Analysis of Weibull Step-Stress Model In Presence of Competing Risk

Samanta, Debasis; Gupta, Arindam; Kundu, Debasis

doi:10.1109/tr.2019.2896319

Cited by 25 publications

(18 citation statements)

References 35 publications

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“…For the complete dataset W, by taking derivatives for Function (9) with respect to each of the four unknown parameters, respectively, the following likelihood equations can be derived.…”

Section: Em Algorithmmentioning

confidence: 99%

Revisit to progressively Type-II censored competing risks data from Lomax distributions

Huang

Gui

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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In survival analysis, more than one factor typically contributes to individual failure. In addition, censoring is inevitable in lifespan tests or reliability studies due to external causes or experimental purposes. In this article, the competing risks model is considered and investigated under progressively Type-II censoring where data is from Lomax distributions. Assumptions are further made that these competitive factors are independently distributed, and the latent lifetimes of these factors follow Lomax distributions where both scale parameters and shape parameters are different. For all unknown parameters, maximum likelihood estimates have been attained by Newton-Raphson (NR) method as well as expectation maximization (EM) method, and then the approximate confidence intervals are acquired, in addition to bootstrap confidence intervals. Furthermore, under square error and LINEX loss functions, Bayes estimates and corresponding highest posterior density credible intervals are successively constructed. Finally, simulation experiments are implemented to access performance of several proposed methods in this article, and laboratory dataset is presented and analyzed for illustrative purposes.

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“…For the complete dataset W, by taking derivatives for Function (9) with respect to each of the four unknown parameters, respectively, the following likelihood equations can be derived.…”

Section: Em Algorithmmentioning

confidence: 99%

Revisit to progressively Type-II censored competing risks data from Lomax distributions

Huang

Gui

2021

Proceedings of the Institution of Mechanical Engineers, Part O:

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show abstract

“…( ) 2 . Considering that the one-sided CI for ( ) is usually used rather than two-sided one, 11 the (1 − )% lower confidence limit for ( ) is given here as…”

Section: The Cis For Reliability Parametersmentioning

confidence: 99%

“…The Weibull distribution is widely used to model the lifetime. [1][2][3] However, the shape of hazard rate function from Weibull distribution is monotonic, which confines the application of Weibull distribution. Alternatively, modified or extended Weibull distributions are proposed.…”

Section: Introductionmentioning

confidence: 99%

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Reliability analysis for q‐Weibull distribution with multiply Type‐I censored data

Jia

2021

Quality & Reliability Eng

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The widely used Weibull distribution could be generalized to be q-Weibull distribution. To fill out the gap in existing literature, the reliability is studied for q-Weibull distribution with multiply Type-I censored data, which is the general form of Type-I censored data. The point estimates and confidence intervals (CIs) for q-Weibull parameters and reliability parameters such as the reliability and remaining lifetime are all focused on. The maximum likelihood estimates (MLE) are obtained by maximizing the likelihood function and transforming it to an unconstrained optimization problem. The least-square estimates (LSEs) are proposed by minimizing the single-variable profile error function derived from reducing the previous multivariable error function. These improvements could make the computation of point estimates efficient. Concerning the CIs, the asymptotic normality of log-transformed MLE is used to guarantee they fall into the value ranges. Particularly, the closed form for the Fisher information matrix is derived using the missing information principal and is combined with the delta method to construct the CIs for reliability. Besides, the bias-corrected and accelerated (BCa) bootstrap method is also applied. Further, a Monte Carlo simulation study is conducted to compare different point estimates and CIs. Finally, an illustrative example is presented to show the application of the study in this paper.

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“…These data include historical SMs running data, parameters, and many kinds of events collected from different cities and counties in Zhejiang Province, China. We have taken types of data that affect electricity meters as input, and constructed six subevaluation indicators by applying statistical analysis methods such as Weibull distribution [17], Bayesian formula and Theil index [18], [19]. The entropy analysis is adopted to fuse indicators and form a complete state evaluation model of SMs.…”

Section: Introductionmentioning

confidence: 99%

An On-Line State Evaluation Method of Smart Meters Based on Information Fusion

Cai

Chen

Ye³

et al. 2019

IEEE Access

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With the rapid development of smart grid construction in many countries, the coverage of smart meters has been greatly improved, but how to ensure the accuracy of measuring the state of smart meters has become a problem for all power utilities. Power utilities usually replace old smart meters with new ones that have reached a certain running time. This replacement method will lead to the replace of some smart meters which can still work normally, resulting in a lot of waste. In order to solve this problem, this paper presents an online evaluation method for smart meters by analyzing their power acquisition data. The data about smart meters from advanced metering infrastructure and the data from smart meters themselves are studied in detail, and six sub-evaluation indicators including reliability, measurement abnormal events, smart meter events, overload, state of clock battery and regional index, that reflect the state of smart meters are extracted. The entropy weight method is adopted to fuse four of these indicators, then the state evaluation model is established based on the fuse of the the six sub-indicators. The model has been verified with actual data, and the results indicate that the state evaluation model can successfully distinguish the states of smart meters and promote more accurate replacement of smart meters to save the operating cost of electricity.

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Analysis of Weibull Step-Stress Model In Presence of Competing Risk

Cited by 25 publications

References 35 publications

Revisit to progressively Type-II censored competing risks data from Lomax distributions

Revisit to progressively Type-II censored competing risks data from Lomax distributions

Reliability analysis for q‐Weibull distribution with multiply Type‐I censored data

An On-Line State Evaluation Method of Smart Meters Based on Information Fusion

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