Pengembangan Diagram Pengendali Simultan Tipe Shewhart Dan CUSUM Berbasis Ranked Set Sampling

Perdana, Sukma Adi (2026) Pengembangan Diagram Pengendali Simultan Tipe Shewhart Dan CUSUM Berbasis Ranked Set Sampling. Doctoral thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Diagram pengendali simultan adalah diagram yang dapat digunakan untuk memonitor mean dan variabilitas secara bersamaan. Saat ini terdapat tiga tipe diagram pengendali simultan yaitu Tipe Shewhart (Max Chart), Tipe CUSUM (Max-CUSUM Chart), dan Tipe EWMA (MaxEWMA Chart). Penggunaan skema Ranked Set Sampling (RSS) dalam pengembangan diagram pengendali simultan terbukti efektif meningkatkan kinerja diagram pengendali tersebut. Pengembangan diagram pengendali simultan MaxEWMA berbasis Ordered RSS dan Ordered Imperfect RSS telah membuktikannya. Kinerja diagram pengendali simultan MaxEWMA berbasis Ordered RSS dan Ordered Imperfect RSS tersebut lebih baik dibandingkan dengan diagram pengendali simultan berbasis skema Simple Random Sampling (SRS). Dalam rangka penetapan batas pengendali dari diagram pengendali simultan tipe Shewhart dan CUSUM berbasis RSS, dikembangkan pula metode penetapan batas pengendali yang ditingkatkan berbasis metode bootstrap. Sehingga penelitian ini mengembangkan diagram pengendali simultan tipe Shewhart dan tipe CUSUM berbasis RSS dengan penetapan batas pengendali yang ditingkatkan berbasis metode bootstrap. Adapun tujuan dari penelitian ini adalah mengembangkan metode penetapan batas pengendali yang ditingkatkan berbasis metode bootstrap dalam menentukan batas pengendali dari diagram pengendali, mengembangkan dan mengevaluasi kinerja diagram pengendali simultan tipe Shewhart berbasis RSS, serta mengembangkan dan mengevaluasi kinerja diagram pengendali simultan tipe CUSUM berbasis RSS. Hasil evaluasi kinerja melalui studi simulasi menunjukkan bahwa metode penetapan batas pengendali yang ditingkatkan berbasis metode bootstrap dapat menentukan batas pengendali yang lebih akurat dan stabil dibandingkan dengan metode bootstrap klasik. Selanjutnya, hasil studi simulasi juga membuktikan bahwa kinerja dari diagram pengendali simultan tipe Shewhart dan CUSUM berbasis RSS lebih unggul dibandingkan diagram pengendali simultan tipe Shewhart dan CUSUM berbasis SRS.
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Simultaneous control charts are statistical instruments designed to concurrently monitor both the process mean and variability. Presently, there are three principal categories of simultaneous control charts: the Shewhart type (Max Chart), the CUSUM type (Max-CUSUM Chart), and the EWMA type (MaxEWMA Chart). The integration of Ranked Set Sampling (RSS) schemes in the development of these charts has been shown to enhance their performance, as evidenced by the creation of MaxEWMA simultaneous control charts based on Ordered RSS and Ordered Imperfect RSS. Notably, these charts demonstrated superior performance compared to their Simple Random Sampling (SRS) counterparts. This research is centered on the development of RSS-based Shewhart and CUSUM simultaneous control charts. To facilitate this, an improved method for control limit determination utilizing the bootstrap technique was developed. The primary objectives of this study are: (1) to develop an improved bootstrap-based method for determining control limits; (2) to develop and evaluate the performance of RSS-based Shewhart simultaneous control charts; and (3) to develop and evaluate the performance of RSS-based CUSUM simultaneous control charts. Performance evaluations through simulation studies indicate that the proposed improved bootstrap method provides more accurate and stable control limits compared to the classical bootstrap method. Furthermore, the results demonstrate that the RSS-based Shewhart and CUSUM simultaneous control charts significantly outperform the SRS-based simultaneous control charts.

Item Type:	Thesis (Doctoral)
Uncontrolled Keywords:	Diagram pengendali simultan, Max Chart, Max-CUSUM Chart, RSS, bootstrap, Simultaneous Control Chart
Subjects:	H Social Sciences > HA Statistics T Technology > TS Manufactures > TS156 Quality Control. QFD. Taguchi methods (Quality control)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49001-(S3) PhD Thesis
Depositing User:	Sukma Adi Perdana
Date Deposited:	31 Jan 2026 06:24
Last Modified:	31 Jan 2026 06:24
URI:	http://repository.its.ac.id/id/eprint/131399

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