Detecting outliers in complex profiles using a χ²control chart method

Abstract

The quality of products or manufacturing processes is sometimes characterized by profiles or functions. A method is proposed to identify outlier profiles among a set of complex profiles which are difficult to model with explicit functions. It treats profiles as vectors in high-dimension space and applies a χ 2 control chart to identify outliers. This method is useful in Statistical Process Control (SPC) in two ways: (i) identifying outliers in SPC baseline data; and (ii) the on-line monitoring of profiles. The method does not require explicit expression of the function between the response and explanatory variables or fitting regression models. It is especially useful and sometimes the only option when profiles are very complex. Given a set of profiles (high-dimension vectors), the median of these vectors is derived. The variance among profiles is estimated by considering the pair-wise differences between profiles. A χ 2 statistic is derived to compare each profile to the center vector. A simulation experiment and manufacturing data are used to illustrate applications of the method. Comparing it with the existing non-linear regression method shows that it has a better performance: it misidentifies fewer non-outlier profiles as outliers than the non-linear regression method, and misidentifies similarly small fractions of outlier profiles as non-outliers.

Profile control charts based on nonparametric L-1 regression methods

“…Zhang and Albin (2009) assume that all the profiles are measured on a fixed grid of locations/times. This way, the profiles can be viewed as long vectors.…”

A Distribution‐Free Multivariate Control Chart for Phase I Applications

“…To fit the purpose of Phase I analysis better, we suggest using simultaneously the false-positive and false-negative rates as measures of performance. 53,54 The false-positive rate, denoted by p I , is the rate of wrongly signaling in-control samples, whereas the false-negative rate, which we denote by p II , is the rate of wrongly 'not signaling' out-of-control samples. It follows that p I measures the usual false alarm rate when the process is in control and 1 p II measures the true alarm rate (i.e., the detection power) when the process is out of control.…”

An Area‐based Methodology for the Monitoring of General Linear Profiles

“…Montgomery and Mastrangelo, 41 Psarakis and Papal, 42 Staudlammer et al, 31 Jensen et al, 43 Noorossana et al, 44 Soleimani et al, 45 Qiu et al, 46 Guo et al, 47 Amiri and Zou, 38 and Zhang et al 48 are some typical examples. Extensive studies have been conducted on nonlinear profiles, some of which could be found in Jin and Shi, 7,49 Lada et al, 50 Ding et al, 51 Jeong et al, 52 Zhou et al, 53 Zhang and Albin, 54 Chicken et al, 55 Chang and Yadama, 56 Paynabar and Jin, 57 Guo et al, 47 Paynabar et al, 58 Fan et al, 59 Nikoo and Noorossana, 60 and McGinnity et al 61 It is good to mention several other studies using other approaches, which are listed as follows: Zeng and Chen 62 used Bayesian hierarchical approach. Zou et al 63 used penalized regression model to detect outliers.…”