Sains Malaysiana 48(8)(2019): 1771–1776

http://dx.doi.org/10.17576/jsm-2019-4808-24

High Breakdown Estimator for Dual Response Optimization in the Presence of Outliers

(Penganggar Penguraian Tinggi untuk Pengoptimuman Gerak Balas Dual dengan Kehadiran Titik Terpencil)

HABSHAH MIDI¹* & NASUHAR AB. AZIZ^1,2

¹Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor Darul Ehsan, Malaysia

²Faculty of Computer & Mathematical Sciences, Universiti Teknologi MARA, Cawangan Kelantan, 18500 Machang, Kelantan Darul Naim, Malaysia

Received: 18 April 2017/Accepted: 30 May 2019

ABSTRACT

Nowadays, dual response surface approach is used extensively, and it is known as one of the powerful tools for robust design. General assumptions are the data is normally distributed, and there is no outlier in the data set. The traditional procedures for robust design is to establish the process location and process scale models of the response variable based on sample mean and sample variance, respectively. Meanwhile, the ordinary least squares (OLS) method is often used to estimate the parameters of the regression response location and scale models. Nevertheless, many statistics practitioners are unaware that these existing procedures are easily influenced by outliers, and hence resulted in less accurate estimated mean response obtained through non-resistant method. As an alternative, the use of MM-location, MM-scale estimator, and MM regression estimator is proposed, in order to overcome the shortcomings of the existing procedures. This study employs a new penalty function optimization scheme to determine the optimum factor settings for robust design variables. The effectiveness of our proposed methods is confirmed by well-known example and Monte Carlo simulations.

Keywords: Dual response surface; MM-location and MM-scale; outliers; penalty function optimization

ABSTRAK

Pada masa kini, pendekatan gerak balas permukaan dual telah digunakan secara meluas, dan ia juga dikenal pasti sebagai salah satu kaedah yang berkuasa untuk reka bentuk teguh. Secara umum, data diandaikan tertabur normal, dan tiada titik terpencil di dalam set data. Prosedur tradisi bagi reka bentuk teguh ialah untuk membina model lokasi dan model skala proses berdasarkan min dan varians sampel. Sementara itu, kaedah kuasa dua terkecil biasa (OLS) sering digunakan untuk menganggar parameter bagi model sambutan regresi untuk proses min dan varians. Walau bagaimanapun, ramai pengamal statistik yang tidak menyedari bahawa prosedur sedia ada sangat senang dipengaruhi oleh titik terpencil dan mengakibatkan penganggaran sambutan min diperoleh daripada kaedah tidak teguh, kurang tepat. Sebagai alternatif, penggunaan kaedah pengganggar teguh MM-lokasi, MM-skala dan MM regresi dicadangkan untuk mengatasi kelemahan prosedur sedia ada. Kajian ini menggunakan skima baru untuk pengoptimunan fungsi penalti bagi menentukan tetapan faktor yang optimum untuk pemboleh ubah reka bentuk teguh. Keberkesanan kaedah baru yang dicadangkan disahkan dengan contoh terkenal dan simulasi Monte Carlo.

Kata kunci: Gerak balas permukaan dual; MM-lokasi dan MM-skala; pengoptimunan fungsi penalti; titik terpencil

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*Corresponding author; email: habshahmidi@gmail.com