Assignable Causes Research Articles

CUSUM charts utilizing reparametrized Birnbaum-saunders model for fault detection and process control

Statistical process control is always intrigued by the design of effective control charts for monitoring production processes and determining assignable causes of variations. It can be challenging to keep track of a positive asymmetric response variable while considering the impact of the input variables. The current work incorporates the Reparametrized Birnbaum Saunders (RBS) model to develop more effective cumulative sum (CUSUM) control charts for analyzing the mean of such a process. We perform a simulation study to evaluate the effectiveness of existing and derived approaches in terms of run length characteristics. The findings showed that when the underlying process distribution is positively asymmetric, the proposed charts provide stronger protection against process alterations as compared to existing methods. Moreover, the suggested control charts are implemented using actual data from a combined cycle power plant.

The multi-objective economic statistical design of the p-chart: NSGA II approach

A control chart is a crucially important tool in statistical process control that is essentially used to differentiate between assignable and chance causes of variation. With the advent of Six Sigma in the parlance of quality management, the control chart assumes more significance to hold the gain in the control phase after attaining process improvement in the improve phase. The sample size, sampling interval, and control limits’ multiplier are three important parameters required to design an effective as well as efficient control chart. Many approaches like economic design, statistical design, and economic statistical design of control charts have been studied by several researchers. All these approaches consider a single objective function. In this paper, we have proposed a multi-objective design of the p-chart, where we are minimizing both out-of-control Average Run Length ( ARL δ ) and the expected cost per cycle ( C E ). Non-dominated Sorting Genetic Algorithm II (NSGA II) is used to solve the proposed multi-objective model. The proposed approach is demonstrated with the help of two numerical examples and the corresponding results are found to be quite encouraging for minimizing both objectives in comparison to another pertinent model given in the literature. Sensitivity analysis has been carried out to give credence to the worth of the proposed approach.

Similarity searching for wafer bin maps by measuring shape, location, and size similarities of defect patterns

A wafer bin map (WBM) is a visual representation of the spatial distribution of defective chips on a wafer. WBMs showing specific defect patterns are usually a result of process-assignable causes; thus, it is important to identify them to eliminate assignable causes. With advances in semiconductor manufacturing technology, identifying new defect patterns, and diagnosing their causes have become critical. However, most existing methods for WBM analysis use a supervised learning approach, which only detects previously known defect patterns. The similarity-search approach is a suitable alternative for defining new defect patterns. The proposed method uses an unsupervised approach to search for similar WBMs by measuring the similarities of three spatial features of defect patterns–shape, location, and size–which are useful for defining new defect patterns and diagnosing their causes. These three similarities are achieved using tensor voting and the mountain function for shape similarity, Euclidean distance for location similarity, and a combination of defect count and average radius for size similarity. The overall similarity was assessed using the weighted average of the three similarities. The weights are determined by quantifying the uncertainty of each similarity based on information entropy theory to better distinguish between similar patterns. The experimental results demonstrate the effectiveness of the proposed method compared to existing methods and highlight its capability to identify and describe the spatial features of defect patterns.

Integration of maintenance policy and statistical process monitoring for a cascade process with multiple assignable causes and random failures

This study develops an integrated model of statistical process monitoring and maintenance policy (MP) for a two-stage cascade process, involving two machines in series where the output of one stage affects the next stage. Instead of a single assignable cause (AC) affecting the quality characteristic, this production process experiences multiple ACs to more precisely simulate real conditions. Traditional and Hotelling’s T2 charts cannot detect the specific stage in which a shift occurs; therefore, this study employs a Cause-selecting control chart. The possibility of equipment failure and system stoppage are considered, with the process failure mechanism following a Weibull distribution. Depending on the conditions affecting the process or equipment, four MPs are considered to acheive the system’s initial condition, resulting in sixteen defined scenarios. The goal is to determine decision variables by minimizing a cost function subject to some statistical measures. This economic-statistical design can improve statistical and/or economic measures. However, it creates a more complex problem. Due to this complexity, a particle swarm optimization algorithm is used for optimization. The proposed model is implemented for a system that produces cotton yarn, with fiber length and skein strength are as the outputs of the first and second stages, respectively. Comparisons with two models validate the proposed model’s performance in cost reduction. A sensitivity analysis is performed for further investigations. The results indicate significant cost savings of the proposed model.

