Statistical Process Control Model Research Articles

An integrated Maintenance and Statistical Process Control Model for a Deteriorating Production Process

This study presents an integrated model of maintenance and statistical process control (SPC) for a production process with three states (in-control, out-of-control, and failure). The process is operational in both in-control and out-of-control states. However, the quality of the process's output deteriorates in an out-of-control state, and the process completely stops in the failure state. If the process enters the out-of-control state and no maintenance action is performed, it eventually enters the failure state. While the failure state is observable, judgment is made about the operational states of the process, i.e., in-control and out-of-control states, based on the quality of the produced items using a control chart. When the process shifts to an out-of-control state, and the control chart identifies this transition, minor repair applies, restoring the process to an in-control state, and continuing the production cycle. However, at most N minor repairs can be conducted during a production cycle. When the process moves to a failure state, the production cycle terminates, and a major repair is conducted. It is assumed after performing each minor repair, the life of the production machine decreases stochastically. In the paper, a mathematical model is developed to determine the optimal sample size, sampling interval, the limits of the control chart, and the maximum number of minor repairs during a process cycle. The model is developed without restrictive assumptions about (1) process failure mechanism (PFM), (2) stochastic process representing the imperfect effect of maintenance, and (3) control charts employed to monitor the process. Hence, from three aspects, the proposed model has a general structure leading to widespread applicability of the model for different working conditions. As a special case, we demonstrated the application of the model considering a Weibull distribution to represent the PFM, a stochastic geometric process (GP) to describe the imperfect effect of maintenance, and X-bar and chi-square control charts to monitor the process. Given the above conditions, numerical examples and sensitivity analyses are conducted. Furthermore, using the properties of GP and considering exponential distribution for PFM, closed-form formulas are derived. The model is optimized using a full enumeration algorithm.

Anomaly detection of the blast furnace smelting process using an improved multivariate statistical process control model

Anomaly detection and early warning of the blast furnace ironmaking process is an important research direction of blast furnace production. In this paper, through the analysis and optimization of the multivariate statistical process control (MSPC) model, MSPC based on TOPSIS and the grey (GT-MSPC) model is established based on the problems of missing alarms, false alarms and untimely prediction in the abnormal detection process of the traditional blast furnace ironmaking production process. First, a composite volatility (CV) that consists of the squared prediction error and T2 is computed to form the MSPC model. The parameters of different training set sizes and different alarm conditions are optimized by using the technique for order preference by similarity to an ideal solution model to optimize the effect of anomaly detection and fault diagnosis. Second, according to the results of the contribution plot, the fault diagnosis of abnormal occurrence is carried out, the main influencing factors of abnormal occurrence are analysed, and the monitoring is strengthened. Finally, the grey model is used to predict CV to realize anomaly early warning and form the GT-MSPC model. By collecting the field data of blast furnace production and performing empirical analysis, the results show that the GT-MSPC model has higher anomaly detectability. The detection rate is 50 % higher than that of the manual observation method, and the GT-MSPC model alarms 16.4861 min earlier than manual detection method. Fault diagnosis can accurately locate the main influencing factors of blast furnace anomalies, such as the furnace body static pressure and differential pressure. In summary, the GT-MSPC model realizes the accurate identification and prediction of anomalies and greatly reduces the occurrence of missing and false alarms and untimely prediction in the blast furnace system, thus reducing the risk of blast furnaces. It can be used to assist field engineers in dealing with abnormal faults and improve the product quality and production safety of blast furnace ironmaking.

Efficacy of statistical process control procedures to monitor deviations in physical behavior for preclinical detection of bovine respiratory disease in feedlot cattle

Opportunities exist to improve the efficacy of antimicrobial treatment and animal welfare standards through use of remote sensor technologies for early detection of bovine respiratory disease (BRD). A post-hoc analysis using statistical process control (SPC) procedures was performed on continuously-recorded physical activity data collected from BRD-diagnosed and healthy calves from Pillen et al. (2016). We hypothesized that SPC models that monitor physical activity traits (step count, motion index, standing time, lying bouts) would yield higher diagnostic accuracies compared to methods based on visual observation of clinical signs of illness for detecting the onset of BRD. Crossbred steers and bulls (n = 266; initial BW = 180 kg) at high risk for BRD were fitted with leg-attached accelerometers (IceQube, IceRobotics, Ltd.) upon arrival at a commercial feedlot and evaluated for 56 d Overall, calves experienced 48% morbidity, with the average day of first treatment occurring 16 d post-feedlot arrival. Shewhart charts were used to evaluate daily changes in each trait as univariate models and combined traits in principal component analysis (PCA)–constructed multivariate models, relative to the day of BRD diagnosis. Diagnostic test sensitivity and specificity were calculated for each model and compared. The univariate models had relatively low sensitivities (< 40%), with specificities ranging from 23 to 81%, and chart signaling occurred up to 2 d prior to visual diagnosis of BRD. The univariate model for step count had the highest accuracy (52.3%), while lying time had the lowest accuracy (32%). The multivariate models that included all 4 physical activity traits or only lying bout behavior had moderate sensitivities (44 to 57%), but low specificities (< 37%), and chart signaling occurred 2 d prior to visual diagnosis. The relatively low diagnostic test accuracies of the SPC models reported in this study may have been due to substantial within-animal daily variation in the physical activity traits and(or) the limited time for adequate model training prior to the onset of BRD cases. Future research should investigate SPC analysis of multifactorial algorithms using physical activity and feeding behavior traits to improve the accuracy of preclinical detection of BRD.

