Statistical Process Control Procedures Research Articles

Detecting mean changes in experience sampling data in real time: A comparison of univariate and multivariate statistical process control methods.

Detecting early warning signals of developing mood disorders in continuously collected affective experience sampling (ESM) data would pave the way for timely intervention and prevention of a mood disorder from occurring or to mitigate its severity. However, there is an urgent need for online statistical methods tailored to the specifics of ESM data. Statistical process control (SPC) procedures, originally developed for monitoring industrial processes, seem promising tools. However, affective ESM data violate major assumptions of the SPC procedures: The observations are not independent across time, often skewed distributed, and characterized by missingness. Therefore, evaluating SPC performance on simulated data with typical ESM features is a crucial step. In this article, we didactically introduce six univariate and multivariate SPC procedures: Shewhart, Hotelling's T², EWMA, MEWMA, CUSUM and MCUSUM. Their behavior is illustrated on publicly available affective ESM data of a patient that relapsed into depression. To deal with the missingness, autocorrelation, and skewness in these data, we compute and monitor the day averages rather than the individual measurement occasions. Moreover, we apply all procedures on simulated data with typical affective ESM features, and evaluate their performance at detecting small to moderate mean changes. The simulation results indicate that the (M)EWMA and (M)CUSUM procedures clearly outperform the Shewhart and Hotelling's T² procedures and support using day averages rather than the original data. Based on these results, we provide some recommendations for optimizing SPC performance when monitoring ESM data as well as a wide range of directions for future research. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Error detection through modified phase II process monitoring under different classical estimators

In real life, the distribution of the errors during any life testing of products or process does not meet the assumption of normality. Statistical process control (SPC) is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behavior, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and to monitor the reliability of machines where the number of errors follows skewed distributions, we develop control charts to keep the process in control. For such situations, we have modified the existing control charts such as Shewhart control chart, exponentially weighted moving average (EWMA), hybrid exponentially weighted moving average (HEWMA) and extended exponentially weighted moving average (EEWMA) control charts. The current study introduced classical estimator based modified control charts for phase-II monitoring by assuming that the errors occur during the process follow skewed distribution called Beta Lehmann 2 Power function distribution (BL2PFD). The proposal for these control charts is based on the percentile estimator. We have compared all these control charts using Monte Carlo simulation studies and real-life applications to compare the proposed control charts. This study shows that an EEWMA control chart based on PE performs better than Shewhart, EWMA and HEWMA control charts, when the underlying distribution of the errors in process monitoring follows BL2PFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

A novel approach of ceramic tile crack detection using morphological operations

In ceramic tiles manufacturing industry, tiles are manufactured at large scale which makes it more challenging to ensure the quality of each tile according to the set standards. Mostly, Statistical Process Control (SPC) is used by tile manufacturers at each step to monitor various processing parameters. SPC procedures are implemented manually that requires sufficient number of experienced human resource to identify defected tiles from a batch of tiles. The manual inspection also gives low accuracy of defect detection due to human errors and hard environment. Considering these drawbacks, in this paper an automated defect detection method is proposed which is based on image processing and morphological operation to ensure the quality and standard of tiles. The proposed method resizes and converts the input RGB image into grayscale image and removes any possible noisy artifacts. An edge detection algorithm is applied on grayscale image to enhance the edges representing the cracks. Afterwards, morphological erosion and dilation operations are applied, one at a time, to get two intermediate images. Finally, edges are detected by subtracting eroded intermediate image from dilated intermediate image. For detection, the proposed algorithm does not require any separate reference image. The algorithm is tested on an image set of sixty different defected tile images and attained 92% average detection accuracy.

