Quantiles of the conditional residual lifetime

Statistics ◽  
2021 ◽  
pp. 1-20
Author(s):  
S. Abrams ◽  
P. Janssen ◽  
N. Veraverbeke
Keyword(s):  
Residual Lifetime

Reliability modeling for multi-state systems with a protective device considering multiple triggering mechanism

2021 ◽  
pp. 1748006X2110133
Author(s):  
Xian Zhao ◽  
Rong Li ◽  
Yu Fan ◽  
Qingan Qiu
Keyword(s):  
Failure Modes ◽  
Operating Time ◽  
Replacement Policy ◽  
Economic Losses ◽  
Residual Lifetime ◽  
Cumulative Number ◽  
Protective Device ◽  
Triggering Mechanism ◽  
Safety Critical ◽  
Markov Chain Imbedding

Failures of safety-critical systems may result in irretrievable economic losses and significant safety hazards, thus enhancing the reliability of safety-critical system is crucial. As applied widely in engineering fields, protective devices are commonly equipped for the systems operating in shock environment to reduce external damage, which has not been taken into consideration in existing literatures. This paper investigates the reliability of multi-state systems with competing failure patterns supported by a protective device. According to the system failure modes, state-based and shock number-based triggering mechanism of the protective device are developed. That is, the protective device is triggered once the system state or cumulative number of shocks exceeds corresponding critical thresholds respectively. After being triggered, the protective device can reduce the probability of damaging shocks for the system. The protective device fails when the number of consecutive valid shocks reaches a threshold. Based on the constructed model, a finite Markov chain imbedding approach is employed to derive reliability indices including distribution functions of system lifetime and residual lifetime, together with expected operating time of the protective device. Moreover, two age-based replacement policies together with a condition-based replacement policy are developed to accommodate different maintenance scenarios and corresponding optimal solutions are acquired. Numerical illustrations based on the application of cooling systems in engines are presented to validate the results.

scholarly journals On estimating optimal regime for treatment initiation time based on restricted mean residual lifetime

Biometrics ◽  
2021 ◽  
Author(s):  
Xin Chen ◽  
Rui Song ◽  
Jiajia Zhang ◽  
Swann Arp Adams ◽  
Liuquan Sun ◽  
...  
Keyword(s):  
Treatment Initiation ◽  
Residual Lifetime ◽  
Initiation Time ◽  
Optimal Regime ◽  
Mean Residual Lifetime

Reliability Properties of Reversed Residual Lifetime

2003 ◽  
Vol 32 (10) ◽  
pp. 2031-2042 ◽  
Author(s):  
Asok K. Nanda ◽  
Harshinder Singh ◽  
Neeraj Misra ◽  
Prasanta Paul
Keyword(s):  
Residual Lifetime

Assessment of Reliability and Overall Life-Time of the Turbo Generator in the Kamýk Power Station

2015 ◽  
Vol 732 ◽  
pp. 297-300
Author(s):  
Petr Tej ◽  
Alena Tejová ◽  
Jana Marková
Keyword(s):  
Czech Republic ◽  
Maximum Stress ◽  
Steel Structure ◽  
Life Time ◽  
Residual Lifetime ◽  
Stress Range ◽  
Power Station ◽  
The Czech Republic ◽  
Turbo Generator ◽  
Loaded Part

This paper presents the results of measurement of the stress and the theoretical analysis of the steel structure of the Kaplan turbo generator in the Kamýk power station in the Czech Republic. Based on the number of load cycles and the finding of the maximum stress range of critical details of the most loaded part, the lower star, the residual lifetime of the turbo generator was determined.

scholarly journals The Reciprocal Generalized Inverse Gaussian Frailty with Application in Life Annuity Business

2020 ◽  
pp. 112-131
Author(s):  
Walter Onchere ◽  
Richard Tinega ◽  
Patrick Weke ◽  
Jam Otieno
Keyword(s):  
Simulation Study ◽  
Unobserved Heterogeneity ◽  
Survival Curve ◽  
Gaussian Model ◽  
Frailty Models ◽  
Residual Lifetime ◽  
Longevity Risk ◽  
Inverse Gaussian ◽  
Life Annuity ◽  
Valuation Of Life

