تجزیه و تحلیل سیستم اندازه گیری چند متغیره در تست چند مکانه: روش آنلاین با استفاده از تجزیه و تحلیل مولفه های اصلی

Multisite testing improves manufacturing throughput and reduces costs by applying simultaneous testing to products with multiple measurement instruments in parallel. It is important to perform measurement system analysis (MSA) on a multisite testing system to assess its testing capability. Traditional MSA methods are designed to be either univariate or multivariate in a single-site system. They are not capable of analyzing a complex multisite testing system where there are multivariate measurements and multiple instruments in parallel. We propose an online multivariate MSA approach to detecting faulty test instruments in a multisite testing system. In order to pinpoint a faulty test instrument in a multisite testing system we compare the performance of each test instrument to the overall performance of all the parallel instruments in the system. A modified principal component analysis (PCA) method is proposed to transform multivariate measurement data with dependent variables into those with independent principal components. Assuming that all the instruments have the same measurement accuracy and precision we consider a faulty instrument as one whose principal component values are beyond the three sigma control limits of the principal component values of all instruments. We conduct an experiment to provide empirical evidence that the proposed approach is capable of identifying the faulty instruments in a multisite testing system. This approach can be implemented as an online monitoring technique so that production is not interrupted until a faulty instrument is identified.

Multisite testing, also known as parallel testing, refers to the simultaneous testing of products using multiple measurement instruments in parallel (Goel and Marinissen, 2005, Khoche et al, 2001, Kramer and Proskauer, 2005, Ma and Lombardi, 2008 and Rivoir, 2004). The semiconductor Automatic Test Equipment (ATE) industry often utilizes multisite testing to reduce test cost and improve production throughput. An ATE is an automated testing device that examines products ranging from simple electronic components (e.g., resistors) to complex electronic devices (e.g., smart phones). It applies a multivariate test vector to a Device-Under-Test (DUT) in order to examine its quality characteristics and identify faulty devices (Hashempour et al., 2005 and He et al., 2006). An ATE only tests one product or subcomponent at a time, leaving expensive test hardware and resources idle more than 50% of the test time (McDonnell, 2006). Multisite testing typically shares a set of test hardware across multiple ATEs. Therefore, it can improve manufacturing throughput without spending money to duplicate test hardware. Measurement system analysis (MSA) is a systematic procedure that identifies the components of variations in the precision and accuracy assessments of measuring instruments used in a measurement system (Niles, 2002). The purposes of MSA are to: (1) determine the extent of the observed variability caused by a test instrument; (2) identify the sources of variability in a testing system; and (3) assess the capability of a test instrument (Burdick, Borror, & Montgomery, 2003). MSA is an important element of Six Sigma as well as the ISO/TS 16949 standards. It examines five types of statistical variations, including the commonly used Repeatability and Reproducibility (R&R). In the field of quality assurance the goal of MSA is to determine if a measurement system satisfies the quality assurance requirements. Existing R&R MSA measures, including the precision-to-tolerance ratio, signal-to-noise ratio, discrimination ratio, and confidence intervals, mainly examine the R&R of univariate measures. When applied to a multivariate testing scenario, these measures would only provide partial information because they do not take into account the correlation or dependency that often exists between multivariate variables ( Hayter and Tsui, 1994 and Nedumaran and Pignatiello, 1998). Multivariate statistical methods, such as the principal component analysis (PCA) and cluster analysis, have been proposed and applied to quality engineering practices that involve highly correlated multivariate measures ( Lowry and Montgomery, 1995 and Yang and Trewn, 2004). However, those methods have never been applied to multisite testing where the variations among the parallel instruments add another layer of complexity on top of measure correlation and dependency. In multisite testing a product is randomly assigned to one of the parallel test instruments assuming that those instruments have the same statistical distribution characteristics in measurement variations. But in reality characteristics such as mean and variance will vary across different instruments as common cause variation is expected in any process. Quantifying the expected level of variation, the common cause variation could facilitate the identification of a faulty instrument as the characteristics of its statistical distribution would be expected to be different. In practice it is difficult to identify the faulty instrument unless we take the production offline and calibrate each instrument from time to time. Taking production offline is very time-consuming and cost-bearing due to the interruption to production. Consequently an online method of evaluating the instruments that reduces the interruption of production processes is preferred. To the best of our knowledge there is limited research related to measurement system analysis in multisite testing. In this paper we propose a PCA-based approach to multivariate measurement system analysis in multisite testing. This approach provides for the in-process monitoring of all instruments and considers a faulty instrument as one whose statistical distribution of measurements differs significantly from the overall distribution across multiple test instruments. We define control limits so that a faulty instrument can be identified and taken offline for calibration when the performance of the instrument goes beyond the control limits, indicating the presence of special cause variation. The rest of the paper is organized as follows. Section 2 provides an introduction to multisite testing. Section 3 introduces existing MSA techniques and their shortcomings. Section 4 proposes the PCA-based measurement system analysis method in multisite testing. Section 5 presents an empirical experiment and results. We provide a conclusion in Section 6.

We proposed an online statistical process control multivariate MSA approach using principal component analysis to detect faulty test instruments in a multisite testing system. Traditional MSA methods are designed to be either univariate or multivariate in a single-site system. They are not capable of analyzing a multisite testing system where both the measurement variances caused by DUTs and those caused by different test instruments need to be examined. In order to pinpoint a faulty test instrument in a multisite testing system, we compared the performance of each test instrument to the overall performance of all parallel instruments in the system. We proposed a modified PCA method to transform multivariate measurement data with correlated variables into those with orthogonal principal components. Assuming that all instruments should have the same measurement accuracy and precision, we considered a faulty instrument as one whose principal component values were beyond the three sigma control limits of the principal component values of all instruments. We conducted an experiment to provide empirical evidence that the proposed approach was capable of identifying the faulty instrument in multisite testing. This approach can be implemented as an online monitoring technique for test instruments so that production is not interrupted until a faulty instrument is identified.