Optimal linear combination of Poisson variables for multivariate statistical process control

In this paper we analyze the monitoring of p Poisson quality characteristics simultaneously, developing a new multivariate control chart based on the linear combination of the Poisson variables, the LCP control chart. The optimization of the coefficients of this linear combination (and control limit) for minimizing the out-of-control ARL is constrained by the desired in-control ARL. In order to facilitate the use of this new control chart the optimization is carried out employing user-friendly Windows© software, which also makes a comparison of performance between this chart and other schemes based on monitoring a set of Poisson variables; namely a control chart on the sum of the variables (MP chart), a control chart on their maximum (MX chart) and an optimized set of univariate Poisson charts (Multiple scheme). The LCP control chart shows very good performance. First, the desired in-control ARL (ARL₀) is perfectly matched because the linear combination of Poisson variables is not constrained to integer values, which is an advantage over the rest of charts, which cannot in general match the required ARL₀ value. Second, in the vast majority of cases this scheme signals process shifts faster than the rest of the charts.     

The Effect of Instance-Space Partition on Significance

This paper demonstrates experimentally that concluding which induction algorithm is more accurate based on the results from one partition of the instances into the cross-validation folds may lead to statistically erroneous conclusions. Comparing two decision tree induction and one naive-bayes induction algorithms, we find situations in which one algorithm is judged more accurate at the p = 0.05 level with one partition of the training instances but the other algorithm is judged more accurate at the p = 0.05 level with an alternate partition. We recommend a new significance procedure that involves performing cross-validation using multiple instance-space partitions. Significance is determined by applying the paired Student t-test separately to the results from each cross-validation partition, averaging their values, and converting this averaged value into a significance value.     

A combined synthetic and np scheme for detecting increases in fraction nonconforming

The applications of attribute control charts cover a wide variety of manufacturing processes in which quality characteristics cannot be measured on a continuous numerical scale or even a quantitative scale. The np control chart is an attribute chart used to monitor the fraction nonconforming p of a process. This chart is effective for detecting large process shifts in p. The attribute synthetic chart is also proposed to detect p shifts. It utilizes the information about the time interval or the Conforming Run Length (CRL) between two nonconforming samples. During the implementation of a synthetic chart, a sample is classified as nonconforming if the number d of nonconforming units falls beyond a warning limit. Unlike the np chart, the synthetic chart is more powerful to detect small and moderate p shifts. This article proposes a new scheme, the Syn-np chart, which comprises a synthetic chart and an np chart. Since the Syn-np chart has both the strength of the synthetic chart for quickly detecting small p shifts and the advantage of the np chart of being sensitive to large p shifts, it has a better and more uniform overall performance. Specifically, it is more effective than the np chart and synthetic chart by 73% and 31%, respectively, in terms of Weighted Average of Average Time to Signal (WAATS) over a wide range of p shifts under different conditions.     

The quality control chart for monitoring multivariate autocorrelated processes

Previously, quality control and improvement researchers discussed multivariate control charts for independent processes and univariate control charts for autocorrelated processes separately. We combine the two topics and propose vector autoregressive (VAR) control charts for multivariate autocorrelated processes. In addition, we estimate AR(p) models instead of ARMA models for the systematic cause of variation. We discuss the procedures to construct the VAR chart. We examine the effects of parameter shifts and by example present procedures to show the feasibility of VAR control charts. We simulate the average run length to assess the performance of the chart.     

A run sum Hotelling’s χ2 control chart

A run sum Hotelling’s χ² control chart is proposed and its average run length (ARL) performance is evaluated using the Markov chain approach. A fast initial response (FIR) feature of this chart is also considered. In the optimization of the run sum χ² chart, computer programs are used to compute the chart’s optimal parameters. It is shown that the run sum χ² chart is superior to the various χ² charts with runs rules and the synthetic χ² chart, for all sizes of shifts in the mean vector, but less sensitive than the multivariate EWMA (MEWMA) chart toward small shifts. The sensitivity of the run sum χ² chart in detecting small shifts can be further enhanced by adding more regions and scores, so that this chart is as competitive as the MEWMA chart. We reckon that the run sum χ² chart is a relatively easy and effective tool for practitioners, as the χ² chart’s statistics can be plotted in its original scale of measurement, in contrast to the MEWMA chart which plots the transformed measurements.     

