Multivariate Statistical Process Control Charts: An Overview

In this paper we discuss the basic procedures for the implementation of multivariate statistical process control via control charting. Furthermore, we review multivariate extensions for all kinds of univariate control charts, such as multivariate Shewhart-type control charts, multivariate CUSUM control charts and multivariate EWMA control charts. In addition, we review unique procedures for the construction of multivariate control charts, based on multivariate statistical techniques such as principal components analysis (PCA) and partial lest squares (PLS). Finally, we describe the most significant methods for the interpretation of an out-of-control signal.quality control, process control, multivariate statistical process control, Hotelling's T-square, CUSUM, EWMA, PCA, PLS

Improved performance of MCUSUM control chart with autocorrelation

In recent years, the importance of quality has become increasingly apparent, and quality control in manufacturing has moved from detecting nonconforming products through inspection to detecting quality abnormalities in the process using statistical process control [1]. where it is used effectively, SPC plays an important role in reducing variation in manufactured items and in increasing the competitiveness of the manufacturer by improving product quality while at the same time decreasing production costs. Charts like the Shewhart X and R charts have found wide use in industry because of their ease of use for technicians and others with minimal training in statistics, since the calculations and plotting can be done by hand. An MCUSUM control chart was constructed with autocorrelated data at different levels of autocorrelation and found to be ineffective in detecting shifts as it occurs. In this article, we have proposed new techniques that can improve the performance of the MCUSUM with autocorrelation using run rule schemes. The techniques was evaluated using ARL measures of performance with 10000 iterations to simulate. The results showed that the performance of MCUSUM with autocorrelation has improved significantly with the new technique which was compared to the existing conventional MCUSUM control chart

A review on the MCUSUM Charts in Detecting the Shifts of the Process with Comparison Study

In this paper, we compare the performance of different MCUSUM methods presented in the literature. First, we briefly introduce MCUSUM methods in multivariate normal distribution. In order to evaluate their performance, we present a comparative study with simulation. Furthermore, we compare the average out-of-control run length of MCUSUM methods under different scenarios of mean shifts, standard deviation shifts, and correlation shifts. The results of the simulation study show that MCUSUM methods have different efficiency in detecting process shifts and based on the required application, the appropriate MCUSUM chart should be selected

Pengendalian Kualitas Pupuk Npk di PT Pupuk Sriwidjaja (PUSRI) Palembang Menggunakan Peta Kendali Maximum Multivariate Cumulative Sum (Max-MCUSUM)

Pupuk NPK merupakan produk pupuk yang baru diproduksi oleh PT Pupuk Sriwidjaja yang sangat mengutamakan kualitas agar pupuk NPK PT PUSRI dapat bersaing, sehingga tidak terjadi kerugian secara finansial bagi produsen dan secara penggunaan bagi konsumen. Dalam penelitian ini, akan dilakukan pengendalian kualitas secara statistik pada pupuk NPK melalui peta kendali. Penelitian akan dilakukan pada 3 variabel utama dan terpenting dalam komposisi pupuk NPK, yaitu nitrogen (N), phospat (P) dan kalium (K), dimana variabel penelitian memiliki hubungan satu sama lain dan memiliki pergeseran proses yang kecil yaitu sebesar 0,92σ, 0,11σ dan 0,18σ. Maka digunakan peta kendali Max-MCUSUM yang lebih sensitif dalam mendeteksi pergeseran proses yang kecil, serta efektif karena memonitor rata-rata dan variabilitas secara simultan dalam satu peta kendali. Setelah dilakukan simulasi, didapatkan batas interval (h) sebesar 29.89. Hasil dari penelitian menggunakan peta kendali Max-MCUSUM pada proses produksi pupuk NPK fase I adalah telah terkendali secara statistik setelah dilakukan identifikasi terhadap penyebab titik yang keluar batas interval dan dilakukan perbaikan. Sedangkan pada fase II, proses produksi pupuk NPK belum terkendali secara statistik Hal ini dikarenakan masih terdapat titik pengamatan yang berada di atas batas interval (h) yang disimbolkan dengan C+. Kemudian, pada perhitungan kapabilitas proses, dapat diketahui bahwa secara multivariat, nilai indeks kapabilitas kinerja proses baik MPp maupun MPpk kurang dari 1. Sehingga dapat disimpulkan bahwa proses produksi pupuk NPK pada PT PUSRI belum kapabel karena memiliki tingkat presisi dan akurasi yang rendah. Analisis Kapalitas; Pengendalian Kualitas Statistika; Peta Kendali Max-MCUSUM; Pupuk NPK; PT Pupuk Sriwidjaja Palemban

A Comparison on the MRL Performances of Optimal MEWMA and Optimal MCUSUM Control Charts

The MEWMA (called the multivariate exponentially weighted moving average) chart and the MCUSUM (called the multivariate cumulative sum) chart are used in process monitoring when a quick detection of small or moderate shifts in the mean vector is desired. The primary objective of this study is to compare the performances of the optimal MEWMA and optimal MCUSUM charts based on their median run length (MRL) profiles. The number of quality characteristics considered is p = 2. Two cases are studied, i.e., Case 1 (a shift in only one variable) and Case 2 (a shift in two variables). A Monte Carlo simulation is conducted using Statistical Analysis Software (SAS) to study and compare the MRL performances for various magnitudes of mean shifts when the process is normally distributed. Overall, the results show that the MRL performances of the MEWMA and MCUSUM charts are comparable

Optimal statistical designs of multivariate EWMA and multivariate CUSUM charts based on average run length and median run leng

Carta kawalan multivariat ialah alat yang berkuasa dalam kawalan proses yang melibatkan kawalan serentak beberapa cirian kualiti yang berkorelasi. Carta-carta multivariat hasil tambah longgokan {MCUSUM) dan multivariat purata bergerak berpemberat eksponen (MEWMA) sentiasa dicadangkan dalam kawalan proses apabila pengesanan cepat anjakan tetap yang keciJ atau sederhana dalam vektor min adalah diingini. A multivariate control chart is a powerful tool in process control involving a simultaneous monitoring of several correlated quality characteristics. The multivariate cumulative sum (MCUSUM) and multivariate exponentially weighted moving average (MEWMA) charts are often recommended in process monitoring when a quick detection of small or moderate sustained shifts in the mean vector is desired

A new multivariate CUSUM chart using principal components with a revision of Crosier's chart

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Integrating SPC and EPC for Multivariate Autocorrelated Process

Statistical process control (SPC) is a widely employed quality control method in industry. SPC is mainly designed for monitoring single quality characteristic. However, as the design of a product/process becomes complex, a process usually has multiple quality characteristics related to it. These characteristics must be monitored by multivariate SPC. When the autocorrelation is present in the process data, the traditional SPC may mislead the results. Hence, the autocorrelated data must be treated to eliminate the autocorrelation effect before employing SPC to detect the assignable causes. Besides, chance causes also have impact on the processes. When the process is out of control but no assignable cause is found, it can be adjusted by employing engineering process control (EPC). However, only using EPC to adjust the process may make inappropriate adjustments due to external disturbances or assignable causes. This study presents an integrated SPC and EPC procedure for multivariate autocorrelated process. The SPC procedure constructs a predicting model using group method of data handling (GMDH), which can transfer the autocorrelated data into uncorrelated data. Then, the Hotelling’s T2 and multivariate cumulative sum control charts are constructed to monitor the process. The EPC procedure constructs a controller utilizing data mining technique to adjust the multiple quality characteristics to their target values. Industry can employ this procedure to monitor and adjust the multivariate autocorrelated process