Assignable Causes Research Articles

A joint monitoring of the process mean and variance with a generally weighted moving average maximum control chart

Single control charts are widely used to control assignable causes that shift the process due to variations in the mean and the dispersion. In the present article, the exponentially weighted moving average maximum (EWMA-Max) control chart is extended to the new single generally weighted moving average maximum (referred as GWMA-Max) control chart for joint monitoring of the process mean and variability. The proposed chart is compared with the EWMA-Max and DEWMA-Max charts in terms of the run-length performance measures. The results reveal that the GWMA-Max chart is very efficient in detecting small shifts in the process mean and variability concurrently. Finally, a practical implementation of the GWMA-Max chart is displayed using real and simulated datasets.

A reliability-oriented integration model of production control, adaptive quality control policy and maintenance planning for continuous flow processes

Many studies reveal that integrating the concepts of production, maintenance and quality control helps reduce costs compared to studying them separately. But almost all the research works in this field are centred on piece part manufacturing. This paper presents an integrated model of the three concepts for the continuous flow process of manufacturing which is vastly different from piece-parts processes, as there is no explicit production unit. To quickly detect the assignable cause occurrence, an adaptive X̄ control chart with variable sampling interval designed for the continuous flow process is employed as the quality control tool. A mathematical definition is presented to describe the proposed model before a genetic algorithm is developed to find the optimal setting values of decision parameters that minimize the expected total cost per unit time. The numerical comparison indicates that the proposed model has reduced the cost by an average of 1.5% than the classical model with fixed sampling interval policy in continuous flow manufacturing. Finally, Taguchi’s design of experiments (DOE) is employed to investigate the main effects of cost and process parameters.

An improved dynamic latent variable regression model for fault diagnosis and causal analysis

AbstractThe advancement of industrial techniques has imposed a high demand for powerful machine learning algorithms to model the increasingly complicated relations in the data. Among them, dynamic models are widely studied to capture the inevitable temporal relations. However, most existing methods only focus on the dynamics between input and output data, failing to exploit other valuable information in the output. In this article, an improved dynamic latent variable regression (LVR) method is proposed to capture both auto‐correlations and cross‐correlations between input and output with an auto‐regressive exogenous model, which is referred to as dynamic regularized LVR with auto‐regressive exogenous input (DrLVR‐ARX). Further, a DrLVR‐ARX‐based fault detection and diagnosis framework is designed to identify the root causes of a detected fault. The framework systematically integrates reconstruction‐based contribution, time‐domain Granger causality, and conditional spectral Granger causality to determine and locate the assignable causes. The effectiveness of the proposed algorithms is demonstrated with two industrial processes.

Integrated maintenance, inventory and quality engineering decisions for multi-product systems

Abstract It is essential for manufacturers to consider the interrelation among quality, inventory, and maintenance decisions to detect imperfect quality products, keep the production system in good operating condition, and manage quality and inventory costs. Hence, this paper aims to develop an integrated model of inventory planning, quality engineering, and maintenance scheduling in which the expected total cost per time unit is minimised by determining the sample size, sampling interval, control limit coefficient, along with production cycle time. In this regard, an imperfect multi-product manufacturing system is considered, in which the inventory shortage in satisfying the demand for each product type and the idle time during the production cycle are not allowed. It is assumed that the process starts in an in-control condition where most produced units are conforming. However, due to the occurrence of an assignable cause (AC), the process mean moves to an out-of-control condition in which a significant fraction of non-conforming units is produced. The efficiency of the proposed mathematical model is evaluated by a numerical example, and then the sensitivity of the proposed model to important inputs is analysed. Finally, a comparative study based on the Taguchi design approach is given to confirm the capability of the proposed model to achieve remarkable cost savings.