Comparison of control charts for low defective rate

It is well known that the conventional p control chart constructed by the normal approximation for the binomial distribution suffers a serious inaccuracy in the monitor process when the true rate of nonconforming items is small. A similar problem also arises in the binomial confidence interval estimation. Adjusted confidence intervals are established in the literature to improve the coverage probability when the binomial proportion is small. In this paper, a new p control chart based on an adjusted confidence interval is established, which can substantially improve the existing control charts when the nonconforming rate is small.     

Monitoring the software development process using a short-run control chart

Techniques for statistical process control (SPC), such as using a control chart, have recently garnered considerable attention in the software industry. These techniques are applied to manage a project quantitatively and meet established quality and process-performance objectives. Although many studies have demonstrated the benefits of using a control chart to monitor software development processes (SDPs), some controversy exists regarding the suitability of employing conventional control charts to monitor SDPs. One major problem is that conventional control charts require a large amount of data from a homogeneous source of variation when constructing valid control limits. However, a large dataset is typically unavailable for SDPs. Aggregating data from projects with similar attributes to acquire the required number of observations may lead to wide control limits due to mixed multiple common causes when applying a conventional control chart. To overcome these problems, this study utilizes a Q chart for short-run manufacturing processes as an alternative technique for monitoring SDPs. The Q chart, which has early detection capability, real-time charting, and fixed control limits, allows software practitioners to monitor process performance using a small amount of data in early SDP stages. To assess the performance of the Q chart for monitoring SDPs, three examples are utilized to demonstrate Q chart effectiveness. Some recommendations for practical use of Q charts for SDPs are provided.     

An integration of NSGA-II and DEA for economic–statistical design of T2-Hotelling control chart with double warning lines

Control charts are the most applicable tools for monitoring the quality of processes. The day-to-day changes in industrial processes and customers’ expectations motivate the process engineers to monitor multiple correlated quality characteristics, simultaneously. Hence, in this paper, the design of a “double warning lines T²-Hotelling” control chart is studied because of the advantages of this multivariate control chart in detecting moderate and small shifts in a process. In this regard, this research aims to optimize a multi-objective economic–statistical design model that considers monitoring costs and statistical features of control chart, concurrently. The non-dominated sorting genetic algorithm II is utilized to obtain a suitable Pareto set for the model. Since it is difficult for the decision makers to select the most efficient solution among the Pareto set, three different methods of data envelopment analysis consisting of Charnes–Cooper–Rhodes model, cross-efficiency technique and aggressive formulation are used to rank the members of Pareto set and to select the most efficient one. Also, in this research the performance of these three methods in discriminating between the efficient solutions is compared to each other. Eventually, a comparative study is conducted to show the better performance of the suggested model in comparison with the corresponding economic design model.

     

Trend Autoregressive Model Exact Run Length Evaluation on a Two-Sided Extended EWMA Chart

The Extended Exponentially Weighted Moving Average (extended EWMA) control chart is one of the control charts and can be used to quickly detect a small shift. The performance of control charts can be evaluated with the average run length (ARL). Due to the deriving explicit formulas for the ARL on a two-sided extended EWMA control chart for trend autoregressive or trend AR(p) model has not been reported previously. The aim of this study is to derive the explicit formulas for the ARL on a two-sided extended EWMA control chart for the trend AR(p) model as well as the trend AR(1) and trend AR(2) models with exponential white noise. The analytical solution accuracy was obtained with the extended EWMA control chart and was compared to the numerical integral equation (NIE) method. The results show that the ARL obtained by the explicit formula and the NIE method is hardly different, but the explicit formula can help decrease the computational (CPU) time. Furthermore, this is also expanded to comparative performance with the Exponentially Weighted Moving Average (EWMA) control chart. The performance of the extended EWMA control chart is better than the EWMA control chart for all situations, both the trend AR(1) and trend AR(2) models. Finally, the analytical solution of ARL is applied to real-world data in the health field, such as COVID-19 data in the United Kingdom and Sweden, to demonstrate the efficacy of the proposed method.     

Beta control charts for monitoring fraction data

p-Charts and np-Charts are commonly used in monitoring variables of the fraction type and these charts assume that the monitored variables are binomially distributed. In this paper we propose a new control chart called Beta Charts, for monitoring fraction data (p). The Beta Chart presents the control limits based on the Beta probability distribution. It was applied for monitoring the variables in three real studies, and it was compared to the control limits with three schemes. The comparative analysis showed that: (i) Beta approximation to the Binomial distribution was more appropriate with values confined in the [0, 1]-interval; and (ii) the charts proposed were more sensitive to the average run length (ARL), in both in-control and out-of-control processes monitoring. The Beta Charts outperform the control charts analyzed for monitoring fraction data.     