A new ViT-Based augmentation framework for wafer map defect classification to enhance the resilience of semiconductor supply chains

Wafer map defect classification plays a crucial role in sustaining the semiconductor supply chain during industrial disruptions by ensuring continuity, resilience, and efficiency while aligning with sustainability principles. Up to 30 percent of production costs is lost to chip testing and yield losses for semiconductor manufacturing supply chain. In the semiconductor practice, wafer map defects recognition plays a linchpin role in the front-end-of-line stage. Defect pattern recognition can directly pinpoint the assignable causes and provide the domain experts with actionable insights. However, various wafer defect types occur differently from each other, which makes the collected wafer map dataset to be highly imbalanced in defect classes. In the face of data imbalance, the classification model usually cannot provide satisfactory classification performance. In this aspect, this paper intends to investigate the wafer defect map classification problem by using Vision Transformer (ViT) as an alternative data augmentation approach. The primary purpose is to alleviate the class-imbalance issue and then the performance of a deep learning-based convolutional neural network for wafer defect classification can be effectively improved. The experimental results demonstrate that the proposed data augmentation method by using ViT proves to be a potential generative model for improving wafer map defect classification, particularly robust on the individual minority class. In a word, the proposed augmentation framework for wafer map defect classification facilitates a more targeted and efficient approach to quality control, resource utilization, and production optimization in maintaining a sustainable semiconductor supply chain, particularly in times of industrial disruption.

Economic Statistical Design of the Variable Sampling Interval CV Chart with Known Shift Size

Control charts are essential in Statistical Process Control (SPC) to enhance the product quality by identifying assignable causes within the process. Extensive study on coefficient of variation (CV) charts has been conducted in recent years, indicating their growing significance in a variety of scientific applications. In order to monitor the quality characteristic, it should be noted that the statistical properties and economic perspectives are both indispensable factors. For the economic design, the optimal design parameters that minimise the expected cost function are obtained. However, this design has a major weakness, where it overlooks the statistical performance of the control chart. Therefore, it is of greater importance to examine the economic statistical design, which includes statistical constraints on the cost model. Although the existing variable sampling interval (VSI) CV chart has excellent statistical qualities, it is deficient in taking into account the economic aspects that are necessary for cost-effective process monitoring. In response, this research proposes the economic statistical design of the variable sampling interval (VSI) CV chart with known shift size. Moreover, the study includes sensitivity analyses of the optimal cost and the optimal design parameters for various input parameters. The effects of misspecification of the shift size on the performance of the VSI CV chart are investigated. Additionally, the comparisons in terms of the economic statistical performance between the VSI CV, Shewhart CV and EWMA CV charts are conducted. In comparison with Shewhart CV and EWMA CV charts, the findings clearly demonstrate that the VSI CV chart performs better in all numerical examples. As a result, this research advocates the use of the economic statistical design of the VSI CV chart in process monitoring and provides insightful information for quality practitioners seeking cost-effectiveness and optimal performance in their processes.

Gold source and deposition in the Sanakham gold deposit, SW Laos: Constrains from textures, trace element geochemistry and in-situ sulfur isotopes of pyrite

The Luang Prabang (Laos) – Loei (Thailand) metallogenetic belt is endowed with major porphyry-skarn, and epithermal gold deposits. The Sanakham gold deposit is a newly discovered hydrothermal vein-type orogenic gold deposits (10.6 t Au @ 3.05 g/t) in the belt, and consist of a series of quartz-sulfide veins that are controlled by secondary structures of the regional NNE-trending brittle-ductile shear zone. Its mineralization can be divided into four stages: (I) quartz–pyrite–arsenopyrite, (II) quartz–pyrite–pyrrhotite–chalcopyrite, (III) quartz–pyrite–base-metal sulfide, and (IV) quartz–carbonate. Three pyrite generations were identified: py1 (stage I) as disseminated euhedral to subhedral coarse grains; py2 (stage II) as subhedral to anhedral fine grains occur around the cataclastic and corrosion textures in py1; py3 (stage III) as subhedral to anhedral fine grains occurred in sulfide veins or veinlets that overprint the existing quartz-sulfides. All three generations of pyrite have low trace-element contents including very low lattice-bound gold (py1: 0.040 ppm; py2: 0.098 ppm; py3: 0.028 ppm) and arsenic (py1: 227 ppm; py2: 133 ppm; py3: 13.3 ppm) contents. Visible gold grains are sited in textures of pyrite grains that relate to brittle cataclastic deformation. Considering the relatively low contents of pyrite in the ores of Sanakham, it is impossible to derive the high-gold grade orebodies through local remobilization of originally lattice-bound gold in pyrite. The py2 might be formed during hydrothermal overprinting and dissolution of py1 led by continuous supply of ore fluids with relatively higher contents of Au, Ag, Cu, Sb, Te, Pb, and Bi. A reduction reaction related to reduced carbon species in wallrock is an assignable cause for gold deposition, even though the fluid-rock interaction and fluid immiscibility processes might be important. The Au- and As-poor pyrites have similar δ34S values (py1: –2.58 to –0.83 ‰; py2: –2.17 ‰ to + 0.25 ‰; py3: –1.24 to –0.60 ‰ ppm) that close to 0 ‰, indicating the sulfur may have been originated from magmatic or mantle sources. Therefore, we propose that the Sankham gold deposit is a member of the orogenic deposit class, but notably characterized by the low concentrations of invisible gold in the relatively As-poor pyrite lattice.

