不同标准差估计方法下过程能力指数估计量的比较研究

估计量是统计推断的基础,通常无偏性是对一个好的估计量的基本要求。通过严格的数学推导,证明人们现在提出的过程能力指数（Cp）的估计量都是有偏的,且都有高估Cp的倾向;之后构造了Cp的两个无偏估计量;探讨了这两个无偏估计量的估计效率;最后通过试算和比较,认为当样本容量n较大,同时估计精度又不要求太高时,可直接使用p作为Cp的估计量;但在样本容量较小,或者对估计精度要求很高的场合,则必须选择p（D）作为Cp的估计量。

A Comparative Study on the Estimator of Process Capability Indices in Terms of Standard Deviation Estimated by Different Methods

As a principal component in the inferential statistics,the unbiased property is desirable for a good estimator.Unfortunately,it is first proved that all the existed estimators of process capability indices（i.e.,Cp）are biased.Furthermore,they tend to overestimated the true value of Cp.Then,the unbias edestimators are put forward,and the efficiency of them is explored as well.It’s suggested that p is used to estimate Cpwhen sample size is rather large,and the precision of the estimation isn’t necessary to be high.Otherwise,it is desired that p（D）as the estimator of Cp.