# Reliability Analysis of Small-Sample Failure Data for Random Truncation High-Voltage Relay
## 4 Conclusions  
(1) In order to solve the problem of inaccurate reliability modeling and evaluations caused by insufficient fault data of long-life high-voltage relays, this paper applies the average rank method to correct the influence of truncation data on the fault rank. Based on this, the minimum average square distance is used to select the optimal empirical distribution function, which avoids the randomness of small-sample fault data. After calculations, it is seen that average square distances of the empirical distribution function \(F_{3}(t_{i})=\frac{i}{n+1}\) and \(F_{5}(t_{i})=\frac{i-0.375}{n+0.25}\) are equal and minimum. Under the assumption of the Weibull distribution, the total least squares method is used to estimate Weibull distribution model parameters. The linear correlation coefficient test and d-test are used for model hypothesis testing and verifying the validity of the parameter estimations.  
(2) In response to the optimal model selection problem for multiple reliability models that pass both the linear correlation test and d-test simultaneously, the root mean square error method and relative root mean square error are introduced, and the optimal Weibull distribution model are determined based on the principle of minimizing both.  
(3) Based on the Weibull model, if the shape parameter is less than 1, it can be inferred that the product is in the early failure period. The reliability level of high-voltage relays is evaluated by estimating MTBF (mean time between failures). After carrying out calculations, it is found that compared with traditional methods, the MTBF obtained by the method proposed in this article is closer to the actual mean life of the product, indicating the effectiveness and superiority of the method proposed in this article. The method proposed in this article can lay the foundation for reliability research such as reliability design and screening, and can provide reference and guidance for the reliability modeling and life assessment of similar products.  
Conceptualization, Y.Z. ([PERSON]) and F.H.; methodology, Y.Z. ([PERSON]) and F.H.; software, F.Y.; validation, Y.Z. ([PERSON]) and F.H.; formal analysis, Y.Z. ([PERSON]); investigation, Y.Z. ([PERSON]) and X.W.; resources, Y.Z. ([PERSON]); data curation, Y.Z. ([PERSON]); writing--original draft preparation, Y.Z. ([PERSON]); writing--review and editing, X.W.; visualization, X.W. and F.Y.; supervision, Y.Z. ([PERSON]); project administration, Y.Z. ([PERSON]); funding acquisition, Y.Z. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Jilin Provincial Major Science and Technology Special Project \"Research on Key Technologies of High Voltage Electrical Systems for Electric Vehicles\" (No. 20220301015 GX).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
Conflicts of Interest: Author [PERSON] was employed by the company China FAW Grp Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.