Attribute statistical process control under nonconstant process deterioration

AbstractA statistical process control (SPC) model is introduced that incorporates sample data on the number of defectives and allows the probability that an assignable cause of variation in each time interval of a finite production process to be nonconstant. A Limited Memory Influence Diagram (LIMID) model is implemented to facilitate the decision in each time interval on whether or not to investigate the potential presence of the assignable cause of variation and restore the process to working condition. The method determines control limits that minimize the costs of inspection, repair, sampling, and operating under the assignable cause of variation. Sample size and sampling intervals can also be adjusted to further reduce the costs of maintaining quality control. This method expands on the capabilities of models that assume that the conditional probability of an assignable cause occurring remains constant throughout the production horizon.

Shewhart control charts – A simple but not easy tool for data analysis

Shewhart control charts (ShCCs) are a powerful and technically simple tool for process variability analysis. However, simultaneously, they cannot be fully algorithmized and require deep process knowledge together with additional data analysis. ShCCs are well known, though, and the number of papers is great, as well as standards on ShCCs work in most countries, there are some serious obstacles for their effective application which are not being discussed in either educational or scientific literature. Just these problems are being considered in this paper. We analyzed two sides of standard assumption about data normality. First, we discuss the widely-spread misconception that measurement data are always distribu­ted according Gauss law. Then, it is shown how the deviation from normality may impact the method of ShCCs’ constructing and interpreting. Using a specific process data, we debate on right and wrong ways to build ShCC. Further, the paper describes two new definitions of assignable causes of variation: not changing (I-type) and changing (X-type) the system. At the end, we discuss how the work with ShCCs should be organized effectively. It is outlined that creating and analyzing ShCCs is always a system question of interaction between the process and the person who tries to improve this process.

A variable sample size side-sensitive synthetic coefficient of variation chart

A major challenge for control charts monitoring the coefficient of variation is to quickly detect shifts in this parameter, so that assignable cause(s) can be quickly removed and the process can operate in an in-control state with a stable coefficient of variation. This is especially so when there are constraints in the sample size. One proposed strategy is to vary the sample size according to the most recent information. However, a side-sensitive synthetic chart monitoring the coefficient of variation with variable sample size is not available. This paper contributes to the literature by developing a variable sample size side-sensitive synthetic chart for the coefficient of variation. The main contributions are in terms of illustrating the operations of the chart, deriving the formulae to evaluate its performance and developing the algorithms to optimize its performance. Comparisons with current charts show that the proposed chart outperforms all existing synthetic-type charts monitoring the coefficient of variation. The proposed chart also outperforms the variable sample size coefficient of variation chart for all shift sizes. In addition, it outperforms the variable sample size run sum and variable sample size Exponentially Weighted Moving Average charts monitoring the coefficient of variation for moderate and large shift sizes.

