In practice, there are processes where the in-control mean and standard deviation of a quality characteristic is not stable. In such cases, the coefficient of variation (CV) is a more appropriate measure for assessing process stability. In this paper, we consider the statistical design of Run Rules based control charts for monitoring the CV of multivariate data. A Markov chain approach is used to evaluate the statistical performance of the proposed charts. The computational results show that the Run Rules based charts outperform significantly the standard Shewhart control chart. Moreover, by choosing an appropriate scheme, the Run Rules based charts perform better than the Rum Sum control chart for monitoring the multivariate CV. An example in a spring manufacturing process is given to illustrate the implementation of the proposed charts.
Woodall and Montgomery [35] in a discussion paper, state that multivariate process control is one of the most rapidly developing sections of statistical process control. Nowadays, in industry, there are many situations in which the simultaneous monitoring or control, of two or more related quality - process characteristics is necessary. Process monitoring problems in which several related variables are of interest are collectively known as Multivariate Statistical Process Control (MSPC).This article has three parts. In the first part, we discuss in brief the basic procedures for the implementa…
This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the a…
In this paper we derive control charts for the variance of a Gaussian process using the likelihood ratio approach, the generalized likelihood ratio approach, the sequential probability ratio method and a generalized sequential probability ratio procedure, the Shiryaev-Roberts procedure and a generalized Shiryaev-Roberts ap- proach. Recursive presentations for the calculation of the control statistics are given for autoregressive processes of order 1. In an extensive simulation study these schemes are compared with existing control charts for the variance. In order to asses the performance of t…
Monitoring the ratio of two normal random variables plays an important role in several manufacturing environments. For short production runs, however, the control charts assumed infinite processes cannot function effectively to detect anomalies. In this paper, we tackle this problem by proposing two one-sided Shewhart-type charts to monitor the ratio of two normal random variables for an infinite horizon production. The statistical performance of the proposed charts is investigated using the truncated average run length as a performance measure in short production runs. In order to help the qu…
Control charts, as had been used traditionally for quality monitoring, were applied alternatively to monitor systems' reliability. In other words, they can be applied to detect changes in the failure behavior of systems. Such purpose imposed modifying traditional control charts in addition to developing charts that are more compatible with reliability monitoring. The latter developed category is known as probability limits control charts. The existing reliability monitoring control charts were only dedicated to binary-state systems, and they can't be used to monitor several states simultaneous…
Support Vector Data Description (SVDD) is a machine learning technique used for single class classification and outlier detection. SVDD based K-chart was first introduced by Sun and Tsung for monitoring multivariate processes when underlying distribution of process parameters or quality characteristics depart from Normality. The method first trains a SVDD model on data obtained from stable or in-control operations of the process to obtain a threshold $R^2$ and kernel center a. For each new observation, its Kernel distance from the Kernel center a is calculated. The kernel distance is compared …
This note introduces a new Bayesian control chart to compare two processes by monitoring the ratio of their percentiles under Weibull assumption. Both in-control and out-of-control parameters are supposed unknown. The chart analyses the sampling data directly, instead of transforming them in order to comply with the usual normality assumption, as most charts do. The chart uses the whole accumulated knowledge, resulting from the current and all the past samples, to monitor the current value of the ratio. Two real applications in the wood industry and in the concrete industry give a first pictur…
In this work, we study the performance of two-sided EWMA charts for monitoring double bounded processes using individual observations. Specifically, the term double bounded refers to observations in the interval (0, 1) and thus, these charts are suitable for monitoring rates, proportions and percentages. There are several models that can be used to describe this kind of data (and the respective processes, as well) such as the Beta distribution, the Simplex distribution and the Unit Gamma distribution. For each of these three models, we provide the statistical design and the performance of the …
In many industrial manufacturing processes, the quality of products depends on the relation between two main ingredients or characteristics. Often, this calls for monitoring the ratio of two normal random variables with statistical process control (SPC) techniques. A large number of studies related to designing control charts monitoring this ratio have been published. However, these studies are based purely on the assumption of independent observations. In practice, autocorrelation between observations can exist and should be modeled to protect against the false alarm rate inflation when imple…
Monitoring several correlated quality characteristics of a process is common in modern manufacturing and service industries. Although a lot of attention has been paid to monitoring the multivariate process mean, not many control charts are available for monitoring the covariance matrix. This paper presents a comprehensive overview of the literature on control charts for monitoring the covariance matrix in a multivariate statistical process monitoring (MSPM) framework. It classifies the research that has previously appeared in the literature. We highlight the challenging areas for research and …
In recent years, the monitoring of compositional data using control charts has been investigated in the Statistical Process Control field. In this study, we will design a Phase II Multivariate Exponentially Weighted Moving Average (MEWMA) control chart with variable sampling intervals to monitor compositional data based on isometric log-ratio transformation. The Average Time to Signal will be computed based on the Markov chain approach to investigate the performance of proposed chart. We also propose an optimal procedure to obtain the optimal control limit, smoothing constant, and out-of-contr…
We review methods for monitoring multivariate time-between-events (TBE) data. We present some underlying complexities that have been overlooked in the literature. It is helpful to classify multivariate TBE monitoring applications into two fundamentally different scenarios. One scenario involves monitoring individual vectors of TBE data. The other involves the monitoring of several, possibly correlated, temporal point processes in which events could occur at different rates. We discuss performance measures and advise the use of time-between-signal based metrics for the design and comparison of …