Bayesian networks for statistical process control with attribute data

PurposeBayesian networks (BNs) are implemented for monitoring a process via statistical process control (SPC) where attribute data are available on output from the system. The paper aims to discuss this issue.Design/methodology/approachThe BN provides a graphical and numerical tool to help a manager understand the effect of sample observations on the probability that the process is out-of-control and requires investigation. The parameters for the BN SPC model are statistically designed to minimize the out-of-control average run length (ARL) of the process at a specified in-control ARL and sample size.FindingsThe BN model outperforms adaptivenpcontrol charts in all experiments, except for some cases where only a large change in the proportion of sample defects is relevant. The BN is particularly useful when small sample sizes are available and when managers need to detect small changes in the proportion of defects produced by the process.Research limitations/implicationsThe BN model is statistically designed and parameters are chosen to minimize out-of-control ARL. Future advancements will address the economic design of BNs for SPC with attribute data.Originality/valueThe BNs allow qualitative knowledge to be combined with sample data, and the average percentage of defects can be modeled as a continuous random variable. The framework of the BN easily permits classification of the system operation into two or more states, so diagnostic analysis can be performed simultaneously with statistical inference.

A generalized version of Ben-Daya-Rahim (2000) and Rahim-Banerjee (1993) cost models in economic design of X-control charts for systems with early replacement and preventive maintenance under decreasing integrated hazard

A remarkable deal of recent research in process management is devoted to combining the maintenance policies with statistical process control models such as optimal design of control charts. To optimize the design parameters (the sample size, the sampling intervals, the control limits coefficient, the maintenance level and the truncated time), Rahim and Banerjee and Ben-Daya and Rahim generalized cost models simplified the joint models of maintenance and economic design of control charts by assuming constant integrated hazard over sampling intervals. As an alternative to the constant approach, a decreasing integrated hazard procedure is applied in this paper for determining the inspection intervals as a conservative strategy along with increase in overall cost. A numerical study based on the -control chart with normal quality characteristic distribution and Weibull () shock model is provided to investigate the performance of this approach in comparison with the traditional one.

Modified short-run statistical process control for test and measurement process

The key characteristics of test and measurement (T&M) manufacturing are short-run, multi-product families and testing at multi-stations. These characteristics render statistical process control (SPC) inefficacious because inherently meagre data do not warrant meaningful control limits. Measurement errors increase the risks of false acceptance and rejection, thereby leading to such consequences as unnecessary process adjustments and loss of confidence in SPC. This study presents a modified SPC model that incorporates measurement uncertainty from guard bands into the $$ \overline{\mathrm{Z}} $$ and W charts, thereby addressing the implications of short runs, multi-stations and measurement errors on SPC. The implementation of this model involves two phases. Phase I retrospective analysis computes the input parameters, such as the standard deviation of the measurement uncertainty, measurement target and estimate of the population standard deviation. Thereafter, five-band setting and sensitivity factor are proposed to estimate process standard deviation to maximise the opportunity to detect the assignable causes with low false-reject rate. Lastly, the $$ \overline{\mathrm{Z}} $$ and W charts are generated in Phase II using standardised observation technique that considers the measurement target and estimated process standard deviations. Run tests based on Nelson rules interpret the charts. Validation was performed in three case studies in an actual industry.

