A discrete inverse Weibull distribution and estimation of its parameters

“…More specifically, the approach can be structured in three phases: offline identification of the degradation levels by an unsupervised ensemble clustering method, previously proposed by some of the authors [37] (see Appendix A.1), i.e., the identification of the health states of the Markov model that are explained by the different operating conditions experienced by the equipment during its life (whose number is generally "a priori" unknown, making the problem unsupervised) by an unsupervised ensemble clustering method, previously proposed by some of the authors [37] (see Appendix A.1); fleet data Maximum Likelihood Estimation (MLE) of the parameters of the discrete Weibull distributions [38]- [40] that are assumed to describe the transitions among the states and estimation of their uncertainties by the Fisher Information Matrix (FIM) [41]; use of the inferred degradation model in a direct Monte Carlo (MC) simulation to estimate the RUL of a new equipment of the fleet [42].…”

Section: Notation and List Of Acronymsmentioning

confidence: 99%

Remaining useful life estimation in heterogeneous fleets working under variable operating conditions

Al‐Dahidi

Maio

Baraldi

et al. 2016

Reliability Engineering & System Safety

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Abstract. The availability of condition monitoring data for large fleets of similar equipment motivates the development of data-driven prognostic approaches that capitalize on the information contained in such data to estimate equipment Remaining Useful Life (RUL). A main difficulty is that the fleet of equipment typically experiences different operating conditions, which influence both the condition monitoring data and the degradation processes that physically determine the RUL. We propose an approach for RUL estimation from heterogeneous fleet data based on three phases: firstly, the degradation levels (states) of an homogeneous discrete-time finite-state semi-markov model are identified by resorting to an unsupervised ensemble clustering approach. Then, the parameters of the discrete Weibull distributions describing the transitions among the states and their uncertainties are inferred by resorting to the Maximum Likelihood Estimation (MLE) method and to the Fisher Information Matrix (FIM), respectively. Finally, the inferred degradation model is used to estimate the RUL of fleet equipment by direct Monte Carlo (MC) simulation. The proposed approach is applied to two case studies regarding heterogeneous fleets of aluminum electrolytic capacitors and turbofan engines. Results show the effectiveness of the proposed approach in predicting the RUL and its superiority compared to a fuzzy similarity-based approach of literature. Keywords

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“…Some distributions discretized by this method introduced in the literature are: Inverse Rayleigh distribution (Hussain and Ahmad, 2014), Lindley distribution Bakouch et al, 2014), Type II generalized Exponential distribution , Gamma distribution (Chakraborty and Chakravarty, 2012), Inverse Weibull distribution (Aghababaei Jazi et al, 2010), Burr XII and Pareto distributions (Krishna and Pundir, 2009), Rayleigh distribution , geometric Weibull distribution (Bracquemond and Gaudoin, 2003), among others.…”

Section: Discretization By Survival Functionmentioning

confidence: 99%

A Comparative Study Between Two Discrete Lindley Distributions

Oliveira

Mazucheli

Achcar

2017

CeN

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The methods to generate a probability function from a probability density function has long been used in recent years. In general, the discretization process produces probability functions that could be alternatives to traditional distributions used in the analysis of count data as geometric, Poisson and negative binomial distributions. The discretization also avoids the use of a continuous distribution in the analysis of strictly discrete data. In this paper, using the method based on an infinite series, proposed by , we studied an alternative discrete Lindley distribution to those studies in Bakouch et al. (2014). For both distributions, a simulation study is carried out to examine the bias and mean squared error for the maximum likelihood estimators of the parameters as well the coverage probability and the length of coverage probability. For the discrete Lindley distribution obtained by infinite series method, we present the analytical expression for bias reduction of the maximum likelihood estimator. Some examples using real data from the literature show the potential of these distributions. Despite the discretization methods are quite different, the resulting distributions are interchangeable, however the distribution generated by an infinite series has simple mathematical expressions and can be used directly to count data in the presence of covariates.

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A discrete inverse Weibull distribution and estimation of its parameters

Cited by 137 publications

References 19 publications

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Generating discrete analogues of continuous probability distributions-A survey of methods and constructions

Remaining useful life estimation in heterogeneous fleets working under variable operating conditions

A Comparative Study Between Two Discrete Lindley Distributions

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