Youn Min Chou

Transforming non-normal data to normality in statistical process control

Quality characteristics analyzed in statistical process control (SPC) often are required to be normally distributed. This is true in many types of control charts and acceptance sampling plans, as well as in process capability studies. If a characteristi..

Lower confidence limits on process capability indices

Lower confidence limits are derived for the common measures of process capability, usually indicated by Cp, CPU, CPL, and Cpk. The measures are estimated based on a random sample of observations from the process when the process is assumed to be normall..

On the distributions of the estimated process capability indices

The exact distributions of the estimated process capability indices are presented and their means, variances, and mean-squared errors are given. The basic assumption is that the process measurements are taken from a normal distribution. Theresults in this article are useful in evaluating process capability.

Applying Hotelling's T2 Statistic to Batch Processes

In this paper we show the usefulness of Hotellings T2 statistic for monitoring batch processes in both Phase I and Phase II operations. Discussions of necessary adaptations, such as in the formulas for computing the statistic and its distribution, are included. In a Phase I operation, where the focus is on detecting and removing outliers, consideration is given to batch processes where the batch observations are taken from either a common multivariate normal distribution or a series of multivariate normal distributions with different mean vectors. In a Phase II operation, where the monitoring of future observations is of primary concern, emphasis is placed on the application of the T2 statistic using a known or estimated in-control mean vector. A variety of data sets taken from different types of industrial batch processes are used to illustrate these techniques.

SELECTING A BETTER SUPPLIER BY TESTING PROCESS CAPABILITY INDICES

Process capability indices Cp, CPU, and CPL have been widely used to provide measures of process performance. In this article tests on comparing the capability of two processes are presented. Critical values are given to determine which process is more ..

Determination of source contributions to ambient PM2.5 in Kaohsiung, Taiwan, using a receptor model.

ABSTRACT Ambient particulates of PM2.5 were sampled at three sites in Kaohsiung, Taiwan, during February and March 1999. In addition, resuspended PM2.5 collected from traffic tunnels, paved roads, fly ash of a municipal solid waste (MSW) incinerator, and seawater was obtained. All the samples were analyzed for twenty constituents, including water-soluble ions, organic carbon (OC), elemental carbon (EC), and metallic elements. In conjunction with local source profiles and the source profiles in the model library SPECIATE EPA, the receptor model based on chemical mass balance (CMB) was then applied to determine the source contributions to ambient PM2.5. The mean concentration of ambient PM2.5 was 42.6953.68 μj.g/m3 for the sampling period. The abundant species in ambient PM2.5 in the mass fraction for three sites were OC (12.7-14.2%), SO4 2- (12.8-15.1%), NO3 - (8.110.3%), NH4+ (6.7-7.5%), and EC (5.3-8.5%). Results of CMB modeling show that major pollution sources for ambient PM2.5 are traffic exhaust (18-54%), secondary aerosols (30-41% from SO4 2- and NO3 -), and outdoor burning of agriculture wastes (13-17%).

Prediction Intervals for Screening Using a Measured Correlated Variate

At least I units are required whose values of a performance variable Y fall below the upper specification limit U. They are obtained by screening units on a correlated variable X until m units are obtained whose values of X meet the threshold W. The numbers I and m are specified in advance of screening, and W needs to be determined. Two cases are discussed: one with all parameters known and one with all parameters unknown. The analysis in this paper amounts to the application of a binomial model in addition to the bivariate normal screening model previously discussed in Owen, Mclntire, and Seymour (1975) and in Owen and Su (1977). When the bivariate distribution parameters are unknown, finding W is similar to the prediction interval problem discussed in the literature. Some illustrative tables and examples are included.

Multi-analyte profiling reveals matrix metalloproteinase-9 and monocyte chemotactic protein-1 as plasma biomarkers of cardiac aging