Designing a Log-Logistic-Based EWMA Control Chart Using MOPSO and VIKOR Approaches for Monitoring Cardiac Surgery Performance

This study aims to develop a risk-adjusted Exponentially Weighted Moving Average (EWMA) control chart for computer-based performance monitoring in cardiac surgery. Patients have distinct risk factors that impact the surgical process before it even begins. As a result, risk adjustment is carried out utilizing the Accelerated Failure Time (AFT) model to consider these factors. Before using the risk-adjusted EWMA chart, the optimal parameter design should be established, considering the required statistical and economic factors. A model for Multi-Objective Decision Making (MODM) with multiple assignable causes has been proposed to accomplish this. The model is solved using a two-stage methodology based on the Multi-Objective Particle Swarm Optimization (MOPSO) method and the VIekriterijumsko KOmpromisno Rangiranje (VIKOR) method. An actual case study for cardiovascular patients has been undertaken to demonstrate the performance and effectiveness of the suggested model. The multi-objective and pure economic models have been thoroughly compared. The economic model with statistical constraints and the multi-objective model have also been compared again. The findings suggest that the multi-objective design of the risk-adjusted EWMA chart exhibits higher statistical performance in both cases against a small augment in cost.

Joint production, maintenance and quality control chart optimization for a degrading manufacturing–reworking system with assignable causes

Joint production, maintenance and quality control chart optimization for a degrading manufacturing–reworking system with assignable causes

An economic-statistical design of synthetic Tukey’s control chart with Taguchi’s asymmetric loss functions under log-normal distribution

The synthetic Tukey’s control chart (denoted by Syn-TCC) applies a single observation in the process monitoring and is relatively robust to outliers. For a complex process, the probability distribution of quality characteristic must be carefully identified and the loss of quality characteristic, which is defined as the deviation from the target value, must be accurately estimated so that the quality state of the process may be more comprehensively described. However, the literature rarely studied the economic design of the Syn-TCC with Taguchi’s loss function under non normality. In the present study, it is assumed that the quality characteristic follows a log-normal distribution and Taguchi’s asymmetric linear and quadratic loss functions are involved to develop the economic-statistical design of the Syn-TCC for multiple assignable causes. A case study is presented to illustrate the application of this economic-statistical design of the Syn-TCC to an IC package industry. The sensitivity analysis of this case study reveals that a larger production lot size and larger two coefficients of loss functions generally lead to a higher total expected cost.

Intermittent sampling for statistical process control with the number of defectives

An intermittent sampling model for statistical process control (SPC) is introduced to monitor the quality of output from a production process where the number of defective units in a sample is measured in selected time periods. A Limited Memory Influence Diagram (LIMID) model is implemented to determine the time periods in which to collect samples and the decision strategy to minimize total costs of quality control. In periods where samples are collected, the observed defectives determine whether the process is stopped to investigate and repair an assignable cause of variation. Based on sample results, the process can alternatively be allowed to run without interruption until the next predetermined sampling interval, or the results may suggest collecting a sample again in the next period. The model only requires the user to know the result of the current sample to make a decision, in contrast to Bayesian methods that require calculations based on all prior samples and a history of actions. Despite the limited and intermittent nature of the information, the model provides lower quality costs than existing methods for a wide range of production time horizons.

Development of taxonomy for classifying defect patterns on wafer bin map using Bin2Vec and clustering methods

A wafer consists of several chips, and serial electrical tests are conducted for each chip to investigate whether the chip is defective. A bin indicates the test results for each chip with information on which tests the chip failed. A wafer bin map (WBM) shows the locations and bins of the defects on the wafer. WBMs showing spatial patterns of defects usually result from assignable causes in the wafer fabrication process; hence, they should be classified in advance. The existing defect-pattern taxonomies do not consider bins, although useful information can be obtained from them. We propose a taxonomy that consists of the shape, size, location, and bin dimensions. The bin dimension is developed using Bin2Vec method, which determines RGB (red-green-blue) code for each bin according to the spatial similarity between bins. Three levels of the bin dimension are defined by analyzing a large number of WBMs using Bin2Vec and clustering methods. Compared with the existing taxonomies, the proposed taxonomy has the advantage of identifying major bins of defect patterns, new defect patterns, and non-critical defect patterns. A high-quality training dataset was obtained using the proposed taxonomy; consequently, a defect pattern classification model with satisfactory classification performance could be obtained.