Robust Optimization of an Imperfect Process when the Mean and Variance are Jointly Monitored under Dependent Multiple Assignable Causes

Abstract Imperfect processes experience fault productions over time due to specific causes. Integrating the statistical process control, maintenance policy, and economic production quantity has led to more favorable results for the imperfect processes in literature. When monitoring a process, multiple assignable causes (ACs) may shift it to an out-of-control state. As indicated recently, if the interdependency of ACs is neglected, the total cost will be underestimated. Moreover, the mean and variance can simultaneously be affected by the occurrence of ACs. A non-central chi-square (NCS) chart was suggested for its decent performance against X-R chart in detecting the process disturbances and lowering quality loss cost. Besides, the increased occurrence rate of ACs over time leads to higher quality and maintenance costs. Employing a non-uniform sampling (NUS) scheme can significantly reduce costs. In the literature of modeling for imperfect processes under multiple ACs, all input parameters have always been fixed. The effectiveness of the models depends somewhat on the accurate estimates of these parameters. In reality, the estimation of parameters may be associated with uncertainty. For the first time, a robust design approach is proposed for designing NCS chart by considering the interval estimation of uncertain parameters. A particle swarm optimization (PSO) algorithm is used to present solutions. The proposed model is investigated through a real numerical example.

A production-inventory model under quality-maintenance policy with rework process in the presence of random failures and multiple assignable causes

ABSTRACT This research presents simultaneous design of production planning, maintenance strategy and control chart in which two issues are considered: (1) multiple assignable cause and (2) equipment failure. The first one means that various factors may shift the process to an out-of-control state; while the second one means that the equipment is not always available and may be suddenly failed. Also, to reduce the production costs, a rework process is performed on the nonconforming items right after the regular cycle. Furthermore, three types of maintenance activities are applied based on system conditions. The corrective maintenance is conducted when the equipment failure occurs. The preventive maintenance is accomplished when the process continues until the end of the cycle, and the predictive maintenance is performed whereas the chart issues a true alarm. To check the effectiveness of the model, three comparative studies are examined. The first one compares the suggested model with a similar model without the rework process; the second one demonstrates the importance of employing the statistical process monitoring; and the last one compares the model with a similar model without considering the equipment failure. The results show the superiority of the integrated model compared to the others in the cost-saving.

Joint design of control chart and maintenance policy under multiple assignable causes and random failures by considering the statistical constraints

ABSTRACT In modern industries, statistical process monitoring (SPM) and maintenance management are extensively employed to increase the production rate of conforming items. Aiming at minimizing the expected total cost per time unit subject to some statistical constraints, this study proposes a hybrid quality-maintenance model for imperfect short-run process. To bring the proposed model closer to real short-run systems, it is considered that the process mean may shift to an out-of-control condition due to occurrence of several types of assignable causes. Furthermore, it is supposed that the time-to-failure follows a non-homogenous Poisson process implying that the system may suddenly fail with an increasing failure rate function. Moreover, a non-uniform sampling scheme is developed in order to improve the system reliability. Finally, the main advantages of the proposed model are highlighted by conducting two comparative studies. The first one illustrates the efficiency of the non-uniform sampling scheme in increasing the in-control time interval and decreasing the expected total cost. The second one confirms the importance of considering the system failure on both the expected total cost and in-control time interval.

Economic-statistical design of fully adaptive multivariate control charts under effects of multiple assignable causes

Fully adaptive multivariate control charts are efficient to monitor several quality characteristics simultaneously. Charts with assuming a single assignable cause (AC) have been investigated in many studies. However, due to the usual complexity of production processes, the assumption of single AC is not close to real-world conditions. In this paper, by a proper Markov chain approach, we develop an economic-statistical design of a variable-parameter (VP) multivariate control chart to monitor the process mean subject to multiple assignable causes. Numerical examples based on the Taguchi method have been provided and for some parameters, sensitivity analysis is given. Moreover, a comparison between proposed model and fix-parameter (FP) model is done to evaluate the savings of using the adaptive control chart. The results indicate that the proposed VP control charts outperform FP control charts.