Background— We have previously shown that cardiac sarcopenia occurs with age in C57/BL6J mice. However, underlying mechanisms and plasma biomarkers of cardiac aging have not been identified. Accordingly, the objective of this study was to identify and evaluate plasma biomarkers that reflect cardiac aging phenotypes. Methods and Results— Plasma from adult (7.5±0.5 months old, n=27) and senescent (31.7±0.5 months old, n=25) C57/BL6J mice was collected, and levels of 69 markers were measured by multi-analyte profiling. Of these, 26 analytes were significantly increased and 3 were significantly decreased in the senescent group compared with the adult group. The majority of analytes that increased in the senescent group were inflammatory markers associated with macrophage functions, including matrix metalloproteinase-9 (MMP-9) and monocyte chemotactic protein-1 (MCP-1/CCL-2). Immunoblotting (n=12/group) showed higher MMP-9 and MCP-1 levels in the left ventricle (LV) of senescent mice (P<0.05), and their expression levels in the LV correlated with plasma levels (&rgr;=0.50 for MMP-9 and &rgr; =0.62 for MCP1, P<0.05). Further, increased plasma MCP-1 and MMP-9 levels correlated with the increase in end-diastolic dimensions that occurs with senescence. Immunohistochemistry (n=3/group) for Mac-3, a macrophage marker, showed increased macrophage densities in the senescent LV, and dual-labeling immunohistochemistry of Mac-3 and MMP-9 revealed robust colocalization of MMP-9 to the macrophages in the senescent LV sections, indicating that the macrophage is a major contributor of MMP-9 in the senescent LV. Conclusions— Our results suggest that MCP-1 and MMP-9 are potential plasma markers for cardiac aging and that augmented MCP-1 and MMP-9 levels and macrophage content in the LV could provide an underlying inflammatory mechanism of cardiac aging.Background —We have previously shown that cardiac sarcopenia occurs with age in C57/BL6J mice. However, underlying mechanisms and plasma biomarkers of cardiac aging have not been identified. Accordingly, the objective of this study was to identify and evaluate plasma biomarkers that reflect cardiac aging phenotypes. Methods and Results —Plasma from adult (7.5±0.5 months old, n=27) and senescent (31.7±0.5 months old, n=25) C57/BL6J mice was collected and levels of 69 markers were measured by multi-analyte profiling. Of these, 26 analytes were significantly increased and 3 were significantly decreased in the senescent group compared to the adult group. The majority of analytes that increased in the senescent group were inflammatory markers associated with macrophage functions, including matrix metalloproteinase-9 (MMP-9) and monocyte chemotactic protein-1 (MCP-1/CCL-2). Immunoblotting (n=12/ group) showed higher MMP-9 and MCP-1 levels in the left ventricle (LV) of senescent mice (p<0.05), and their expression levels in the LV correlated with plasma levels (rho=0.50 for MMP-9 and rho=0.62 for MCP1, p<0.05). Further, increased plasma MCP-1 and MMP-9 levels correlated with the increase in end diastolic dimensions that occurs with senescence. Immunohistochemistry (n=3/ group) for Mac-3, a macrophage marker, showed increased macrophage densities in the senescent LV; and dual labeling immunohistochemistry of Mac-3 and MMP-9 revealed robust co-localization of MMP-9 to the macrophages in the senescent LV sections, indicating that the macrophage is a major contributor of MMP-9 in the senescent LV. Conclusions —Our results suggest that MCP-1 and MMP-9 are potential plasma markers for cardiac aging and that augmented MCP-1 and MMP-9 levels and macrophage content in the LV could provide an underlying inflammatory mechanism of cardiac aging.

The control chart for individual observations from a multivariate non-normal distribution

The Hotellings T2statistic has been used in constructing a multivariate control chart for individual observations. In Phase II operations, the distribution of the T2statistic is related to the F distribution provided the underlying population is multivariate normal. Thus, the upper control limit (UCL) is proportional to a percentile of the F distribution. However, if the process data show sufficient evidence of a marked departure from multivariate normality, the UCL based on the F distribution may be very inaccurate. In such situations, it will usually be helpful to determine the UCL based on the percentile of the estimated distribution for T2. In this paper, we use a kernel smoothing technique to estimate the distribution of the T2statistic as well as of the UCL of the T2chart, when the process data are taken from a multivariate non-normal distribution. Through simulations, we examine the sample size requirement and the in-control average run length of the T2control chart for sample observations taken from a multivariate exponential distribution. The paper focuses on the Phase II situation with individual observations.

Systematic patterns in T2 charts

Nonrandom or systematic patterns occurring in a univariate Shewhart control chart have often been used as indicators of extraneous sources of process variation. Proper diagnosis of these patterns can lead to process improvement by reducing the overall system variation. Similarly, in multivariate statistical process control, many different systematic patterns may occur in the control charts used to monitor the process. The purpose of this paper is to examine the process conditions that lead to the occurrence of certain nonrandom patterns in a T2 control chart. Examples resulting from cycles, mixtures, trends, process shifts, and autocorrelated data are identified and presented. Results are applicable to a Phase I operation or a Phase II operation where the T2 statistic is based on the most common covariance matrix estimator.