Design multivariate statistical process control procedure in the case of Ethio cement

PurposeThis study aims to design a multivariate control chart that improves the applicability of the traditional Hotelling T2 chart. This new type of multivariate control chart displays sufficient information about the states and relationships of the variables in the production process. It is used to make better quality control decisions during the production process.Design/methodology/approachMultivariate data are collected at an equal time interval and are represented by nodes of the graph. The edges connecting the nodes represent the sequence of operation. Each node is plotted on the control chart based on their Hotelling T2 statistical distance. The changing behavior of each pair of input and output nodes is studied by the neural network. A case study from the cement industry is conducted to validate the control chart.FindingsThe finding of this paper is that the points and lines in the classic Hotelling T2 chart are effectively substituted by nodes and edges of the graph respectively. Nodes and edges have dimension and color and represent several attributes. As a result, this control chart displays much more information than the traditional Hotelling T2 control chart. The pattern of the plot represents whether the process is normal or not. The effect of the sequence of operation is visible in the control chart. The frequency of the happening of nodes is recognized by the size of nodes. The decision to change the product feature is assisted by finding the shortest path between nodes. Moreover, consecutive nodes have different behaviors, and that behavior change is recognized by neural network.Originality/valueModifying the classical Hotelling T2 control chart by integrating with the concept of graph theory and neural network is new of its kind.

Efficacy of statistical process control procedures to identify deviations in continuously measured physiological and behavioral variables in beef heifers resulting from an experimentally combined viral-bacterial challenge.

The objective of this experiment was to determine if statistical process control (SPC) procedures coupled with remote continuous data collection could accurately differentiate between animals experimentally inoculated with a viral-bacterial (VB) challenge or phosphate buffer solution (PBS). Crossbred heifers (N = 38; BW = 230 ± 16.4 kg) were randomly assigned to treatments by initial weight, average daily gain (ADG), bovine herpes virus 1, and Mannheimia haemolytica serum titers. Feeding behavior, dry matter intake (DMI), animal activity, and rumen temperature were continuously monitored remotely prior to and following VB challenge. VB-challenged heifers exhibited decreased (P < 0.01) ADG and DMI, as well as increased (P < 0.01) neutrophils and rumen temperature consistent with a bovine respiratory disease (BRD) infection. However, none of the heifers displayed overt clinical signs of disease. Shewhart and cumulative summation (CUSUM) charts were evaluated, with sensitivity and specificity computed on the VB-challenged heifers (n = 19) and PBS-challenged heifers (n = 19), respectively, and the accuracy was determined as the average of sensitivity and specificity. To address the diurnal nature of rumen temperature responses, summary statistics (mean, minimum, and maximum) were computed for daily quartiles (6-h intervals), and these quartile temperature models were evaluated separately. In the Shewhart analysis, DMI was the most accurate (95%) at deciphering between PBS- and VB-challenged heifers, followed by rumen temperature (94%) collected in the 2nd and 3rd quartiles. Rest was most the accurate accelerometer-based traits (89%), and meal duration (87%) and bunk visit (BV) frequency (82%) were the most accurate feeding behavior traits. Rumen temperature collected in the 3rd quartile signaled the earliest (2.5 d) of all the variables monitored with the Shewhart, followed by BV frequency (2.8 d), meal duration (2.8 d), DMI (3.0 d), and rest (4.0 d). Rumen temperature and DMI remained the most accurate variables in the CUSUM at 80% and 79%, respectively. Meal duration (58%), BV frequency (71%), and rest (74%) were less accurate when monitored with the CUSUM analysis. Furthermore, signal day was greater for DMI, rumen temperature, and meal duration (4.4, 5.0, and 3.7 d, respectively) in the CUSUM compared to Shewhart analysis. These results indicate that Shewhart and CUSUM charts can effectively identify deviations in feeding behavior, activity, and rumen temperature patterns for the purpose of detecting sub-clinical BRD in beef cattle.

Selection of within-run quality control rules for laboratory biomarkers.

