Monitoring Simple Linear Profiles in the Leather Industry (A Case Study)

Abstract Sometimes, the quality of a process or product can be characterized by a relationship between a response variable and one explanatory variable, which is referred to as profile. In this paper, we introduce an example of a simple linear profile from the dyeing process of shoe leather in the leather industry and conduct a step-by-step Phase I analysis. For this purpose, we use two of the most powerful Phase I methods including the F method by Mahmoud and Woodal

From Profile to Surface Monitoring: SPC for Cylindrical Surfaces Via Gaussian Processes

Quality of machined products is often related to the shapes of surfaces that are constrained by geometric tolerances. In this case, statistical quality monitoring should be used to quickly detect unwanted deviations from the nominal pattern. The majority of the literature has focused on statistical profile monitoring, while there is little research on surface monitoring. This paper faces the challenging task of moving from profile to surface monitoring. To this aim, different parametric approaches and control-charting procedures are presented and compared with reference to a real case study dealing with cylindrical surfaces obtained by lathe turning. In particular, a novel method presented in this paper consists of modeling the manufactured surface via Gaussian processes models and monitoring the deviations of the actual surface from the target pattern estimated in phase I. Regardless of the specific case study in this paper, the proposed approach is general and can be extended to deal with different kinds of surfaces or profiles

Hotelling’s t² control charts based on robust estimators

Under the presence of multivariate outliers, in a Phase I analysis of historical set of data, the T² control chart based on the usual sample mean vector and sample variance covariance matrix performs poorly. Several alternative estimators have been proposed. Among them, estimators based on the minimum volume ellipsoid (MVE) and the minimum covariance determinant (MCD) are powerful in detecting a reasonable number of outliers. In this paper we propose a T² control chart using the biweight S estimators for the location and dispersion parameters when monitoring multivariate individual observations. Simulation studies show that this method outperforms the T²control chart based on MVE estimators for a small number of observations

Phase-II Monitoring of AR (1) Autocorrelated Polynomial Profiles

In some statistical process control applications, quality of a process or product can be characterized by a relationship between a response and one or more independent variables, which is typically referred to a profile. In this paper, polynomial profiles are considered to monitor processes in which there is a first order autoregressive relation between the error terms in each profile. A remedial measure is first proposed to eliminate the effect of autocorrelation in phase-ІІ monitoring of autocorrelated profiles. Then, three methods are employed to monitor polynomial profiles where their performances are compared using the average run length criterion

An optimization of on-line monitoring of simple linear and polynomial quality functions

This research aims to introduce a number of contributions for enhancing the statistical performance of some of Phase II linear and polynomial profile monitoring techniques. For linear profiles the idea of variable sampling size (VSS) and variable sampling interval (VSI) have been extended from multivariate control charts to the profile monitoring framework to enhance the power of the traditional T^2 chart in detecting shifts in linear quality models. Finding the optimal settings of the proposed schemes has been formulated as an optimization problem solved by using a Genetic Approach (GA). Here the average time to signal (ATS) and the average run length (ARL) are regarded as the objective functions, and ATS and ARL approximations, based on Markov Chain Principals, are extended and modified to capture the special structure of the profile monitoring. Furthermore,the performances of the proposed control schemes are compared with their fixed sampling counterparts for different shift levels in the parameters. The extensive comparison studies reveal the potentials of the proposed schemes in enhancing the performance of T^2 control chart when a process yields a simple linear profile. For polynomial profiles, where the linear regression model is not sufficient, the relationship between the parameters of the original and orthogonal polynomial quality profiles is considered and utilized to enhance the power of the orthogonal polynomial method (EWMA4). The problem of finding the optimal set of explanatory variable minimizing the average run length is described by a mathematical model and solved using the Genetic Approach. In the case that the shift in the second or the third parameter is the only shift of interest, the simulation results show a significant reduction in the mean of the run length distribution of the EWMA4 technique

Model robust profile monitoring for the generalized linear mixed model for Phase I analysis

The generalized linear mixed model (GLMM) becomes very popular in profile monitoring, especially when the production processes follow nonnormal distribution. In most of the real-life applications in industry, medicine, biology...and so on researchers assume that the response variable follows a Bernoulli or Binomial distribution. The majority of previous studies in profile monitoring focused on parametric modeling using the logistic regression model, with both fixed or random effects, under the assumption of correct model specification. This research considers those cases where the parametric logistic regression model for the family of profiles is unknown or at least uncertain. Consequently, we propose two mixed model methods to monitor profiles from the exponential family: a nonparametric (NP) regression method based on the penalized spline regression technique and a semiparametric method (model robust profile monitoring for the generalized linear mixed model) which combines the advantages of both the parametric and NP methods. Several Hotelling T2 charts that have been studied for a binary response variable with replicates for Phase I profile monitoring. The performance of the proposed method is evaluated by using mean squares of errors and probability of signals criteria. The results showed satisfactory performance of the proposed control charts.Scopu

Monitoring and performance analysis of regression profiles

There are many cases in industrial and non-industrial sections where the quality characteristics are in the form of profiles. Profile monitoring is a relatively new set of techniques in statistical quality control that is used in situations where the state of product or process is presented by regression models. In the past few years, most research in the field of profile monitoring has mainly focused on the use of effective statistical charting methods, study of more general shapes of profiles, and the effects of violations of assumptions in profile monitoring. Despite several research on the application of artificial neural networks to statistical quality control, no research has investigated the application of neural networks in monitoring profiles. Likewise, there is no research in the literature on the process capability analysis in profile processes. The process capability analysis is to evaluate the ability of a process to meet the customer/engineering specifications and must be done in Phase I of profile monitoring. In a review study on profile monitoring, Woodall (2007) pointed out the importance of process capability analysis in profiles. In this research, we use artificial neural networks (ANN) to detect and classify shifts in linear profiles. Three monitoring methods based on ANN are developed to monitor linear profiles in Phase II. We compare the results for different shift scenarios with existing methods in linear profile monitoring and discuss the results. Furthermore, in this thesis, we evaluate the estimation of process capability indices (PCIs) in linear profiles. We propose a method based on the relationship between proportions of non-conformance and the process capability indices in the profile process. In most existing profile monitoring methods in the literature, it is assumed that the profile design points are deterministic (fixed) so they are unchanged from one profile to another one. In this research, we investigate the estimation of the PCI in normal linear profiles for different scenarios of deterministic and arbitrary (random) data acquisition schemes as well as fixed or linear functional specification limits. We apply the proposed method in estimating the PCI in a yogurt production process. This thesis also focuses on the investigation of the process capability analysis in profiles with non-normal error terms. In this study, we review the methods for estimating PCI in non-normal data and carry out a comprehensive comparison study to evaluate the performance of these methods. Then these methods are applied in the leukocyte filtering process to evaluate the PCI with effect of non-normality in a blood service section. In addition, we develop a new method based on neural networks to estimate the parameters of the Burr XII distribution, which is required in some of the PCI estimation methods with non-normal environments. Finally, in this research we propose five methods to estimate process capability index in profiles where residuals follow non-normal distributions. In a comparison study using Monte Carlo simulations we evaluate the performance of the proposed methods in terms of their precision and accuracy. We provide conclusions and recommendation for the future research at the end