Applied Nonparametric Statistics in Reliability

Gámiz, María Luz; Kulasekera, K. B.; Limnios, Nikolaos; Lindqvist, Bo Henry

doi:10.1007/978-0-85729-118-9

Cited by 36 publications

(33 citation statements)

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“…To do so, we constructed point estimators for the survival function using the Kaplan-Meier estimator, and its complement, the cumulative density function [10]. As shown below, our estimate of these functions falls within the 90% confidence interval for the empirical function.…”

Section: Methodsmentioning

confidence: 85%

“…From an estimate of the probability density, we then constructed an estimate of the survival function [10] and compared it against the empirical survival function. We determined the empirical survival function from the data using the Kaplan-Meier estimator, which is defined as follows:…”

Section: Methodsmentioning

confidence: 99%

“…where n i is the number of the population at risk in each time interval, t i , and f i is the number of failures in each time period [10] [11].Ŝ(t) gives a point estimate of the survival function, accounting for censoring of the data, specifically right-censored data [10]. Right-censoring of data is when a member of a population is removed from a study with an indefinite end result.…”

Section: Methodsmentioning

confidence: 99%

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A Reliability Analysis of Personnel Protection Systems at the Spallation Neutron Source

Spannaus¹

2015

SIURO

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In this paper we present and analyze field gathered system reliability data from the Oxygen monitoring and Access Control systems managed by the Protection Systems team at the Spallation Neutron Source at the Oak Ridge National Laboratory. The time span of the data varies from roughly fourteen years for systems in place as the linear accelerator was being built and tested, to a few months for the newest instrument beam lines.We analyzed the time to fail for the above systems, accounting for censored data, and developed a nonparametric probability model of the overall reliability for each system. From this probabilistic model, we were able to estimate the survivor and hazard functions, and find good correlation between these estimates and their empirical counterparts. Moreover, we used our model to find whether or not each system's life distribution is New Better than Used.

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Section: Methodsmentioning

confidence: 85%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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A Reliability Analysis of Personnel Protection Systems at the Spallation Neutron Source

Spannaus¹

2015

SIURO

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“…That is, we first estimate the regression parameters as it is explained in Section 3.2 and, second we obtain the survival function evaluated at the observed data times transformed to the baseline time-scale (see Section 3.3). To calculate the local linear estimator we have considered the Epanechnikov kernel, K(t) = (1 − t 2 )I(| t |≤ 1), and the bandwidth parameter has been chosen using the reference rule (see Gámiz et al [28], pp. 44).…”

Section: Simulation Studymentioning

confidence: 99%

“…To estimate the baseline survival function we have considered the local linear estimator proposed in Section 3.3, equation (8). As in Section 4 we have calculated the estimator using the Epanechnikov kernel and the bandwidth parameter has been chosen using the reference rule (following the suggestions by Gámiz et al [28], pp. 44), which provides the value b = 0.0707.…”

Section: The Proposed Approachmentioning

confidence: 99%

Local linear smoothing to estimate accelerated lifetime model with censoring and truncation

López-Montoya

Gámiz‐Pérez

Martínez-Miranda

2015

Applied Mathematical Modelling

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Local linear smoothing to estimate accelerated lifetime model with censoring and truncation. Applied Mathematical Modelling, 39(16), doi: 10.1016Modelling, 39(16), doi: 10. /j.apm.2015 This is the accepted version of the paper.This version of the publication may differ from the final published version. Permanent University of Granada María Dolores Martínez-Miranda University of Granada Cass Business School, City University London AbstractA nonparametric Accelerated Failure Time (AFT ) model is considered to evaluate the dependability measures of a water supply system laid in a city of the Mediterranean Sea. To do it, a set of breakdown data of sections of pipe of the system is available.Unlike the usual methods that assume a parametric family for the underlying lifetime, we propose an AFT model with an unspecified distribution for the underlying lifetime.To carry out the model fitting we suggest a two-stage procedure. Firstly, we estimate the influence of certain factors over the lifetime of the system. Secondly, we propose modern and flexible statistical tools based on counting processes to construct a smooth estimate the reliability measure of a specific system. We prove the good asymptotic properties of the estimator.Simulation experiments show that the proposed methods have a good performance for finite samples and improve on the performance of other semi-parametric methods commonly used in practice.

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Data Visualization in Reliability of Repairable Systems: The SiZer Map Tool

Gámiz

López-Montoya

Martínez-Miranda

et al. 2020

Wiley StatsRef: Statistics Reference Online

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In this article, the graphical exploratory tool SiZer Map is constructed for the inference of the rate of occurrences of events that follow a nonhomogeneous Poisson process. SiZer Map is defined considering nonparametric local linear kernel estimators for the rate function and its first derivative. The bandwidth parameter is the viewing scale, and the considered time interval is the localization space. The shape characteristics of the rate function are distinguished from those which are merely an artifact of the sampling variability of the data through confidence intervals for the first derivative. The proposal is illustrated with some real data sets that represent recurrent events in time.

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Applied Nonparametric Statistics in Reliability

Cited by 36 publications

References 0 publications

A Reliability Analysis of Personnel Protection Systems at the Spallation Neutron Source

A Reliability Analysis of Personnel Protection Systems at the Spallation Neutron Source

Local linear smoothing to estimate accelerated lifetime model with censoring and truncation

Data Visualization in Reliability of Repairable Systems: The SiZer Map Tool

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