Aims: As shown in literature, several authors have adopted various individual frailty mixing distributions as a way of dealing with possible heterogeneity due to unobserved covariates in a group of insurers. This research contribution is to generalize the frailty mixing distribution to nest other classes of frailty distributions not in literature and apply the proposed distributions in valuation of life annuity business. Methodology: A simulation study is done to assess the performance of the aforementioned models. The baseline parameters is estimated using Bayesian Inference and a better model is suggested for valuation of life annuity business. Results: As a result of generalizing the frailty some new classes of frailty distributions are constructed such as; the Reciprocal Inverse Gaussian Frailty, the Inverse Gamma Frailty, the Harmonic Frailty and the Positive Hyperbolic Frailty. From the simulation study, the proposed new frailty models shows that ignoring frailty leads to an underestimation of future residual lifetime since the survival curve shifts to the right when heterogeneity is accounted for. This is consistent with frailty literature. The Reciprocal Inverse Gaussian model closely represents the Association of Kenya Insurers graduated rates with a slight increase in survival due to longevity risk. Conclusion: The proposed new frailty models show an increase in the insurers expected liability when unobserved heterogeneity is accounted for. This is consistent with frailty literature and thus can be applied to avoid underestimating the insurer’s liability in the context of life annuity business. The RIG model as proposed in estimating future liability by directly adjusting the AKI mortality rates shows an increase in longevity risk. The extent of heterogeneity of the insured group determines the level of risk. The RIG frailties should be considered for multivariate cases where the insureds are clustered in groups.

scholarly journals Statistical properties and different methods of estimation of transmuted Rayleigh distribution

2017 ◽  
Vol 40 (1) ◽  
pp. 165-203 ◽  
Author(s):  
Sanku Dey ◽  
Enayetur Raheem ◽  
Saikat Mukherjee
Keyword(s):  
Stochastic Ordering ◽  
Real Data ◽  
Rayleigh Distribution ◽  
Statistical Properties ◽  
Point Of View ◽  
Strength Parameter ◽  
Residual Lifetime ◽  
Mean Deviation ◽  
Unknown Parameters ◽  
Anderson Darling

This article addresses the various properties and different methods of estimation of the unknown parameters of the Transmuted Rayleigh (TR) distribution from the frequentist point of view. Although, our main focus is on estimation from frequentist point of view,  yet, various mathematical and statistical properties of the TR distribution (such as quantiles, moments, moment generating function, conditional moments,  hazard rate, mean residual lifetime, mean past lifetime,  mean deviation about mean and median, the stochastic ordering,  various entropies, stress-strength parameter  and order statistics) are derived.  We briefly describe different frequentist methods of estimation approaches, namely, maximum likelihood estimators, moments estimators, L-moment estimators, percentile based estimators, least squares estimators, method of maximum product of spacings,  method of Cram\'er-von-Mises, methods of Anderson-Darling and right-tail Anderson-Darling and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. Finally, the potentiality of the model is analyzed by means of two real data sets which is further illustrated by obtaining bias and standard error of the estimates and the bootstrap percentile confidence intervals using bootstrap resampling.

Lifetime estimation of tantalum capacitor for mobile applications using empirical and experimental techniques: a DOE approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Cherry Bhargava ◽  
Pardeep Kumar Sharma ◽  
Ketan Kotecha
Keyword(s):  
Mobile Applications ◽  
Empirical Method ◽  
Circuit Board ◽  
Experimental Techniques ◽  
Residual Lifetime ◽  
Content Type ◽  
Accelerated Life ◽  
Tantalum Capacitor ◽  
Faulty Component ◽  
The Military

PurposeCapacitors are one of the most common passive components on a circuit board. From a tiny toy to substantial satellite, a capacitor plays an important role. Untimely failure of a capacitor can destruct the entire system. This research paper targets the reliability assessment of tantalum capacitor, to reduce e-waste and enhance its reusable capability.Design/methodology/approachThe residual lifetime of a tantalum capacitor is estimated using the empirical method, i.e. military handbook MILHDBK2017F, and validated using an experimental approach, i.e. accelerated life testing (ALT). The various influencing acceleration factors are explored, and experiments are designed using Taguchi's approach. Empirical methods such as the military handbook is used for assessing the reliability of a tantalum capacitor, for ground and mobile applications.FindingsAfter exploring the lifetime of a tantalum capacitor using empirical and experimental techniques, an error analysis is conducted, which shows the validity of empirical technique, with an accuracy of 95.21%.Originality/valueThe condition monitoring and health prognostics of tantalum capacitors, for ground and mobile applications, are explored using empirical and experimental techniques, which warns the user about its residual lifetime so that the faulty component can be replaced in time.

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