Optimising production, maintenance, and quality control for imperfect manufacturing systems considering timely replenishment

To optimise production planning, maintenance strategies, and quality control in imperfect manufacturing systems, most existing works set the buffer stocking time at the cycle start time. However, excess inventory holding costs will be incurred if the buffer is stocked too early. This means that while the abovementioned setting can make the optimisation model simple, it might increase costs. Taking the uncertain practical buffer stocking time of an imperfect manufacturing system into account, this study aimed to find the production cycle, maintenance frequency, quality inspection cycle, and number of inspections that will minimise the expectation unit cost of the system. To this end, we developed a new model to optimise production, maintenance, and quality control considering timely replenishment. First, excess inventory holding and shortage costs were considered and the production process was divided into five scenarios based on the buffer stocking time and inspection time for assignable causes. Second, the link between production, maintenance, and quality was addressed by capturing the dynamic and random behaviour of production systems. An x-bar control chart was integrated into the model to monitor quality. A case study and sensitivity analysis were undertaken to verify the effectiveness and superiority of the proposed optimisation strategy.

An improved features selection approach for control chart patterns recognition

<span lang="EN-US">Control chart patterns (CCPs) are an essential diagnostic tool for process monitoring using statistical process control (SPC). CCPs are widely used to improve production quality in many engineering applications. The principle is to recognize the state of a process, either a stable process or a deterioration to an unstable process. It is used to significantly narrow the set of possible assignable causes by shortening the diagnostic process to improve the quality. Machine learning techniques have been widely used in CCPs. Artificial neural networks with multilayer perceptron (ANN-MLP) are one of the standard tools used for this purpose. This paper proposes an improved features selection method to select the best features as input representation for control chart patterns recognition. The results demonstrate that the proposed approach can effectively recognize CCPs even for small patterns with a mean shift of less than 1.5 sigma. The dimensional reduction was achieved by employing Relief, correlation, and Fisher algorithms (RCF) for feature selection and (ANN-MLP) as a classifier (RCF-ANN). This study provides an experimental result that compares the performance before and after dimensional reduction.</span>

Multivariate Process Control Chart Pattern Classification Using Multi-Channel Deep Convolutional Neural Networks

Statistical process control (SPC) charts are commonly used to monitor quality characteristics in manufacturing processes. When monitoring two or more related quality characteristics simultaneously, multivariate T2 control charts are often employed. Like univariate control charts, control chart pattern recognition (CCPR) plays a crucial role in multivariate SPC. The presence of non-random patterns in T2 control charts indicates that a process is influenced by one or more assignable causes and that corrective actions should be taken. In this study, we developed a deep learning-based classification model for recognizing control chart patterns in multivariate processes. To address the problem of the insufficient representation of one-dimensional (1D) data, we explore the advantages of using two-dimensional (2D) image data obtained from a threshold-free recurrence plot. A multi-channel deep convolutional neural network (MCDCNN) model was developed to incorporate both 1D and 2D representations of control chart data. This model was tested on multivariate processes with different covariance matrices and compared with other traditional algorithms. Moreover, the effects of imbalanced datasets and dataset size on classification performance were analyzed. Simulation studies revealed that the developed MCDCNN model outperforms other techniques in identifying multivariate non-random patterns. For the most significant one, our proposed MCDCNN method achieved a 10% improvement over traditional methods. The overall results suggest that the developed MCDCNN model can be beneficial for intelligent SPC.

A joint design of production, maintenance planning and quality control for continuous flow processes with multiple assignable causes

A joint design of production, maintenance planning and quality control for continuous flow processes with multiple assignable causes

An Extension of Yang and Rahim’s Model to Determine Design Parameters in Multivariate Control Charts Under Multiple Assignable Causes and Weibull Shock Model

Abstract One of the most important issues in the operation of any one- or multi-variable control chart is to determine the design parameters. Because in practice, production processes are affected by several assignable causes, several papers have been published to determine the design parameters. In all the papers presented so far, it has been assumed that after the occurrence of one of the assignable causes until the issuance of the true alarm, no other assignable cause occurs. Contrary to popular opinion, this paper argues that the formulas presented under this assumption for the average cost and quality cycle time in previous papers are incorrect and shows how the formula can be corrected. Therefore, this paper theoretically and numerically examines the conditions of occurrence of this assumption and its relationship with the design parameters in the design of multivariate control charts. A new economic model for determining design parameters is also presented. Numerical results show that the old formulas have a significant under-estimation of the average cost per unit time of the quality cycle. Also, a numerical study for economic and economic-statistical design of T 2 {T^{2}} control chart is presented under the proposed model.