Reliability Analysis of Zero‐Failure Data with Poor Information

Abstract

For costly and dangerous experiments, growing attention has been paid to the problem of the reliability analysis of zerofailure data, with many new findings in world countries, especially in China. The existing reliability theory relies on the known lifetime distribution, such as the Weibull distribution and the gamma distribution. Thus, it is ineffective if the lifetime probability distribution is unknown. For this end, this article proposes the grey bootstrap method in the information poor theory for the reliability analysis of zero-failure data under the condition of a known or unknown probability distribution of lifetime. The grey bootstrap method is able to generate many simulated zero-failure data with the help of few zero-failure data and to estimate the lifetime probability distribution by means of an empirical failure probability function defined in this article. The experimental investigation presents that the grey bootstrap method is effective in the reliability analysis only with the few zero-failure data and without any prior information of the lifetime probability distribution.

Estimation on Reliability Models of Bearing Failure Data

“…By exploring discrete random variable and analyzing the expectation interval and information capacity of certain entropy, Aviyente et al [24,25] successfully solved the time frequency distribution problem and interval forecast problem of entropy. Xia [26] proposed a grey bootstrap method based on poor information theory, which conducted a reliability analysis of zero-failure data when the probability distribution information is known or unknown in life test, thus providing a strong theoretical reference to the reliability of poor information of zero-failure data.…”

Dynamic Prediction for Accuracy Maintaining Reliability of Superprecision Rolling Bearing in Service

“…Information, such as precision recession trajectory, probability distribution, and accuracy reliability function, varies with the movement process. e prediction problem for accuracy reliability involves the interaction between internal factors and the external environment [1][2][3][4][5]. According to the existing research, the reliability theory of rolling bearings is primarily concerned with fatigue failure and static reliability problems and assumes that the lifetime data obey the Weibull distribution or lognormal distribution [6][7][8].…”

Reliability Evaluation for the Running State of the Manufacturing System Based on Poor Information

“…Viewing the existing research on poor information, the research and application of the problems involving poor information have drawn much attention and made remarkable progresses. For instance, based on poor information, Wang et al [12] proposed a dynamic bootstrap grey method to estimate multisensor measurement results with small data samples and an unknown data distribution, having a lower relative estimation error of the measurement results compared to the grey bootstrap method and the Monte Carlo method; considering unknown probability distribution and very small sample data, He et al [13] undertook performance analysis for material and structure using fuzzy norm method in uncertainty metric with poor information; on account of data rich but information poor, Ferraro [14] considered adopting procedures for efficient data sharing as a low-cost way to shorten development cycles; Xia [15] proposed the grey bootstrap method in the information poor theory for the reliability analysis of zero-failure data under the condition of a known or unknown probability distribution of lifetime; based on the grey theory, Zhang et al [16] introduced the reliability assessment method to analyze the mechanism motion.…”