Study on segmented distribution for reliability evaluation

In practice, the failure rate of most equipment exhibits different tendencies at different stages and even its failure rate curve behaves a multimodal trace during its life cycle. As a result,traditionally evaluating the reliability of equipment with a single model may lead to severer errors.However, if lifetime is divided into several different intervals according to the characteristics of its failure rate, piecewise fitting can more accurately approximate the failure rate of equipment. Therefore, in this paper, failure rate is regarded as a piecewise function, and two kinds of segmented distribution are put forward to evaluate reliability. In order to estimate parameters in the segmented reliability function, Bayesian estimation and maximum likelihood estimation（MLE） of the segmented distribution are discussed in this paper. Since traditional information criterion is not suitable for the segmented distribution, an improved information criterion is proposed to test and evaluate the segmented reliability model in this paper. After a great deal of testing and verification,the segmented reliability model and its estimation methods presented in this paper are proven more efficient and accurate than the traditional non-segmented single model, especially when the change of the failure rate is time-phased or multimodal. The significant performance of the segmented reliability model in evaluating reliability of proximity sensors of leading-edge flap in civil aircraft indicates that the segmented distribution and its estimation method in this paper could be useful and accurate.

SEMI-QUANTITATIVE CHARACTERIZATION OF SEGMENT DISTRIBUTION IN LLDPE BASED ON THERMAL SEGREGATION

Based on successive multiple-step isothermal crystallization and self-nucleation annealing methods, a novel semi-quantitative method for the characterization of segment distribution in linear low density polyethylene (LLDPE) was established by treating the thermal analysis data using the Gibbs-Thomson equation. The method was used to describe the segment distribution of Ziegler-Natta catalyzed LLDPE (Z-N LLDPE), metallocene catalyzed LLDPE (m-LLDPE) and two commercial LLDPEs with wide molecular weight distribution. The differences of the results obtained from the two thermally treated samples were compared. The results of segment distribution of the polymers were discussed according to their microstructure data and were compared with their characteristics. It can be deduced from the results that this characterization method is effective to characterize the sequence structure of the branched ethylene copolymers.

STRUCTURAL CHARACTERIZATION OF POLYETHYLENES BY DSC ANALYSIS AFTER CRYSTALLIZATION SEGREGATION

The molecular structure of polyethylene (PE) samples with various comonomers including propylene, I-butane and 1-hexene was investigated by DSC and C-13-NMR techniques. The density of the samples varies from 0.948 g/cm(3) to 0.917 g/cm(3), and the molecular weight determined by the GPC method is in the range of 1 similar to2 x 10(5). The branch paint content of the samples was determined by C-13-NMR measurements and was found to be less than 20 per 1000 C atoms along the main chain. Crystallization segregation DSC technique (CSDSC) was used to characterize the branch point distribution or the segment length distribution of PEs. The crystallization segregation was performed in a successive annealing process at decreasing temperatures. The interval of two successive annealing temperatures was 6 K, and the time length of each annealing step was 2.5 h. The CSDSC results clearly indicate that all the PE samples used, including some metallocene PEs, more or less exhibit their non-uniformity in segment length distribution, and bimodal or multimodal CSDSC curves were usually observed. For quantitative characterization of the CSDSC curves and the segment length distribution two parameters, the average melting point, T-mAV, and the root-mean-square deviation of melting temperature, (DeltaT(m)(AV)(2))(1/2), were proposed. TmAV is corresponding to the average segment length due to branching and (DeltaT(m)(AV)(2))(1/2) gives information about the: width of the segment length distribution. Experimental results show that both the degree of average melting temperature depression and the width of the distribution seem to increase with increasing the branching content and are dependent on the type of comonomers. Very good reproducibility and additivity of the CSDSC method were evidenced experimentally. It was concluded that the CSDSC technique is a sensitive and convenient method for characterizing the segment length distribution of branched polyethylenes and will be of great interest in structure-property relationship studies of crystalline polymers.