相關性存在下之統計製程管制法的研究

The Investigation of Correlation on the Performance of the Statistical Process Control Methods and Development of a New Control Procedure

王英欽(Ying-Chin Wang)

指導教授 ： 鄭春生 博士

元智大學/工程學院/工業工程與管理學系/碩士(1992年)

摘要

傳統之統計製程管制是根據獨立、常態分配之合理樣本組(rational
subgroup)資料，來分析製程是否在管制內。由於生產形態及管制目的之
改變，管制個別值數據已成為自動化生產、JIT 及在機器上連線及時
(on-line，real time)量測等環境下必然趨勢。另外管制所有個別值數據
較管制樣本組，能夠提供更多之製程資訊。由於個別數據之相關性，使得
傳統之管制法不適用於此等環境下。目前相關性數據之管制，大多是以時
間序列法來模式化，並以傳統管制法來管制獨立之殘差。這種方法雖然可
符合獨立性之要求，但卻非常無效率。本研究之目的是探討相關數據對於
傳統 Shewhart、CUSUM 及 Shewhart-CUSUM 管制法之影響，並發展適用
於管制具相關性個別數據之統計製程管制法，以達到製程管制之目的。

關鍵字

相關性數據﹔管制圖﹔平均連串長度

並列摘要

The assumptions of statistical process control methods are that
process data are normally and independently distributed. The
most important of these assumptions is that of independence of
the observations. However,measurements from industrial pro-
cesses are often serial correlated. It has been shown that a
higher Type I error in the form of many false alarms may result
if the correlation structure of the observations is not taken
into account. Most researchers apply the traditional control
methods to the uncorrelated residuals of a time series model.
It is shown that this approach may be feasible but not effect-
ive. The research investigates the impact of correlation on the
performance of the traditional Shewhart and CUSUM control sch-
emes on the basis of average run length. This research will
also develop and test a new control procedure suitable for the
con- trol of correlated data.

並列關鍵字

Correlated data ； control chart ； average run length