Potential of multivariate statistical process monitoring based on the biogas composition to detect free ammonia intoxication in anaerobic reactors

Three anaerobic digestion reactors were initially maintained at steady-state with low nitrogen input, then progressively exposed to increasing nitrogen input until extreme ammonia intoxication, leading to interruption of biogas production. Such interruption occurred for a free ammonia nitrogen (FAN) concentration of about 5 g Lslurry−1. A fourth reactor used as a control was maintained at low nitrogen steady-state. The biogas composition (CH4, CO2, H2 and H2S) was recorded over time and data were fed into a multivariate statistical process control model based on principal components analysis (PCA-MSPC). Static PCA-MSPC failed to distinguish between the actual reactor performance decrease and the drift of the in-control process baseline. However, recursively updated PCA-MSPC (effective memory length of 14 days, i.e. 0.25 hydraulic retention time) allowed detection of the early signs of FAN induced process dysfunction, which were simultaneous with drastic changes in the microbiome of the replicate reactors. However, the process control model was not able to adapt to a drastic modification of the microbiome. Propionate continuously accumulated since the detection of the first signs of process dysfunction.

Modified SPC for short run test and measurement process in multi-stations

Due to short production runs and measurement error inherent in electronic test and measurement (T&M) processes, continuous quality monitoring through real-time statistical process control (SPC) is challenging. Industry practice allows the installation of guard band using measurement uncertainty to reduce the width of acceptance limit, as an indirect way to compensate the measurement errors. This paper presents a new SPC model combining modified guard band and control charts ( chart and W chart) for short runs in T&M process in multi-stations. The proposed model standardizes the observed value with measurement target (T) and rationed measurement uncertainty (U). S-factor (Sf) is introduced to the control limits to improve the sensitivity in detecting small shifts. The model was embedded in automated quality control system and verified with a case study in real industry.

Failure Prediction Using Sequential Pattern Mining in the Wire Bonding Process

In the semiconductor packaging system composed of complex assembly processes, it is necessary to detect faults early to minimize the time and cost required to produce semiconductor chip scraps and to improve production yield. Early detection of faults is possible by performing a failure prediction analysis during the semiconductor packaging process. In this paper, we consider a statistical process control model for predicting the final failure of a printed circuit board lot based on observed event sequences in the wire bonding process step. To estimate the parameters efficiently in the predictive model, we propose a two-stage process. Here, irrelevant subsequences of events are deleted by a sequential mining approach at the first step, and a predictive model is constructed with the remaining subsequences of events using the logistic regression and bagged least absolute shrinkage and selection operator (LASSO) estimate, which we call the B-LASSO method. In particular, to resolve problems caused by unbalanced data, the B-LASSO uses case-control sampling rather than simple random sampling with replacement. The performance of the B-LASSO is compared with other competing methods by analyzing a work-site dataset to confirm that the B-LASSO is superior.

Ensemble-Bayesian SPC: Multi-mode process monitoring for novelty detection

ABSTRACTWe propose a monitoring method based on a Bayesian analysis of an ensemble-of-classifiers for Statistical Process Control (SPC) of multi-mode systems. A specific case is considered, in which new modes of operations (new classes), also called “novelties,” are identified during the monitoring stage of the system. The proposed Ensemble-Bayesian SPC (EB-SPC) models the known operating modes by categorizing their corresponding observations into data classes that are detected during the training stage. Ensembles of decision trees are trained over replicated subspaces of features, with class-dependent thresholds being computed and used to detect novelties. In contrast with existing monitoring approaches that often focus on a single operating mode as the “in-control” class, the EB-SPC exploits the joint information of the trained classes and combines the posterior probabilities of various classifiers by using a “mixture-of-experts” approach. Performance evaluation on real datasets from both public repositories and real-world semiconductor datasets shows that the EB-SPC outperforms both conventional multivariate SPC as well as ensemble-of-classifiers methods and has a high potential for novelty detection including the monitoring of multimode systems.

Transfer of a static PCA-MSPC model from a steady-state anaerobic reactor to an independent anaerobic reactor exposed to organic overload

A static multivariate statistical process control model based on principal component analysis (PCA-MSPC) was developed for an anaerobic reactor maintained in steady-state, joining the biogas composition (CH4, CO2, H2) to the total solids (TS), volatile solids (VS), total inorganic carbon (TIC) and total ammonia nitrogen (TAN) contents of the slurry. The principal component analysis (PCA) highlighted a lack of correlation between the individual process variables (IPVs) measured in the slurry and the gas phase. The application of this model to the data set collected for an independent anaerobic reactor (fed with the same substrate) progressively led from steady-state to critical volatile fatty acids (VFA) intoxication did not allow evaluating its process status. A second static PCA-MSPC model was built for the steady-state reactor in excluding the TS and VS content of the slurry and was successfully transferred to the overfed reactor. The TA² and SPE control charts built for the overfed reactor using this second model closely reflected its process status and delivered valuable warning signals approaching the VFA intoxication. The gas phase composition (CH4, CO2, H2) brought the main contribution to these warnings.