Max-EWMA Chart Using Beta and Simplex Distributions for Time and Magnitude Monitoring

Control charts are used to detect assignable causes in different manufacturing and nonmanufacturing processes. This study presents a new maximum exponentially weighted moving average (Max-EWMA) chart for joint unit interval time and magnitude monitoring. To this end, beta distribution is considered for time whereas simplex distribution is used for magnitude. Average run length (ARL), standard deviation of run length (SDRL), and different quantiles are used to evaluate the performance of the Max-EWMA chart. A real data example is also included in the study to show the application of the proposed chart. The results provide evidences that the Max-EWMA chart is efficient in detecting small- to medium-sized shifts.

Two‐dimensional wavelet based statistical monitoring of image data

AbstractStatistical process monitoring techniques are widely used to monitor process stability. In high volume and highly automated processes, effective methods are required to monitor several quality characteristics of interest. Advances in imaging technology have paved the grounds to capture and analyze product images from different perspectives in real time. Advantages of considering images have led to their increasing role in process monitoring. When images are used for process monitoring, complicated data structures should be analyzed. Various methods including data transformation and dimension reduction have been proposed in the literature to cope with these complexities. In this paper, a two‐dimensional (2D) wavelet based method is proposed to monitor image data. A likelihood ratio test (LRT) is developed to monitor the expected values of wavelet coefficient, and the derived likelihood ratio based statistic is monitored over time to detect out‐of‐control conditions as well as change point estimation. This information can help practitioners to diagnose the process, find the potential assignable cause(s) and return the process to the in‐control state. One of the advantages of the proposed method compared to other competing methods is that the performance of the proposed method does not depend on the fault location. Simulation studies indicate satisfactory performance for the proposed method in detecting out‐of‐control conditions and estimating change points. Moreover, the performance of the proposed method is also compared to two existing approaches. The results reveal that the proposed approach performs superior in detecting either diagonal or square defects.

Monitoring reliability under competing risks using field data

Many modern products fail due to one of multiple causes called competing risks. In this article, we propose variable features for monitoring product failure by control charts under competing risks. Failure reports arrive one at a time from a sample of population of units. Features are derived from both the reports and the assumed competing-risk statistical model. To assess the efficacy of different feature subsets in detecting shifts in the failure-time process, we consider control charts based on random forests and compare the average run length performances under different shift scenarios. We demonstrate the control charts with both simulated data sets and actual field data set from a consulting problem. We also propose graphical fault-diagnosis methods for identifying assignable causes of alarm signals. Control charts based on the proposed features will provide valuable information to manufacturers in planning for warranty, part-replacement, or repair.

Determination of the stability of a potable water production line using lean six sigma method: A case study of XYZ water factory

The research, being a case study, aims to determine the stability of the potable water production line of XYZ water factory, for possible improvement, using tools from the lean six sigma (LSS) methodology. This research was carried out on the mean weekly laboratory results of physicochemical water parameters (pH, conductivity, turbidity, alkalinity, chloride, total dissolved solids (TDS), magnesium, nitrates, sulphate, hardness, calcium, lead, copper, iron, and zinc) for regulatory purpose. The data obtained were analysed using control charts from the minitab 2021 ® statistical software package. The values of the parameters (except iron) in the control charts were beyond the conventional limits at various points in time throughout the period. The research results showed that the water production process is not stable, indicative of assignable causes of variability in the production line for all the parameters. Therefore, there is need to carry out investigations to know the causes and take action to correct them. This could be achieved by deploying the appropriate tools in the lean six sigma (DMAIC) methodology.

Insights into Variations in COVID-19 Infections in Malaysia

The present study aims to visualize the variations in the number of confirmed daily COVID-19 infections during the third wave in Malaysia through the application of control charts. This study also attempts to propose the target number of daily new cases that would bring the pandemic situation in Malaysia under control by utilizing the confirmed daily cases in Malaysia starting from 8th September 2020 until 30th June 2021. A modified Shewhart control chart was adopted to monitor the variations before and after the commencement of National Immunisation Programme (NIP). The chart shows a declining trend in the number of cases after the rollout of NIP whereby several days were brought to a state of statistical-in-control. But in less than three months after NIP commencement, there were huge variations in COVID-19 cases leading to drastic increase in the mean number of cases. These signal the presence of unnatural or assignable causes of variations which could be attributed to failure of curbing the risks of transmission, existence of various variants in the community, easing of containment measures and less adherence to the COVID-19 Standard Operating Procedures (SOPs). Significant shifts in the mean values prompt the development of a 3-phase modified Shewhart control chart. From the 3-phase chart, a series of daily number new cases that can be set as the target value to bring the pandemic situation in Malaysia under control, while flattening the epidemiological curve in the very near term.

