摘要
当试验次数为n,成功次数介于X_1,X_2时(X_1≤X_2),本文给出了在这种不确定数据下成败型元件的可靠性p的极大似然估计和精确置信下限。对于由成败型元件组成的串联和并联系统,本文也给出了在不确定数据下,系统可靠性的精确解。最后讨论了极大似然估计的某些性质。
For a pass-fail component, if the sucessus number X in n tests is unknown but between X1 and X2, Fan[91] gave the maximum likelihood estimate (mle) and approximate lower confidence limit (LCT) of reliability p. The similar problems for systems are also discussed. In the present paper, We introduce a more reasonable likelihood funetion, and obtain the mle and exact LCT of reliability using Bayes method. The mle and exact LCT for series and paralell systems are also derived with indefinite sucessus number for each component. Finally, We studied the properties of Likelihood functions and the corresponding mle.