Economic−statistical design of Vp control schemes for joint monitoring of mean and variance in the presence of multiple assignable causes

ABSTRACTThis paper presents a new statistical process control model for the economic–statistical optimization of a Variable-Parameter (Vp) Shewhart control scheme for monitoring processes where multiple assignable causes may occur. The assignable causes affect not only the mean but also the variance of a specific quality characteristic by leading to progressive process deterioration. The contemporary occurrence of the assignable causes and the different corrective action for each assignable cause makes the proposed model more realistic. The operation of the proposed control scheme is stochastically modelled by means of the Markov chain theory. The design parameters vary to get an economic and statistical performance optimization of the control scheme. An extended numerical investigation is utilized to demonstrate the economic and statistical superiority of the proposed model against simpler approaches. An example from aviation industry is presented to illustrate the application of the model.

Quality Cost Analysis of Typical Forging Based on SPC and DEA Model

In order to control the quality costs of forgings efficiently and ensure the optimization of enterprise production value input and benefit output, using piston, output shaft and other typical forgings as application objects, choosing cold and warm forging process instead of the former single hot forging or cold forging process, reinforcing Statistical Process Control (SPC) of processing quality and appropriately distributing quality failure cost and quality assurance cost in order to efficiently match the total cost of quality, quality process capacity index and production program so that the stability of forging quality can be improved. Using Data Envelopment Analysis (DEA) to contrast and analysis the quality cost data of new process and old process, of which the result shows that the technical input and benefit output of new process accord with mass production requirements in the prior period of enterprise industrialization.

An integrated model based on statistical process control and maintenance for two-stage dependent processes

ABSTRACTThe close relationship between quality and maintenance of manufacturing systems has contributed to the development of integrated models which use the concept of statistical process control (SPC) and maintenance. This article demonstrates the integration of the Shewhart individual-residual (ZX − Ze) joint control chart and maintenance for two-stage dependent processes by jointly optimizing their policies to minimize the expected total costs associated with quality, maintenance and inspection. To evaluate the effectiveness of the proposed model, two stand-alone models—a maintenance model and an SPC model—are proposed. Then a numerical example is given to illustrate the application of the proposed integrated model. The results show that the integrated model outperforms the two stand-alone models with regard to the expected cost per unit time. Finally, a sensitivity analysis is conducted to develop insights into time parameters and cost parameters that influence the integration efforts.

Impact of Mahalanobis space construction on effectiveness of Mahalanobis-Taguchi system

Mahalanobis–Taguchi system (MTS) is a pattern recognition technique that aids in quantitative decisions by constructing a multivariate measurement scale using data analytic methods. In this paper, the importance of constructing the Mahalanobis space (MS) is demonstrated using the data from Soylemezoglu et al. (2010). The data collected from ten attributes for normal observations are treated using a control chart approach, similar to statistical process control models. Two MS models are constructed using the data inside the control limits of ±3σ and ±2σ for each variable and benchmarked in terms of accuracy, sensitivity, specificity and relative sensitivity. In addition, the impact of attribute selection is also demonstrated. This study shows that (1) a reliable MS is important for effective deployment of MTS; (2) the construction of MS, as well as selection of variables, should be driven by domain experts since understanding data in order to determine the normal observations require in-depth knowledge in the particular field of application and (3) for novice practitioners, filtering normal data using different control limits, applying MTS using alternative MS models, and investigating different combinations of significant features for the same application, and then determining the best MS model can be more effective.

A variable parameter Shewhart control scheme for joint monitoring of process mean and variance

This paper presents a new Statistical Process Control model for the economic optimization of a variable-parameter control chart monitoring a process operation where two assignable causes may occur, one affecting the mean and the other the variance of the process. Therefore, it is possible for the process to operate in statistical control, when none of the two assignable causes has occurred, or under the effect of one or both the assignable causes. By making the assumption that the occurrence rate of each assignable cause is exponential, a Markov chain approach is utilized to determine the probabilities that the process operates at any of the above possible states. The model uses an economic (or an economic/statistical) optimization criterion for the time to the next sampling instance, the size of the next sample, as well as the control limits of the inspection. That is, all design parameters of the control scheme are selected so as to minimize the total expected quality-related costs. The superiority of the proposed model is estimated by comparing its expected quality control cost vs. the outcome of the Fp (Fixed-parameter) Shewhart control chart, the Variable Sample Size (VSS) control chart, the Variable Sampling Interval (VSI) and the Variable Sample Size and Sampling Interval (VSSI) control chart, for a benchmark of examples. The numerical investigation indicates that the economic improvement of the proposed model may be significant.

