基于OC函数的装备性能双边检验犯错概率研究  

Research on Errors Probabilities in Two-Sided Test of Equipment Performance Based on OC Function

作　　者：宋花玉[1] SONG Hua-yu(Shaanxi Provincial Party School of CPC,Xi′an 710000,China)

机构地区：[1]陕西省委党校,陕西西安710000

出　　处：《航空计算技术》2023年第5期6-10,共5页Aeronautical Computing Technique

基　　金：国家自然科学基金项目资助(11571011)。

摘　　要：为了减少服从正态分布的装备性能在均值的双边检验中犯两类错误的概率,建立了正态分布装备性能均值双边检验施行特征函数。以施行特征函数为工具,对检验中显著性水平和样本容量的变化对两类错误的概率的影响规律,以及两类错误的概率之间的关系进行了深入研究。结果发现:当样本容量固定时,检验犯两类错误的概率之间存在严格的负相关关系,此种情况下,要使犯两类错误的概率都很小是不可能的。在保持犯第Ⅰ类错误的概率不变的情况下,增加样本容量,犯第II类错误的概率会减小;但当均值μ的真值在检验值μ_(0)一定的邻域范围之内时,犯第Ⅱ类错误的概率减小幅度很小;只有当μ的真值在μ_(0)的一定邻域范围之外时,犯第Ⅱ类错误的概率减小幅度才较大。因此,要想使犯两类错误的概率都很小,只有当μ的真值在μ_(0)的一定邻域范围之外,且样本容量足够大时才能实现。In order to reduce the probabilities of making two types of errors in the mean two-sided test of normal distribution equipment performance,the operational characteristic function of the mean two-sided test of normal distribution equipment performance is established.Based on the operational characteristic function,the influence of the change of significance level and sample size on the probabilities of two types of errors and the relationship between the two types of errors are studied.It is found that when the sample size is fixed,there is a strict negative correlation between the probabilities of making two types of errors.If the probability of the I error is kept constant,the probability of the II error will decrease with increasing the sample size,but when the true value ofμis within a certain neighborhood of the test pointμo,the reduction in the probability of making the II error is small,and the reduction in the probability of making the II error is large only when the true value ofμis outside a certain neighborhood.In order to make the probabilities of making two types of errors is very small,only when the true value ofμis out of a certain neighborhood range and the sample size is large enough can it be realized.

关 键 词：装备性能 正态分布 双边检验 两类错误 施行特征函数 负相关关系 

分 类 号：E92[军事—军事装备学]