Abstract
Only very few failure data can be obtained for the time censored test of high-reliability and long-life products. For very few failure data, the current methods fail to obtain both the point estimation and confidence interval of reliability parameters. If the point estimation and confidence interval of reliability parameters are obtained based on different methods, the results tend to be unreliable. In this study, based on the existing research, a Bayesian reliability evaluation method for very few failure data under the Weibull distribution was proposed. First, the range of failure probability was limited based on the convexity and self-features of the Weibull distribution function. Second, based on the background of the sample with very few failure data, the pretest distribution function and parameters were set and solved. The point estimation and confidence interval model of failure probability based on the Bayesian formula was established. The improved match distribution curve method was used to compute both the point estimation and confidence interval of reliability parameters. Furthermore, by comparing the results of numerical examples, the calculation results obtained by the proposed method were verified as being very reasonable. Finally, taking wet friction plates as an example, the results showed the effectiveness of this method in engineering practice.
Highlights
In product design, research and development, production, improvement, and other aspects, it is usually necessary to verify the reliability of the product through reliability tests
In the Weibull distribution, the match distribution curve method was improved for the characteristics of very few failure data, and the range of failure probability was limited according to the value of the shape parameters m and further improved the accuracy of the evaluation range. is method can analyze the reliability evaluation of products under the condition of few failure data, including the point estimation of parameters and the confidence interval estimation of parameters and fundamentally solve “disjointed” problems between parameter point estimation and parameter interval estimation
In the reliability test of products with higher reliability, test results often show a situation in which very few test samples fail during the entire reliability test or even no sample failures, and the number of such failed samples is less than 10%, and this is called the minimum data failure test
Summary
Research and development, production, improvement, and other aspects, it is usually necessary to verify the reliability of the product through reliability tests. Xu and chen [13] proposed the method of the two-sided modified Bayesian (M-Bayesian) credible limit and used this method to study the failure probability and reliability confidence interval evaluation method under the condition of no failure data. It can be seen from the current research that the use of the distribution curve method is often limited to the point estimation of the parameters. It is rarely used in the parameter confidence interval solving process. In the Weibull distribution, the match distribution curve method was improved for the characteristics of very few failure data, and the range of failure probability was limited according to the value of the shape parameters m and further improved the accuracy of the evaluation range. is method can analyze the reliability evaluation of products under the condition of few failure data, including the point estimation of parameters and the confidence interval estimation of parameters and fundamentally solve “disjointed” problems between parameter point estimation and parameter interval estimation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
