UUM Electronic Theses and Dissertation
UUM ETD | Universiti Utara Malaysian Electronic Theses and Dissertation
FAQs | Feedback | Search Tips | Sitemap

Robust control charts via winsorized and trimmed estimators

Ayu, Abdul Rahman (2020) Robust control charts via winsorized and trimmed estimators. Doctoral thesis, Universiti Utara Malaysia.

[thumbnail of permission to deposit-grant the permission-901746.pdf] Text
permission to deposit-grant the permission-901746.pdf
Restricted to Repository staff only

Download (966kB) | Request a copy
[thumbnail of s901746_01.pdf] Text

Download (32MB)
[thumbnail of references_901746.docx] Text

Download (85kB)


In process control, cumulative sum (CUSUM), exponentially weighted moving average (EWMA), and synthetic control charts are developed to detect small and moderate shifts. Small shifts which are hard to detect can be costly to the process control if left undetected for a long period. These control charts are not reliable under non-normality as the design structure of the charts is based on the sample mean. Sample mean is sensitive to outliers, a common cause of non-normality. In circumventing the problem, this study applied robust location estimators in the design structure of the control charts, instead of the sample mean. For such purpose, four robust estimators namely 20%-trimmed mean, median, modified one-step M-estimator (MOM), and winsorized MOM (WMOM) were chosen. The proposed charts were tested on several conditions which include sample sizes, shift sizes, and different types of non-normal distributions represented by the g-and-h distribution. Random variates for each distribution were obtained using SAS RANNOR before transforming them to the desired type of distribution. Robustness and detection ability of the charts were gauged through average run length (ARL) via simulation study. Validation of the charts’ performance which was done through real data study, specifically on potential diabetic patients at Universiti Utara Malaysia shows that robust EWMA chart and robust CUSUM chart outperform the standard charts. The findings concur with the results of simulation study. Even though robust synthetic chart is not among the best choice as it cannot detect small shifts as quickly as CUSUM or EWMA, its performance is much better than the standard chart under non-normality. This study reveals that all the proposed robust charts fare better than the standard charts under non-normality, and comparable with the latter under normality. The most robust among the investigated charts are EWMA control charts based on MOM and WMOM. These robust charts can fast detect small shifts regardless of distributional shapes and work well under small sample sizes. These characteristics suit the industrial needs in process monitoring.

Item Type: Thesis (Doctoral)
Supervisor : Syed Yahaya, Sharipah Soaad and Ali Atta, Abdu Mohammed
Item ID: 9837
Uncontrolled Keywords: Average run length, Non-normality, Robust control charts, Robust estimators, Statistical process control.
Subjects: Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA299.6-433 Analysis
Divisions: Awang Had Salleh Graduate School of Arts & Sciences
Date Deposited: 11 Sep 2022 04:09
Last Modified: 11 Sep 2022 04:09
Department: Awang Had Salleh Graduate School of Art & Sciences
Name: Syed Yahaya, Sharipah Soaad and Ali Atta, Abdu Mohammed
URI: https://etd.uum.edu.my/id/eprint/9837

Actions (login required)

View Item
View Item