Publication Date

5-2019

Date of Final Oral Examination (Defense)

3-4-2019

Type of Culminating Activity

Thesis

Degree Title

Master of Science in Mathematics

Department

Mathematics

Major Advisor

Partha Mukherjee, Ph.D.

Advisor

Jaechoul Lee, Ph.D.

Advisor

Jodi Mead, Ph.D.

Abstract

The statistical process control (SPC) chart is an effective tool for the analysis, interpretation, and visualization of data from sequential processes. Commonly used SPC charts such as the Shewhart, CUSUM and EWMA charts are widely implemented in detecting distributional shifts in various processes. With recent scientific and technological advancements, massive amounts of data continue to be generated by production, medical, agricultural and many other industrial processes. Conventional SPC charts have significant drawbacks in monitoring such processes, specifically when the velocity of the data flow is greater than the run time of the monitoring procedure. In the literature, dynamic sampling control charts (Li and Qiu, 2014) are becoming popular due to their ability to adaptively control the next sampling time of the monitoring process. In this thesis, we incorporate similar ideas to conventional SPC charts for the real-time monitoring of big data processes.

Traditional SPC charts are designed to give a warning signal at a particular time point if a process reading plots beyond its control limit(s). This approach does not provide ample information of the likelihood of a potential shift in the process. We implement existing methods of designing control charts with p-values, which gives information about the performance of the current observations and potentially, of observations in near future. The control chart gives a signal for a mean shift if the p-value is less than some pre-specified significance level. We utilize the computed p-values of the charting statistic in designing variable sampling schemes, specifically the dynamic sampling schemes which are an increasing function of the p-value. The resulting control charts have variable sampling intervals, and hence skips several observations. Thus, their computing times are much faster than traditional charts.

This thesis provides guidance on how to incorporate dynamic sampling schemes for monitoring big data streams in other types of SPC charts. We perform extensive simulation studies to compare the performance of the dynamic sampling control charts with conventional control charts. Our results show that the dynamic sampling versions of three commonly used SPC charts can monitor big data streams efficiently.

DOI

Master of Science in Mathematics

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