Pan J N, Li C I, Chen F Y
Department of Statistics, National Cheng Kung University, No. 1, University Road, Tainan City 701, Taiwan, Republic of China,
Environ Monit Assess. 2014 Oct;186(10):6369-84. doi: 10.1007/s10661-014-3861-z. Epub 2014 Jun 5.
Traditionally, the process capability index is developed by assuming that the process output data are independent and follow normal distribution. However, in most environmental cases, the process data are autocorrelated. The autocorrelated process, if unrecognized as an independent process, can lead to erroneous decision making and unnecessary quality loss. In this paper, three new capability indices with unbiased estimators are proposed to relieve the independence assumption for the-nominal-the-best and the-smaller-the-better cases. Furthermore, we use mean squared error (MSE) and mean absolute percent error (MAPE) to compare the accuracy of our proposed indices to previous autocorrelated indices. The results show that our proposed capability indices outperform the predecessors.
传统上，过程能力指数是在假设过程输出数据相互独立且服从正态分布的情况下得出的。然而，在大多数实际情况下，过程数据是自相关的。如果将自相关过程误认作独立过程，可能会导致错误的决策和不必要的质量损失。本文针对“标称最佳”和“越小越好”的情况，提出了三种具有无偏估计量的新能力指数，以放宽独立性假设。此外，我们使用均方误差（MSE）和平均绝对百分比误差（MAPE）来比较我们提出的指数与先前自相关指数的准确性。结果表明，我们提出的能力指数优于先前的指数。
