Abstract
Since their introduction in 1954, cumulative sum (CUSUM) control charts have seen a widespread use beyond the conventional realm of statistical process control (SPC). While off-the-shelf implementations aimed at practitioners are available, their successful use is often hampered by inherent limitations which make them not easily reconcilable with real-world scenarios. Challenges commonly arise regarding a lack of robustness due to underlying parametric assumptions or requiring the availability of large representative training datasets. We evaluate an adaptive distribution-free CUSUM based on sequential ranks which is self-starting and provide detailed pseudo-code of a simple, yet effective calibration algorithm. The main contribution of this paper is in providing a set of ready-to-use tables of control limits suitable to a wide variety of applications where a departure from the underlying sampling distribution to a stochastically larger distribution is of interest. Performance of the proposed tabularized control limits is assessed and compared to competing approaches through extensive simulation experiments. The proposed control limits are shown to yield significantly increased agility (reduced detection delay) while maintaining good overall robustness.
Highlights
IntroductionThe advent of modern statistical process control (SPC) arose out of the post industrial revolution realization that to yield goods of acceptable quality a manufacturing process ought to operate within prespecified margins of error (in other words it ought to be stable or in control) [1]
From a historical perspective, the advent of modern statistical process control (SPC) arose out of the post industrial revolution realization that to yield goods of acceptable quality a manufacturing process ought to operate within prespecified margins of error [1].In oversimplified terms, control charts are central to SPC and serve to continuously monitor a process to assess whether the observed deviations from the nominal process are due to mere chance or not.Control charts were first introduced by W
The following decades witnessed a substantial research interest and output resulting in important SPC developments including, but not limited to, cumulative sum (CUSUM) [5] and exponentially weighted moving average (EWMA) [6] control charts as well as Bayesian approaches [7,8,9]
Summary
The advent of modern statistical process control (SPC) arose out of the post industrial revolution realization that to yield goods of acceptable quality a manufacturing process ought to operate within prespecified margins of error (in other words it ought to be stable or in control) [1]. The present work aims to shrink the above-mentioned gap by providing ready-to-use tables of control limits for an adaptive self-starting distribution-free CUSUM suitable to a wide variety of applications where a process is monitored for a departure from the underlying sampling distribution to a stochastically larger distribution. While this procedure has previously briefly been outlined and used by this author in [16,17], respectively, it is first thoroughly proposed and assessed in the current work.
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