自相关过程能力指数置信区间的构建与评价

过程能力指数是指过程处于控制状态下的实际加工能力，其计算方法通常要求过程是独立同分布的，而实际过程中数据往往表现出一定的自相关性。评价过程控制的能力指数是一个基于样本观测值的统计量，需要对其进行统计检验。当过程自相关时，还需要对其进行统计推断。本文提出了自相关下过程能力指数置信区间的构建方法，并从理论和模拟两个角度研究自相关对该置信区间的影响，给出了自相关情形下置信区间的计算步骤。模拟和实证均表明：正自相关会导致常规方法估计出的置信区间偏大且上移，负自相关会导致置信区间估计偏小且下移，本文提出的方法能很好地解决置信区间估计不准确的问题，能较准确地评价过程的实际生产能力。

Confidence Interval Construction and Evaluation for Auto-correlated Process Capability Indices

A process capability index is defined as the actual processing capacity when process in control. Its calculation usually requires that the process is independent and identically distributed, but the actual process data tend to exhibit certain autocorrelation. As the process control evaluation method, process capability index is a statistic based on sample observation, so it needs to be statistically tested. When the process is auto-correlated, it also needs to do statistical inference. This paper proposes the construction method of capability index confidence intervals for the auto-correlated process, studys the impact of autocorrelation on confidence interval from theory and simulation, and the calculation procedure is presented. The results of simulation and empirical study show that, the positive auto-correlation will cause the estimated confidence interval calculated by conventional method larger and move upwards, and the negative auto-correlation will leads to confidence interval estimation smaller and downward. The proposed method in this paper can well solve the problem of inaccurate confidence interval estimation, which can accurately reflect the actual production capacity of process.