Pattern detection in phase I monitoring using runs-based tests

Control charts are useful to monitor if a process is in a state of statistical control (in-control) or if changes have occurred due to the presence of any assignable causes. To this end, the pattern of points displayed on a control chart plays an important role. A process is declared as in-control when the plotted points display a random pattern. On the other hand, when the points display a nonrandom pattern, with or without one or more points falling beyond the control limits, the process may be declared out-of-control. Thus, the constellation of points, along with the type of the displayed pattern in a control chart can provide useful clues about the possible presence and diagnosis of assignable causes, which can then be dealt with in an appropriate manner. In this work, we propose a methodology using randomness tests based on the theory of runs that can be applied in a supplementary manner in order to assess the statistical significance of a pattern on a Phase I Shewhart X ¯ chart in an objective way. Five common nonrandom patterns with corresponding tests are considered. The performance of the tests is evaluated in terms of their false alarm rate and power, via simulation. An illustration based on some real data is provided. Conclusions and practical recommendations are offered.

A nonlinear process monitoring strategy with a 2-phase fault diagnosis approach

The article delves into the development of Statistical Fault Detection and Diagnosis Strategies for an Integrated Steel Plant (ISP) taking into account the nonlinear relationship amongst the monitored Process and Feedstock Characteristics. The strategies being devised is based on Neural Network Fitting model cum Principal Component Analysis based technique (NNF-PCA) and Kernel Principal Component Analysis (KPCA) based technique. For detection of fault(s) Hotelling T2 chart based on (Principal Component Analysis) PCA and KPCA scores were employed and an ensemble strategy amalgamating KPCA and Self Organizing Map neural network has also been proposed for the detection of the out-of-control observations or faults. The article also proposes a 2-phase Fault Diagnosis approach christened as Preliminary Diagnosis phase and Specific Diagnosis phase. The Preliminary Diagnosis phase is based on Pattern Analysis of the control chart monitoring statistic observations and the Specific Diagnosis phase is based on the employment of appropriate Fault Diagnostic Statistic. The Preliminary Diagnosis reveals the broader source of assignable cause for the onset of the fault(s) and the Specific Diagnosis reveals the relative contribution of the individual Process and Feedstock characteristics. An in-depth comparative analysis between the NNF-PCA based strategy and KPCA based strategy w.r.t. three comparative aspects and four comparative parameters were carried out with their findings being duly highlighted which revealed the slight effectiveness of the KPCA based strategy with respect to the NNF-PCA based counterpart.

Statistical design of an adaptive synthetic X¯$\bar{X}$ control chart for autocorrelated processes

AbstractThis paper aims to design a variable parameters synthetic control chart for first‐order AR(1) autocorrelated data following a Gaussian process. To improve the statistical performance in detecting small changes and maintaining a low false alarm rate, the variable parameters control chart was combined with the Conforming Run Length (CRL) sub‐chart to determine when to implement tight or relaxed control and intervene to identify an assignable cause. The statistical design of the proposed chart was performed under a discrete‐time Markov chain approach and a non‐linear programming mathematical model to obtain, using a genetic algorithm (GA), the values of the design parameters that minimise the average time to signal the out‐of‐control state (). A sensitivity analysis was performed to examine the behaviour of the in the face on changes in the parameters. Also, a performance evaluation was conducted to compare the proposed chart with other adaptive synthetic charts, the synthetic control chart and the chart developed by Costa and Machado. Our results indicate that this proposal is faster to detect small changes in the process mean considering the autocorrelation of the data.