Statistical Process Control Based on Kalman Filter in Manufacturing Process

In order to reduce the impact of data noise to quality control and make monitor results more precise in manufacturing process, the method of statistical process control based on Kalman filter was proposed. In this method, the statistical process control model based on Kalman filter was built and the quality control method of exponentially weighted moving average based on Kalman filter was put forward. While monitoring manufacturing process, first the technology of Kalman filter was used to smooth data and to reduce noise, and then control charts were built by the method of exponentially weighted moving average to monitor quality. Finally, the performance of the exponentially weighted moving average method based on Kalman filter and the tranditional exponentially weighted moving average method was compared. The performance result illustrates the feasibility and validity of the proposed quality monitor method.

Determining Statistical Process Control Baseline Periods in Long Historical Data Streams

In statistical process control (SPC), models are built from baseline data that are observations during successful production. Often the baseline data has to be extracted from a long steam of historical data that includes observations from both successful and unsuccessful productions. Baseline periods have to be identified correctly to ensure that the SPC models are correct and, subsequently, the on-line monitoring based on these models is effective.This paper proposes a new method to identify baseline periods in a long historical dataset. The method identifies baseline periods where the quality is good, the quality variable has a stable distribution, and the time intervals are sufficiently long. The proposed method is tested on a real dataset from a melting process and yields a baseline that is considered reasonable and convincing to the process engineers. Simulation experiments also show that the proposed method is robust to the distribution of the quality variable by consistently identifying correct baseline periods across different distributions. In contrast, two existing methods of change-point identification are very sensitive to distribution assumptions.

Blood phenylalanine concentrations in patients with PAH‐deficient hyperphenylalaninaemia off diet without and with three different single oral doses of tetrahydrobiopterin: Assessing responsiveness in a model of statistical process control

Tetrahydrobiopterin (BH(4)) cofactor loading is a standard procedure to differentiate defects of BH(4) metabolism from phenylalanine hydroxylase (PAH) deficiency. BH(4) responsiveness also exists in PAH-deficient patients with high residual PAH activity. Unexpectedly, single cases with presumed nil residual PAH activity have been reported to be BH(4) responsive, too. BH(4) responsiveness has been defined either by a >or=30% reduction of blood Phe concentration after a single BH(4) dose or by a decline greater than the individual circadian Phe level variation. Since both methods have methodological disadvantages, we present a model of statistical process control (SPC) to assess BH(4) responsiveness. Phe levels in 17 adult PKU patients of three phenotypic groups off diet were compared without and with three different single oral dosages of BH(4) applied in a double-blind randomized cross-over design. Results are compared for >or=30% reduction and SPC. The effect of BH(4) by >or=30% reduction was significant for groups (p < 0.01) but not for dose (p = 0.064), with no interaction of group with dose (p = 0.24). SPC revealed significant effects for group (p < 0.01) and the interaction for group with dose (p < 0.05) but not for dose alone (p = 0.87). After one or more loadings, seven patients would be judged to be BH(4) responsive either by the 30% criterion or by the SPC model, but only three by both. Results for patients with identical PAH genotype were not very consistent within (for different BH(4) doses) and between the two models. We conclude that a comparison of protein loadings without and with BH(4) combined with a standardized procedure for data analysis and decision would increase the reliability of diagnostic results.

A Comparison of Statistical Process Control (SPC) and On-Line Multivariate Analyses (MVA) for Injection Molding

Abstract Manufacturing process automation is often impeded by limitations related to automatic quality assurance. Many plastics manufacturers use univariate statistical process control (SPC) for quality control by charting the critical process states relative to defined control limits. Alternatively, principal component analysis (PCA) and projection to latent stuctures (PLS) are multivariate methods that measure the process variance by the distance to the model (DModX) and the Hotelling t-squared (T2) values. A methodology for robust model development is described to perturb the manufacturing process for process characterization based on a design of experiments; best subset analysis is used to provide an optimal set of regressors for univariate SPC. Four different statistical models were derived from the same data set for a highly instrumented injection molding process. The performance of these models was then assessed with respect to fault diagnosis and defect identification when the molding process was subjected to twelve common process faults. Across two hundred molding cycles, the univariate SPC models correctly diagnosed five of the twelve process faults with one false positive, detecting only eighteen of twenty four defective products while indicating two false positives. With the same molding cycles, PCA and PLS provided nearly identical performance by correctly diagnosing ten of the twelve process faults and detecting twenty three of the twenty four defective products; PCA indicated two false positives while PLS indicated only one false positive.