Causal relevance to improve the prediction accuracy of dynamical systems using inductive reasoning

In this paper, the concept of causal relevance (CR) is introduced in the context of the fuzzy inductive reasoning (FIR) modelling and simulation methodology. The idea behind CR is to quantify how much influence each system variable has, from the spatial and temporal points of view, on the prediction of the output. This paper introduces the FIR inference engine, and describes how it can be improved by means of the CR concept, helping to reduce uncertainty during the forecasting stage. The FIR inference engine is based on the k-nearest neighbour classification rule, commonly used in the field of pattern recognition, and uses a Euclidean distance measure to compute the distance between neighbours. In this paper, a weight-Euclidean distance measure is proposed that is able to find better quality neighbours by using the CR concept. Applications from different fields are studied in the light of the prediction process, and a comparison between the accuracy of the predictions obtained when using the classical inference engine and the CR option is performed. The results obtained from this research show that FIR predictions are more accurate and precise when the CR option is used, especially for systems where classical FIR forecasting performs rather poorly.     

Unified fusion rules for multisensor multihypothesis network decision systems

In this paper, we present a fusion rule for distributed multihypothesis decision systems where communication patterns among sensors are given and the fusion center may also observe data. It is a specific form of the most general fusion rule, independent of statistical characteristics of observations and decision criteria, and thus, is called a unified fusion rule of the decision system. To achieve globally optimum performance, only sensor rules need to be optimized under the proposed fusion rule for the given conditional distributions of observations and decision criterion. Following this idea, we present a systematic and efficient scheme for generating optimum sensor rules and hence, optimum fusion rules, which reduce computation tremendously as compared with the commonly used exhaustive search. Numerical examples are given, which support the above results and provide a guideline on how to assign sensors to nodes in a signal detection networks with a given communication pattern. In addition, performance of parallel and tandem networks is compared.     

Convergence Properties of Iterative Learning Control Processes in the Sense of the Lebesgue‐P Norm

This paper addresses the convergence issue of first‐order and second‐order PD‐type iterative learning control schemes for a type of partially known linear time‐invariant systems. By taking advantage of the generalized Young inequality of convolution integral, the convergence is analyzed in the sense of the Lebesgue‐p norm and the convergence speed is also discussed in terms of Q_p factors. Specifically, we find that: (1) the sufficient condition on convergence is dominated not only by the derivative learning gains, along with the system input and output matrices, but also by the proportional learning gains and the system state matrix; (2) the strictly monotone convergence is guaranteed for the first‐order rule while, in the case of the second‐order scheme, the monotonicity is maintained after some finite number of iterations; and (3) the iterative learning process performed by the second‐order learning scheme can be Q_p‐faster, Q_p‐equivalent, or Q_p‐slower than the iterative learning process manipulated by the first‐order rule if the learning gains are appropriately chosen. To manifest the validity and effectiveness of the results, several numerical simulations are conducted. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Using Rule Quality Measures for Rule Base Refinement in Knowledge-Based Predictive Maintenance Systems

Abstract

As today’s manufacturing domain is becoming more and more knowledge-intensive, knowledge-based systems (KBS) are widely applied in the predictive maintenance domain to detect and predict anomalies in machines and machine components. Within a KBS, decision rules are a comprehensive and interpretable tool for classification and knowledge discovery from data. However, when the decision rules incorporated in a KBS are extracted from heterogeneous sources, they may suffer from several rule quality issues, which weakens the performance of a KBS. To address this issue, in this paper, we propose a rule base refinement approach with considering rule quality measures. The proposed approach is based on a rule integration method for integrating the expert rules and the rules obtained from data mining. Within the integration process, rule accuracy, coverage, redundancy, conflict, and subsumption are the quality measures that we use to refine the rule base. A case study on a real-world data set shows the approach in detail.     

Design and optimization of EWMA control charts for in-control,indifference, and out-of-control regions

The design of quality control charts is normally carried out considering a process shift size that is considered important to be detected. The EWMA control chart is one of the best available options to use when good performance is needed to detect small process shifts. This paper presents a method for design of EWMA charts for control processes, in which the detection of small shifts is not necessary, and at the same time is effective in detecting important shifts. In such cases the EWMA control chart can also be designed successfully to deal with these requirements. A Markov chain approach is also applied to determine the ARL of the modified EWMA control chart. The implementation and interpretations are provided and numerical examples are used to illustrate the application procedure. We also investigate some basic properties of the proposed scheme. Genetic algorithms have been used to carry out this design.     

