The development of performance measures and diagnostic procedures for X(bar) and S(2) charts
Rahn, Gregory Ernest
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Permalink
https://hdl.handle.net/2142/19024
Description
Title
The development of performance measures and diagnostic procedures for X(bar) and S(2) charts
Author(s)
Rahn, Gregory Ernest
Issue Date
1992
Doctoral Committee Chair(s)
Kapoor, Shiv G.
Department of Study
Industrial and Enterprise Systems Engineering
Discipline
Industrial Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Statistics
Industrial Engineering
Language
eng
Abstract
In today's competitive marketplace, companies must continually strive for improved quality and productivity of its products and processes just to maintain its competitive position. For this reason, quality systems were developed to improve quality through the design and manipulation of process resources over time. When examining a specific portion of a process, called a QC window, statistical process control methods, such as Shewhart charts, are responsible for the observation, evaluation, and diagnosis of processes to aid in the decision and implementation of corrective action.
This dissertation develops methods to improve the evaluation and diagnostic elements of the QC window. To enhance the evaluation capability of Shewhart control charts, performance measures in terms of operational characteristics, are defined and developed for the X chart, S$\sp2$ chart, and both charts combined. These performance measures are analyzed with respect to process shifts in both mean and variance. In addition, performance is enhanced by: (a) enforcing four rules on the S$\sp2$ chart to improve sensitivity to variance shifts (b) modifying the control limits on both the X and S$\sp2$ charts to capitalize on the distinct relationships between rules as well as quantifying the tradeoff between the probability of a false alarm ($\alpha$) and the probability of a false indication of control ($\beta$).
To support the diagnostic capability of Shewhart charts, a sequential diagnostic procedure is developed that estimates the mean and variance of a process given observed control chart performance. Once the current state of the process is identified, the decision and implementation of corrective action can then be performed to position the process at its desired state. By improving the evaluation and diagnostic capability of control charts, the work presented in this thesis expands the role of control charts, thus enabling them to reach their full potential.
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