This paper introduces a popular dimension reduction method, sliced inverse regression (SIR), into multivariate statistical process monitoring. Provides an extension of SIR for the single-index model by adopting the idea from partial least squares (PLS). Our partial sliced inverse regression (PSIR) method has the merit of incorporating information from both predictors (x) and responses (y), and it has capability of handling large, nonlinear, or "n<p" dataset. Two statistics with their corresponding distributions and control limits are given based on the X-space decomposition of PSIR for the pur…
Background: All-in-one station-based health monitoring devices are implemented in elder homes in Hong Kong to support the monitoring of vital signs of the elderly. During a pilot study, it was discovered that the systolic blood pressure was incorrectly measured during multiple weeks. A real-time solution was needed to identify future data quality issues as soon as possible. Methods: Control charts are an effective tool for real-time monitoring and signaling issues (changes) in data. In this study, as in other healthcare applications, many observations are missing. Few methods are available for…
A scope in quality control, which has recently received a great deal of attention is profile that characterizes the quality of a product or process by a relationship between two or more variables. In this paper, we propose an EWMA chart for phase II monitoring of multivariate simple linear profile in which several correlated response variables have linear relationships with one explanatory variable. The statistical performance of this scheme is evaluated in terms of out-of-control average run length. Although it seldom signals for small shifts, it is superior to previous works in detecting mod…
The most popular tool used in the industry for monitoring a process is the Shewhart control chart. The major disadvantage of the Shewhart control chart is that it is not very efficient in detecting small process average shifts. To increase the sensitivity of Shewhart control charts to small shifts additional supplementary runs rules has been suggested. In this paper we introduce and study the modified r/m control chart which has an improved sensitivity to small and moderate process average shifts as compared with the standard Shewhart X-bar control chart and corresponding control charts propos…
In this article an SPC case study is presented. It consists of monitoring a manufacturing process used for different products of similar kind. So far, each of these products is monitored individually. However, if there is e.g. a quality problem with one joint component, this signal will be distributed over different control charts. Therefor a standardization is introduced, similar to short run SPC methods. Then control chart methods are applied to detect process deviations. If there are observations out of control, a next step is taken and process information are analysed in order to derive po…
In this note, we revisit the $g$ and $h$ control charts that are commonly used for monitoring the number of conforming cases between the two consecutive appearances of nonconformities. It is known that the process parameter of these charts is usually unknown and estimated by using the maximum likelihood estimator and the minimum variance unbiased estimator. However, the minimum variance unbiased estimator in the control charts has been inappropriately used in the quality engineering literature. This observation motivates us to provide the correct minimum variance unbiased estimator and investi…
This article is a case study illustrating the use of a multivariate statistical method for screening potential chemical markers for early detection of post-harvest disease in storage fruit. We simultaneously measure a range of volatile organic compounds (VOCs) and two measures of severity of disease infection in apples under storage: the number of apples presenting visible symptoms and the lesion area. We use multivariate generalised linear mixed models (MGLMM) for studying association patterns of those simultaneously observed responses via the covariance structure of random components. Remark…
Monitoring multichannel profiles has important applications in manufacturing systems improvement, but it is non-trivial to develop efficient statistical methods due to two main challenges. First, profiles are high-dimensional functional data with intrinsic inner- and inter-channel correlations, and one needs to develop a dimension reduction method that can deal with such intricate correlations for the purpose of effective monitoring. The second, and probably more fundamental, challenge is that the functional structure of multi-channel profiles might change over time, and thus the dimension red…
The memory-type control charts, such as EWMA and CUSUM, are powerful tools for detecting small quality changes in univariate and multivariate processes. Many papers on economic design of these control charts use the formula proposed by Lorenzen and Vance (1986) [Lorenzen, T. J., & Vance, L. C. (1986). The economic design of control charts: A unified approach. Technometrics, 28(1), 3-10, DOI: 10.2307/1269598]. This paper shows that this formula is not correct for memory-type control charts and its values can significantly deviate from the original values even if the ARL values used in this form…
Monitoring of project performance is a crucial task of project managers that significantly affect the project success or failure. Earned Value Management (EVM) is a well-known tool to evaluate project performance and effective technique for identifying delays and proposing appropriate corrective actions. The original EVM analysis is a monetary-based method and it can be misleading in the evaluation of the project schedule performance and estimation of the project duration. Earned Duration Management (EDM) is a more recent method which introduces metrics for the project schedule performance eva…
Classical statistical process control often relies on univariate characteristics. In many contemporary applications, however, the quality of products must be characterized by some functional relation between a response variable and its explanatory variables. Monitoring such functional profiles has been a rapidly growing field due to increasing demands. This paper develops a novel nonparametric $L$-1 location-scale model to screen the shapes of profiles. The model is built on three basic elements: location shifts, local shape distortions, and overall shape deviations, which are quantified by th…
Control charts have traditionally been used in industrial statistics, but are constantly seeing new areas of application, especially in the age of Industry 4.0. This paper introduces a new method, which is suitable for applications in the healthcare sector, especially for monitoring a health-characteristic of a patient. We adapt a Markov chain-based approach and develop a method in which not only the shift size (i.e. the degradation of the patient's health) can be random, but the effect of the repair (i.e. treatment) and time between samplings (i.e. visits) too. This means that we do not use m…
In many applications, a control procedure is required to detect potential deviations in a panel of serially correlated processes. It is common that the processes are corrupted by noise and that no prior information about the in-control data are available for that purpose. This paper suggests a general nonparametric monitoring scheme for supervising such a panel with time-varying mean and variance. The method is based on a control chart designed by block bootstrap, which does not require parametric assumptions on the distribution of the data. The procedure is tailored to cope with strong noise,…