A real-time inventory decision system using Western Electric run rules and ARMA control chart

Inventory management is an important area of production control. In 1999, Pfohl et al. [Pfohl, H.-C., Cullmann, O., & Stölzle, W. (1999). Inventory management with statistical process control: Simulation and evaluation. Journal of Business Logistics, 20, 101–120] developed a real-time inventory decision support system by using the individual control charts for monitoring the inventory level (i.e., stock quantity) and the market demand, in which a series of decision rules are provided to help the inventory manager to determine the time and the quantity to order. In the present paper, a real-time inventory decision system is proposed by incorporating Western Electric run rules into the decision rules of the system. Since the data of demand sometimes present a pattern of time series (i.e., autocorrelation may exist in the data of demand), in the proposed decision system the ARMA control chart is employed to monitor the market demand and the individual control chart is used to monitor the inventory level. A simulation study is conducted to investigate the effects of demand pattern and autocorrelation on the proposed inventory decision system and to verify the effectiveness of the system. The index “service level” is selected as the key indicator for the system performance. Based on the results of the simulation study, it is shown that the performance of the proposed inventory decision system is quite consistent with service level always greater than 90% for various demand patterns.     

A nonparametric exponentially weighted moving average signed-rank chart for monitoring location

Nonparametric control charts can provide a robust alternative in practice to the data analyst when there is a lack of knowledge about the underlying distribution. A nonparametric exponentially weighted moving average (NPEWMA) control chart combines the advantages of a nonparametric control chart with the better shift detection properties of a traditional EWMA chart. A NPEWMA chart for the median of a symmetric continuous distribution was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see Gibbons and Chakraborti, 2003). This is called the nonparametric exponentially weighted moving average Signed-Rank (NPEWMA-SR) chart. However, important questions remained unanswered regarding the practical implementation as well as the performance of this chart. In this paper we address these issues with a more in-depth study of the two-sided NPEWMA-SR chart. A Markov chain approach is used to compute the run-length distribution and the associated performance characteristics. Detailed guidelines and recommendations for selecting the chart’s design parameters for practical implementation are provided along with illustrative examples. An extensive simulation study is done on the performance of the chart including a detailed comparison with a number of existing control charts, including the traditional EWMA chart for subgroup averages and some nonparametric charts i.e. runs-rules enhanced Shewhart-type SR charts and the NPEWMA chart based on signs. Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors. A summary and some concluding remarks are given.     

An Analysis of the Dependence Among Financial Markets by Spatial Contagion

Spatial contagion between two financial markets X and Y appears when there is more dependence between X and Y when they are doing badly than when they exhibit typical performance. In this paper, we introduce an index to measure the contagion effects. This tool is based on the use of suitable copulas associated with the markets and on the calculation of the related conditional Spearman's correlation coefficients. As an empirical application, the proposed index is used to create a clustering of European stock market indices to assess their behavior in the recent years. The whole procedure is expected to be useful for portfolio diversification in crisis periods.     

WYTIWYR: A User Intent-Aware Framework with Multi-modal Inputs for Visualization Retrieval

Retrieving charts from a large corpus is a fundamental task that can benefit numerous applications such as visualization recommendations. The retrieved results are expected to conform to both explicit visual attributes (e.g., chart type, colormap) and implicit user intents (e.g., design style, context information) that vary upon application scenarios. However, existing example-based chart retrieval methods are built upon non-decoupled and low-level visual features that are hard to interpret, while definition-based ones are constrained to pre-defined attributes that are hard to extend. In this work, we propose a new framework, namely WYTIWYR (What-You-Think-Is-What-You-Retrieve), that integrates user intents into the chart retrieval process. The framework consists of two stages: first, the Annotation stage disentangles the visual attributes within the query chart; and second, the Retrieval stage embeds the user's intent with customized text prompt as well as bitmap query chart, to recall targeted retrieval result. We develop aprototype WYTIWYR system leveraging a contrastive language-image pre-training (CLIP) model to achieve zero-shot classification as well as multi-modal input encoding, and test the prototype on a large corpus with charts crawled from the Internet. Quantitative experiments, case studies, and qualitative interviews are conducted. The results demonstrate the usability and effectiveness of our proposed framework.