Maximum hybrid exponentially weighted moving average control chart in the presence of measurement error by using auxiliary information

Hybrid control charts have become part of statistical process control (SPC) but still, need more emphasis. Researchers are developing charts for joint monitoring of process mean and variance shifts just like Max-EWMA and their hybrid version using auxiliary information but are ignoring the effect of measurement error on the efficiency of charts. We propose maximum hybrid exponentially weighted moving average with measurement error using auxiliary information and name it Max-HEWMAMEAI control chart. The efficiency of this chart is proved through calculations of average run lengths ($ARLs$) and standard deviations of run lengths (SDRLs) using the Monte Carlo simulations method whereas, $ARLs$ and $\text{◂⋅▸}SDRLs$ are shown in tabular form. The effect of measurement error on the efficiency of the chart has been analyzed and the impact of multiple measurements to reduce the error effect has been studied using the covariate model. Real-life application is also part of this article to support the simulation results.     

Practitioners guide on parametric,nonparametric, and semiparametric profile monitoring

Profile monitoring is one of the methods used in statistical process control ($SPC$) to understand the functional relationship between response and explanatory variables by tracking this relationship and estimating parameters. SPC is done in two phases: In Phase $I$, a statistical model is created and its parameters estimated using historical data. Phase $II$ implements the statistical model and monitors the live ongoing process. Control charts are graphical tools used to monitor these functional relationships over time in both Phase $I$ and Phase $II$. This study provides a step-by-step application for parametric, nonparametric, and semiparametric methods in profile monitoring and creates an in-depth guideline with comparative analysis studies for novice practitioners. A comparative analysis under each distributional assumption is conducted for various control charts.     

Conditional median run length performance of the synthetic X¯ chart with unknown process parameters

Synthetic-type charts are efficient tools for process monitoring. They are easy to design and implement in practice. The properties of these charts are usually evaluated under the assumption of known process parameters. This assumption is sometimes violated in practice, and process parameters have to be estimated from different phase I data sets collected by different practitioners. This fact causes the between-practitioners variability among the properties of the synthetic-type charts designed for each practitioner. In fact, the shape of the run length distribution of the synthetic-type charts changes with the mean shift size. As a good alternative, the median run length $(MRL)$ metric is argued to evaluate the properties of different control charts. In this paper, the $MRL$ is used as a measure of the synthetic $\overline{X}$ chart's performance, and the conditional $MRL$ properties of the synthetic $\overline{X}$ chart with unknown process parameters are investigated. Both the average $MRL$ ( $AMRL$) and the standard deviation of $MRL$ ( $\text{◂⋅▸}SDMRL$) are used together to investigate the chart's properties when the process parameters are unknown. If the available number of phase I samples is not large enough to reduce the variability of the in-control $MRL$ values to an acceptable level, a bootstrap-type approach is suggested to adjust the control limits of the synthetic $\overline{X}$ chart and to further prevent many unwanted lower in-control $MRL$ values.     

A new double EWMA-t chart with auxiliary information for the process mean

In this paper, we propose an auxiliary-information-based (AIB) double EWMA-$t$ (AIB-DEWMA-$t$) chart for monitoring the process mean. The DEWMA-$t$ chart encompasses the EWMA-$t$ and AIB-EWMA-$t$ charts. The Monte Carlo simulations are used to compute the run length characteristics of the AIB-DEWMA-$t$ chart. Based on detailed run length comparisons, it is found that the AIB-DEWMA-$t$ chart may uniformly and substantially outperform the AIB-EWMA-$t$ chart when detecting different shifts in the process mean. In addition, the AIB-DEWMA-$t$ chart is uniformly more sensitive than the DEWMA-$t$ chart. Similar trends are observed when comparing these control charts with the variable sampling interval feature. A real dataset is also considered to demonstrate the implementation of the proposed chart.     

A one-class peeling method for multivariate outlier detection with applications in phase I SPC

In phase I of statistical process control (SPC), control charts are often used as outlier detection methods to assess process stability. Many of these methods require estimation of the covariance matrix, are computationally infeasible, or have not been studied when the dimension of the data, $p$, is large. We propose the one-class peeling (OCP) method, a flexible framework that combines statistical and machine learning methods to detect multiple outliers in multivariate data. The OCP method can be applied to phase I of SPC, does not require covariance estimation, and is well suited to high-dimensional data sets with a high percentage of outliers. Our empirical evaluation suggests that the OCP method performs well in high dimensions and is computationally more efficient and robust than existing methodologies. We motivate and illustrate the use of the OCP method in a phase I SPC application on a $N=354$, $p=1917$ dimensional data set containing Wikipedia search results for National Football League (NFL) players, teams, coaches, and managers. The example data set and R functions, OCP.R and OCPLimit.R, to compute the respective OCP distances and thresholds are available in the supplementary materials.     

Direct construction of globally D-optimal designs for factors at two levels and main effects models

In developing screening experiments for two-level factors, practitioners typically are familiar with regular fractional factorial designs, which are orthogonal, globally D-optimal (ie, 100% D-efficient), and exist if $N$ is a power of two. In addition, nonregular D-optimal orthogonal designs can be generated for almost any $N$ a multiple of four, the most notable being the family of Plackett and Burman¹ designs. If resource constraints dictate that $N$ is not a multiple of four, while an orthogonal design for two-level factors does not exist, one can still consider a D-optimal design. Exchange algorithms are available in commercial computer software for creating highly D-efficient designs. However, as the number of factors increases, computer searches eventually fail to find the globally optimal design for any $N$ or require impractical search times. In this article, we compile state-of-the-art direct construction methods from the literature for producing globally D-optimal designs for virtually any number of two-level factors as well as any $N$ greater than the number of factors. We summarize the known methods as well as areas for continued research, with the intention of catalyzing research in extending these construction methods.     

Memory-type t charts with multiple auxiliary information for the process mean

Multiple auxiliary information-based (MAIB) memory-type $t$ charts are proposed with fixed and variable sampling intervals for an improved monitoring of the process mean, which include adaptive/nonadaptive cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) $t$ charts. These control charts are constructed based on a unique uniformly minimum variance unbiased estimator of the process mean that requires information on a study variable as well as on several correlated auxiliary variables. The Monte Carlo simulation technique is used to compute the run length characteristics of the proposed charts when sampling from a multivariate normal distribution. The run length comparisons show that the proposed MAIB-$t$ charts outperform their existing auxiliary information based (AIB) and non-AIB $t$ charts, where the normalizing transformation is used for all considered $t$ charts in order to have uniformity in the comparisons. A real data application is also given to support the proposed theory.