An economic-statistical production quantity model under quality-maintenance policy for imperfect manufacturing systems with interaction effect among assignable causes

This study integrates production and maintenance planning with statistical process monitoring in the presence of dependent multiple assignable causes. To adapt the model to the reality, two assumptions are considered: (1) the assignable causes (ACs) are dependent, and (2) the occurrence of ACs can affect both process mean and variability. Given the second assumption, a non-central chi-square (NCS) chart is used to monitor the process. Since the occurrence rate of ACs increases over time, a non-uniform sampling scheme is presented to reduce the out-of-control time period. A sensitivity analysis is presented to explore how the number of AC types influences the cost terms. The results indicate that the more AC types, the higher quality loss and maintenance costs are imposed on the manufacturer. Moreover, three comparative studies are conducted for confirming the effectiveness of the model. The first comparative study shows that the total cost will be less than its real value when the interdependency among the ACs is ignored. The second comparison shows that the NCS chart outperforms the in detecting the process disturbances and leads to a less quality loss cost. Eventually, the last one represents that employing the non-uniform sampling strategy leads to a significant cost savings.

Control Chart Concurrent Pattern Classification Using Multi-Label Convolutional Neural Networks

The detection and identification of non-random patterns is an important task in statistical process control (SPC). When a non-random pattern appears on a control chart, it means that there are assignable causes which will gradually deteriorate the process quality. In addition to the study of a single pattern, many researchers have also studied concurrent non-random patterns. Although concurrent patterns have multiple characteristics from different basic patterns, most studies have treated them as a special pattern and used the multi-class classifier to perform the classification work. This study proposed a new method that uses a multi-label convolutional neural network to construct a classifier for concurrent patterns of a control chart. This study used data from previous studies to evaluate the effectiveness of the proposed method with appropriate multi-label classification metrics. The results of the study show that the recognition performance of multi-label convolutional neural network is better than traditional machine learning algorithms. This study also used real-world data to demonstrate the applicability of the proposed method to online monitoring. This study aids in the further realization of smart SPC.

Unit Interval Time and Magnitude Monitoring Using Beta and Unit Gamma Distributions

Quick detection of an assignable cause is necessary for process accuracy with respect to the specifications. The aim of this study is to monitor the time and magnitude processes based on unit‐interval data. To this end, maximum exponentially weighted moving average (Max‐EWMA) control chart for simultaneous monitoring time and magnitude of an event is proposed. To be precise, beta and unit gamma distributions are considered to develop the Max‐EWMA chart. The chart’s performance is accessed using average run length (ARL), the standard deviation of run length (SDRL), and different quantiles of the run length distribution through extensive Monte Carlo simulations. Besides a comprehensive simulation study, the proposed charting methodology is applied to a real data set. The results show that the proposed chart is more efficient in detecting small to medium‐sized shifts. The results also indicate that simultaneous shifts are detected more quickly as compared to the pure shift.

On-line Recognition of Abnormal Patterns in Bivariate Autocorrelated Process Using Random Forest

It is not uncommon that two or more related process quality characteristics are needed to be monitored simultaneously in production process for most of time. Meanwhile, the observations obtained online are often serially autocorrelated due to high sampling frequency and process dynamics. This goes against the statistical I.I.D assumption in using the multivariate control charts, which may lead to the performance of multivariate control charts collapse soon. Meanwhile, the process control method based on pattern recognition as a non-statistical approach is not confined by this limitation, and further provide more useful information for quality practitioners to locate the assignable causes led to process abnormalities. This study proposed a pattern recognition model using Random Forest (RF) as pattern model to detect and identify the abnormalities in bivariate autocorrelated process. The simulation experiment results demonstrate that the model is superior on recognition accuracy (RA) (97.96%) to back propagation neural networks (BPNN) (95.69%), probability neural networks (PNN) (94.31%), and support vector machine (SVM) (97.16%). When experimenting with simulated dynamic process data flow, the model also achieved better average running length (ARL) and standard deviation of ARL (SRL) than those of the four comparative approaches in most cases of mean shift magnitude. Therefore, we get the conclusion that the RF model is a promising approach for detecting abnormalities in the bivariate autocorrelated process. Although bivariate autocorrelated process is focused in this study, the proposed model can be extended to multivariate autocorrelated process control.