View Proposal

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Proposer

Teoh Wei Lin

Title

Optimal designs of the run sum X̅ chart for the gamma process based on median run length and expected median run length

Goal

To optimally design the run sum X̅ chart for the gamma process

Description

The run sum control chart has been recognised for its simplicity and effectiveness in monitoring small and moderate process shifts. However, it is frequently designed and used under the normality assumption, limiting its practical utilization in non-normal settings, which are common in manufacturing. Therefore, this study aims to derive two optimal designs for the run sum X̅ control chart under non-normal condition, particularly for gamma distribution. Unlike prior studies that rely on average run length (ARL), this research uses median run length (MRL) and expected MRL (EMRL) for performance evaluation, as ARL can be misleading due to the skewed nature of run length distributions. The optimal designs minimize the out-of-control MRL and EMRL, subject to a desirable in-control MRL, for both deterministic and unknown shift-size scenarios, respectively, thereby balancing fast shift detection with a low false alarm rate. A Markov chain approach is used in the development, examining both the zero-state and steady state modes of the chart. The proposed charts will be benchmarked against Shewhart and exponentially weighted moving average charts. It is expected that the optimized run sum X̅ control chart yields lower out-of-control MRL and EMRL values, indicating improved average detection speed.

Resources

M. H. Madrid-Alvarez, J. C. García-Díaz, and V. G. Tercero-Gómez, “A CUSUM Control Chart for Gamma Distribution with Guaranteed Performance,” Quality and Reliability Engineering International 40 (3), 1279–1301 (2024).

Background

The dataset adopted from Madrid-Alvarez (2024) will be utilized in the application example section to illustrate the plotting of the proposed optimal run sum X̅ chart in the report.

Url

External Link

Difficulty Level

Challenging

Ethical Approval

None

Number Of Students

1

Supervisor

Teoh Wei Lin

Keywords

statistical process control, run sum chart, gamma distribution, median run length, optimization

Degrees

Bachelor of Science in Statistical Data Science