Evaluation of process capability indices of linear profiles

Purpose: In profile monitoring, which is a growing research area in the field of statistical process control, the relationship between response and explanatory variables is monitored over time. The purpose of this paper is to focus on the process capability analysis of linear profiles. Process capability indices give a quick indication of the capability of a manufacturing process. Design/methodology/approach: In this paper, the proportion of the non-conformance criteria is employed to estimate process capability index. The paper has considered the cases where specification limits is constant or is a function of explanatory variable X. Moreover, cases where both equal and random design schemes in profile data acquisition is required (as the explanatory variable) is considered. Profiles with the assumption of deterministic design points are usually used in the calibration applications. However, there are other applications where design points within a profile would be i.i.d. random variables from a given distribution. Findings: Simulation studies using simple linear profile processes for both fixed and random explanatory variable with constant and functional specification limits are considered to assess the efficacy of the proposed method. Originality/value: There are many cases in industries such as semiconductor industries where quality characteristics are in form of profiles. There is no method in the literature to analyze process capability for theses processes, however recently quite a few methods have been presented in monitoring profiles. Proposed methods provide a framework for quality engineers and production engineers to evaluate and analyze capability of the profile processes. © Emerald Group Publishing Limited.

Process capability analysis in non normal linear regression profiles

When the distribution of a process characterized by a profile is non normal, process capability analysis using normal assumption often leads to erroneous interpretations of the process performance. Profile monitoring is a relatively new set of techniques in quality control that is used in situations where the state of product or process is represented by a function of two or more quality characteristics. Such profiles can be modeled using linear or nonlinear regression models. In some applications, it is assumed that the quality characteristics follow a normal distribution; however, in certain applications this assumption may fail to hold and may yield misleading results. In this article, we consider process capability analysis of non normal linear profiles. We investigate and compare five methods to estimate non normal process capability index (PCI) in profiles. In three of the methods, an estimation of the cumulative distribution function (cdf) of the process is required to analyze process capability in profiles. In order to estimate cdf of the process, we use a Burr XII distribution as well as empirical distributions. However, the resulted PCI with estimating cdf of the process is sometimes far from its true value. So, here we apply artificial neural network with supervised learning which allows the estimation of PCIs in profiles without the need to estimate cdf of the process. Box-Cox transformation technique is also developed to deal with non normal situations. Finally, a comparison study is performed through the simulation of Gamma, Weibull, Lognormal, Beta and student-t data.

Application of artificial neural networks in linear profile monitoring

In many quality control applications the quality of process or product is characterized and summarized by a relation (profile) between a response variable and one or more explanatory variables. Such profiles can be modeled using linear or nonlinear regression models. In this paper we use artificial neural networks to detect and classify the shifts in linear profiles. Three monitoring methods based on artificial neural networks are developed to monitor linear profiles. Their efficacies are assessed using average run length criterion. © 2010 Elsevier Ltd. All rights reserved.

Integral approach and numerical improvement to calculate the carbon concentration profiles in carburising process

In the present work, the carbon diffusion in steel, where the carbon diffusivity varies with the carbon content, was solved with the integral methods under the third boundary condition. The variation of carbon diffusivity in steel with the carbon content was described with two different functions ie. linear dependence and exponential dependence. The integral approximation for both cases was improved with the numerical computation to more accurately predict the carbon profiles. The integral solution is more accurate than the formulation based on the assumption of a constant diffusivity or those based on the assumption of a constant diffusivity and/or constant carbon content at part surface. It is also more easily used in practice than the numerical method to describe the carburising process and predict the carbon content at steel surface and carbon profiles in treated layer.

Assessing body condition and energy budget components by scoring abdominal profiles in free-ranging pink-footed geese Anser brachyrhynchus

An abdominal profile index (API) was developed for pink-footed geese Anser brachyrhynchus as a measure of body condition. On basis of carcass analysis of 56 adult geese with known API prior to collection, we found significant linear relationships between API against body mass, abdominal fat and total energy content. Hence, changes in API reflect net energy intake rates. As an example of the applicability of the calibration, we compared APIs of individually marked geese before and after long migration episodes and estimated the cost of flight at 8.9 kJ/km. In addition we estimated gain rates at three major staging sites along the spring flyway indicating an increase in fueling rates with latitude. Calibration of APIs and energy contents offers new opportunities for field studies of waterfowl energetics.

Integral approach and numerical improvement to calculate carbon concentration profiles in carburising

The carbon diffusion in steel, where the carbon diffusivity varies with the carbon content, was solved with the integral methods under the third boundary condition. The variation of carbon diffusivity in steel with the carbon content was described with two different functions, linear dependence and exponential dependence. The integral approximation for both cases was improved with the numerical computation to more accurately predict the carbon profiles. The integral solution is more accurate than the formulation based on the assumption of a constant diffusivity or those based on the assumption of a constant diffusivity and/or constant carbon content at part surface. It is also more easily used in practice than the numerical method to describe the carburising process and predict the carbon content at steel surface and carbon profiles in treated layer.