Reliability Parameter Estimation Method for Aviation Piston Engine High-Pressure Pump Based on Modified Grey-Three-Parameter Weibull Distribution Model

High-pressure pumps are essential for maintaining the overall performance of aviation piston engines, making research regarding safety and reliability of these pumps extremely important. In this paper, a modified grey-three-parameter Weibull model is developed for evaluating the reliability parameters of high-pressure pumps in order to overcome the limitations of the traditional methods based on a single prediction method accuracy that require enhancement in operating the random truncated-tailed small-sample scenarios. Firstly, the three parameter Weibull distribution is introduced as the distribution model for the reliability of the high-pressure pumps, targeting the high reliability at the early stage of commissioning. Specifically, the introduction of the position parameter enables a more intuitive determination of the timing of the attrition period. Secondly, a modified grey-three-parameter Weibull distribution model is obtained by combining the grey model with the three-parameter Weibull distribution model and simplifying by least-squares methods to solve the problem of small samples and random truncated tails of the failure data. Moreover, the failure rate and reliability of the high-pressure pump are estimated. Finally, the case calculations are compared with other distributions, methods, and with different sample sizes of 5, 20, and 40. Results show that the RSME of the proposed method is lower than 0.002, which is the minimum value for different distributions and methods. Therefore, the proposed method is proved to perform reliability parameter estimation of high-pressure pumps with high fitting accuracy, meanwhile, the results could be generated rapidly and automatically by the computer modeling, which is more suitable for engineering applications.