多个子样本下过程能力指数估计量的比较研究

过程能力指数(C_p)估计的关键是对总体标准差的估计。在多个子样本情形下,采用4个无偏估计量■,■_s,■_R,■_p分别估计总体标准差σ,证明了直接以此为基础的过程能力指数的估计量都是有偏的,且都有高估C_p的倾向;之后构造了C_p的4个无偏估计量;探讨了其中3个无偏估计量的估计效率;最后结合案例计算了C_p的不同估计值。

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

The key point to estimate the process capability indices(i.e.,C_p) is the estimator of the population standard deviation,which can be represented by the following unbiased estimator:■,■_s, ■_R and■_p.It is verify that all the estimators of C_p based directly on■,■_s,■_R and■_p are biased. Furthermore,they tend to overestimated the true value of C_p.Then,four unbiased estimators are put forward,and the efficiency of three of them is explored as well.Finally,each estimation method is analyzed in an example.