Control Charts for Monitoring Burr Type-X Percentiles

[[abstract]]When the sampling distribution of a parameter estimator is unknown, using normality asymptotically, the Shewhart-type chart may provide improper control limits. To monitor Burr type-X percentiles, two parametric bootstrap charts (PBCs) are proposed and compared with the Shewhart-type chart via a Monte Carlo simulation. Simulation results exhibit that the proposed PBCs perform well with a short average run length to signal out-of-control when the process is out-of-control, and have more adequate control limits than the Shewhart-type chart in view of in-control false alarm rate. An example regarding single fiber strength is presented for illustrating the proposed PBCs.[[incitationindex]]SCI[[booktype]]紙

Measuring process capability for bivariate non-normal process using the bivariate burr distribution

As is well known, process capability analysis for more than one quality variables is a complicated and sometimes contentious area with several quality measures vying for recognition. When these variables exhibit non-normal characteristics, the situation becomes even more complex. The aim of this paper is to measure Process Capability Indices (PCIs) for bivariate non-normal process using the bivariate Burr distribution. The univariate Burr distribution has been shown to improve the accuracy of estimates of PCIs for univariate non-normal distributions (see for example, [7] and [16]). Here, we will estimate the PCIs of bivariate non-normal distributions using the bivariate Burr distribution. The process of obtaining these PCIs will be accomplished in a series of steps involving estimating the unknown parameters of the process using maximum likelihood estimation coupled with simulated annealing. Finally, the Proportion of Non-Conformance (PNC) obtained using this method will be compared with those obtained from variables distributed under the bivariate Beta, Weibull, Gamma and Weibull-Gamma distributions

An Introduction to Statistical Issues and Methods in Metrology for Physical Science and Engineering

This article provides an overview of the interplay between statistics and measurement. Measurement quality affects inference from data collected and analyzed using statistical methods while appropriate data analysis quantifies the quality of measurements. This article brings material on statistics and measurement together in one place as a resource for practitioners. Both frequentist and Bayesian methods are discussed

Process capability index Cpk for monitoring the thermal performance in the distribution of refrigerated products

The temperature of refrigerated products along the cold chain must be kept within pre-defined limits to ensure adequate safety levels and high product quality. Because temperature largely influences microbial activities, the continuous monitoring of the time-temperature history over the distribution process usually allows for the adequate control of the product quality along both short- and medium-distance distribution routes. Time-Temperature Indicators (TTI) are composed of temperature measurements taken at various time intervals and are used to feed analytic models that monitor the impacts of temperature on product quality. Process Capability Indices (PCI), however, are calculated using TTI series to evaluate whether the thermal characteristics of the process are within the specified range. In this application, a refrigerated food delivery route is investigated using a simulated annealing algorithm that considers alternative delivery schemes. The objective of this investigation is to minimize the distance traveled while maintaining the vehicle temperature within the prescribed capability level261546

SPC Methods for Detecting Simple Sawing Defects Using Real-Time Laser Range Sensor Data

Effective statistical process control (SPC) procedures can greatly enhance product value and yield in the lumber industry, ensuring accuracy and minimum waste. To this end, many mills are implementing automated real-time SPC with non-contact laser range sensors (LRS). These systems have, thus far, had only limited success because of frequent false alarms and have led to tolerances being set excessively wide and real problems being missed. Current SPC algorithms are based on manual sampling methods and, consequently, are not appropriate for the volume of data generated by real-time systems. The objective of this research was to establish a system for real-time LRS size control data for automated lumber manufacturing. An SPC system was developed that incorporated multi-sensor data, and new SPC charts were developed that went beyond traditional size control methods, simultaneously monitoring multiple surfaces and specifically targeting common sawing defects. In this paper, eleven candidate control charts were evaluated. Traditional X-bar and range charts are suggested, which were explicitly developed to take into account the components of variance in the model. Applying these methods will lead to process improvements for sawmills using automated quality control systems, so that machines producing defective material can be identified and prompt repairs made

Application of the generalized lambda distributions in a statistical process control methodology

In statistical process control (SPC) methodology, quantitative standard control charts are often based on the assumption that the observations are normally distributed. In practice, normality can fail and consequently the determination of assignable causes may result in error. After pointing out the limitations of hypothesis testing methodology commonly used for discriminating between Gaussian and non-Gaussian populations, a very flexible family of statistical distributions is presented in this paper and proposed to be introduced in SPC methodology: the generalized lambda distributions (GLD). It is shown that the control limits usually considered in SPC are accurately predicted when modelling usual statistical laws by means of these distributions. Besides, simulation results reveal that an acceptable accuracy is obtained even for a rather reduced number of initial observations (approximately a hundred). Finally, a specific user-friendly software have been used to process, using the SPC Western Electric rules, experimental data originating from an industrial production line. This example and the fact that it enables us to avoid choosing an a priori statistical law emphasize the relevance of using the GLD in SPC

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