored sampling

S. Sengupta (2010)

Applicationes Mathematicae

The problem considered is that of unbiased estimation of reliability for a two-parameter exponential distribution under time censored sampling. We give necessary and sufficient conditions for the existence of uniformly minimum variance unbiased estimator and also provide a characterization of a complete class of unbiased estimators in situations where unbiased estimators exist.

Weighting, likelihood ratio order and life distributions

Magdalena Skolimowska, Jarosław Bartoszewicz (2006)

Applicationes Mathematicae

We use weighted distributions with a weight function being a ratio of two densities to obtain some results of interest concerning life and residual life distributions. Our theorems are corollaries from results of Jain et al. (1989) and Bartoszewicz and Skolimowska (2006).

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