Based on random censored data, the maximum likelihood estimation method of parameters of the weibull distribution is put forward. By the parameters estimation, the reliability analysis of the engineering data of rocket engine trials is given. The estimation values of shape parameters and reliability analysis show that the method is feasible.

Maximum likelihood estimation of weibull distribution based on random censored data and its application

The random censorship model (RCM) is commonly used in biomedical science for modeling life distributions. The popular non-parametric Kaplan–Meier estimator and some semiparametric models such as Cox proportional hazard models are extensively discussed in the literature. In this paper, we propose to fit the RCM with the assumption that the actual life distribution and the censoring distribution have a proportional odds relationship. The parametric model is defined using Marshall–Olkin's extended Weibull distribution. We utilize the maximum-likelihood procedure to estimate model parameters, the survival distribution, the mean residual life function, and the hazard rate as well. The proportional odds assumption is also justified by the newly proposed bootstrap Komogorov–Smirnov type goodness-of-fit test. A simulation study on the MLE of model parameters and the median survival time is carried out to assess the finite sample performance of the model. Finally, we implement the proposed model on two real-life d...

Fitting and testing the Marshall–Olkin extended Weibull model with randomly censored data

In this paper, we have discussed a random censoring test with incomplete information, and proved that the maximum likelihood estimator (MLE) of the parameter based on the randomly censored data with incomplete information in the case of the exponential distribution has the strong consistency.

Consistency of MLE of the parameter of exponential lifetime distribution for random censoring model with incomplete information

The method and effects of extracting information from different fatigue test data were analyzed and compared according to the test data in engineering in this paper. By probability statistical analysis, the life data of ignored censored data were collected and analyzed to fit the distribution types and P–S–N curves. Otherwise, the life data including censored data were estimated by maximum likelihood estimation and K–S test. It is shown that the practice of simply ignoring censored data will underestimate the fatigue performance of the test sample in different degrees after analysis and comparison of the two results. Therefore, according to different types of test data, the influence of censored data should be considered fully in order to select the appropriate treatment method. Censored data in engineering usually should not be ignored.

Study on Processing Method and Engineering Application of Censored Data

This paper analyzes the characteristics of the enterprise after-sale service records for field failure data, and summarizes the types of field data. Maximum likelihood estimation method and the least squares method are presented for the complexity and difficulty of field failure data processing, and Monte Carlo simulation method is proposed. Monte Carlo simulation, the relatively simple calculation method, is an effective method, whose result is closed to that of the other two methods. Through the after-sale service records analysis of a specific electromagnetic flowmeter enterprises, this paper illustrates the effectiveness of field failure data processing methods. Copyright © 2014 IFSA Publishing, S. L.

Point Estimation Method of Electromagnetic Flowmeters Life Based on Randomly Censored Failure Data

Let (x, i≥1) be i.i.d.r.v'.s with P(x_1≤x)=F(x, α, λ), where α0, λ0, F(x, α, λ)=1-e~(-λx~α)(x0), F(x, α, λ)=0 (x≤0) in which both of α and λ are unknown. Let (y_1, i≥1) be a sequence of independent random variables with P(y_i≤x)=G_i(x), G_i(0)=0(i≥1). Suppose that the two sequences are independent of each other. Set t_i=min(x_i, y_i), δ_i=I(x_i≤y_i) (i≥2), I(A) being the indicator function of A. As well-known, maximum likelihood estimators ■_n and ■_n of α, λ based on data (t_1, δ_1), …, (t_n, s_n) are the solution of the following equations: In the present paper, we have proved the following theorem: ① If there exists x0 such that ■ 1/n sum 1 to n G_i(x)1, then ■_n and ■_n are consistent estimators of α and λ respetively. ② If there exists x0 such that ■ 1/n sum 1 to n G_i(x)1 and there exist limits ■ 1/n sum 1 to n · G_i(y) for almost all y w.r.t. Lebesgue measure, then both ■_n and ■_n are strongly consistent.

On the consistency of maximum likelihood estimators based on randomly censored data in the weibull distribution case

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On the consistency of maximum likelihood estimators based on randomly censored data in the weibull distribution case