Reliability Inference for a Copula-Based Series System Life Test Under Multiple Type-I Censoring

Hsu, Tsung-Ming; Emura, Takeshi

doi:10.1109/tr.2016.2515589

Cited by 27 publications

(15 citation statements)

References 32 publications

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Section: Introduction and Problem Descriptionmentioning

confidence: 99%

“…Copula models are a highly flexible and convenient way of describing the dependence structure of a multivariate distribution independent of the marginal distributions. While the usage of copulas became a well-established modeling tool in finance, copula models become more and more popular in reliability models as can be seen in the recent studies of Hsu 18 and Zhang. 19 The aim of this study, which was jointly conducted with Infineon Technologies Austria AG, is to find maximal and minimal allowable tolerance limits UTL and LTL for the initial measurements, ie, an upper and a lower guardband UG = USL − UTL and LG = LTL − LSL, respectively, such that the reliability and conformity requirements of the devices are fulfilled over their whole specified lifetime duration.…”

Section: Introduction and Problem Descriptionmentioning

confidence: 99%

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Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data

Hofer

Leitner

Lewitschnig

et al. 2017

Quality & Reliability Eng

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Design and production of semiconductor devices for the automotive industry are characterized by high reliability requirements, such that the proper functioning of these devices is ensured over the whole specified lifetime. Therefore, manufacturers let their products undergo extensive testing procedures that simulate the tough requirements their products have to withstand. Such tests typically are highly accelerated, to test the behavior of the products over the whole lifetime. In case of drift of electrical parameters, manufacturers then need to find appropriate tolerance limits for their final electrical product tests, such that the proper functioning of their devices over the whole specified lifetime is ensured. In this study, we present a statistical model for the determination of tolerance limits that minimize yield loss. The model considers longitudinal measurements of continuous features, based on censored data from stress tests. The tolerance limits are derived from multivariate distributions where the dependence structure is described by different copulas. Based on extensive numerical testing, we are able to provide insights into the properties of our model for different drift behaviors of the devices.

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Section: Introduction and Problem Descriptionmentioning

confidence: 99%

Section: Introduction and Problem Descriptionmentioning

confidence: 99%

Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data

Hofer

Leitner

Lewitschnig

et al. 2017

Quality & Reliability Eng

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“…The Clayton copula structure function [31,32] is selected when the wave height is positively correlated with the period and the scatter plot has tail correlation in its joint distribution:…”

Section: Double Entropy Joint Distribution Function Of Wave Height Anmentioning

confidence: 99%

“…Table 3 shows the probability values of wave heights for different periods, for example, if the period is determined as T ≥ 2, P(H ≤ 2, T ≥ 2) = 0.8849. The probability values of wave heights for different periods, and the periodic probability values for different wave heights can be calculated from Equations (31) and (32). Figures 8 and 9 are conditional probability diagrams for different combinations of wave heights and periods.…”

Section: Double Entropy Joint Distribution Function and Engineering Amentioning

confidence: 99%

Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

Liu

Chen

Jiang

et al. 2019

Entropy

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Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

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“…Xu et al presented a full Bayesian method to analysis the masked data in step‐stress accelerated life testing (SSALT). Hsu et al proposed the Bayesian analysis of SSALT model under the assumption that the masking probability depends on the component. Cai et al discussed the statistical inference for a series system with masked data under progressively interval censoring.…”

Section: Introductionmentioning

confidence: 99%

E‐Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

Cai

Shi

Lin

2019

Concurrency and Computation

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Summary In this paper, we consider the statistical analysis of parallel system with inverse Weibull distributed components. Due to cost and time constraints, the causes of system failures are masked and the type‐II censored observations might occur in the collected data. Under the symmetric and asymmetric loss functions, the expected Bayesian (E‐Bayesian) method and the hierarchical Bayesian method are proposed to estimate the parameters, as well as the reliability function. Numerical simulations using the Monte Carlo (MC) method are given to demonstrate the performances of the estimations under different masking levels and effective sample sizes. Finally, one data set is analyzed for illustrative purpose.

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Reliability Inference for a Copula-Based Series System Life Test Under Multiple Type-I Censoring

Cited by 27 publications

References 32 publications

Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data

Determination of tolerance limits for the reliability of semiconductor devices using longitudinal data

Double Entropy Joint Distribution Function and Its Application in Calculation of Design Wave Height

E‐Bayesian and hierarchical Bayesian estimations for parallel system model in the presence of masked data

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