In order to release correct biomarker results of a laboratory test, it is a regulatory requirement to apply quality control standards for controlling analytical errors. Releasing an incorrect test result might lead to wrong diagnosis or treatment of a patient in medical decision-making. In laboratory medicine, one of the means to control analytical errors is statistical process control procedures proposed by James O.Westgard and his coworkers nowadays known as "Westgard rules." To judge their performance for discriminating in-control from out-of-control processes, power curves are used. In this article, we describe functions for the power curves of the within-run Westgard rules. Based on these power curves, we use a benchmark approach for selecting a quality control procedure out of the set of Westgard rules. It is shown that two graphical procedures proposed by Westgard and his coworkers can be reduced to this benchmark approach. Besides, a commonly used measure in laboratory medicine for describing out-of-control processes is critically examined revealing the threat of selecting too optimistic quality control rules.

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.

Control Charts for the Shape Parameter of Skewed Distribution

The weighted distributions are useful when the sampling is done using an unequal probability of the sampling units. The Weighted Power function distribution (WPFD) has applications in the fields of reliability engineering, management sciences and survival analysis. WPFD is more beneficial in Statistical process control (SPC). SPC is defined as the use of statistical techniques to control a process or production method. SPC tools and procedures can help to monitor process behaviour, discover problems in internal systems, and find solutions for production issues. To identify and remove the variation in different reliability processes and also to monitor the reliability of machines where the number of errors follows WPFD, we develop control charts to keep the process in control. A memory-based control chart like an exponentially weighted moving average (EWMA) control chart and an extended exponentially weighted moving average (EEWMA) control chart are discussed and compared each other. The proposal of these control charts is based on the modified maximum likelihood estimator (MMLE) under the shape parameter of WPFD. We have presented Monte Carlo simulation technique and a real-life application to compare the proposed control charts. This study shows that an EEWMA control chart based on MMLE performs better than EWMA control chart, when the underlying distribution of the errors in process monitoring follows WPFD. These findings can be useful for researchers and practitioners in dealing with production errors and optimizing the output.

Efficacy of statistical process control procedures to identify deviations in continuously measured physiologic and behavioral variables in beef steers experimentally challenged with Mannheimia haemolytica.

The objective of this experiment was to determine if statistical process control (SPC) procedures coupled with the remote continuous collection of feeding behavior patterns, accelerometer-based behaviors, and rumen temperature can accurately differentiate between animals experimentally inoculated with Mannheimia haemolytica (MH) or PBS. Thirty-six crossbred steers (BW = 352 ± 23 kg) seronegative for MH were randomly assigned to bronchoselective endoscopic inoculation with MH (n = 18) or PBS (n = 18). Electronic feed bunks were used to measure DMI and feeding behavior traits, accelerometer-based neck collars measured feeding- and activity-behavior traits, and ruminal thermo-boluses measured rumen temperature. Data were collected for 28 d prior to and following inoculation. Steers inoculated with MH exhibited elevated (P < 0.02) levels of neutrophils and rumen temperature indicating that MH challenge effectively stimulated immunologic responses. However, only nine of the MH steers exhibited increased serum haptoglobin concentrations indicative of an acute-phase protein response and one displayed clinical signs of disease. Shewhart charts (SPC procedure) were used for two analyses, and sensitivity was computed using all MH-challenged steers (n = 18), and a subset that included only MH-challenged haptoglobin-responsive steers (n = 9). Specificity was calculated using all PBS steers in both analyses. In the haptoglobin-responsive only analysis, DMI and bunk visit (BV) duration had the greatest accuracy (89%), with accuracies for head-down (HD) duration, BV frequency, time to bunk, and eating rate being less (83%, 69%, 53%, and 61%, respectively). To address the diurnal nature of rumen temperature, data were averaged over 6-h intervals, and quarterly temperature models were evaluated separately. Accuracy for the fourth quarter rumen temperature was higher (78%) than the other quarterly temperature periods (first = 56%, second = 50%, and third = 67%). In general, the accelerometer-based behavior traits were highly specific ranging from 82% for ingestion to 100% for rest, rumination, and standing. However, the sensitivity of these traits was low (0% to 50%), such that the accuracies were moderate compared with feeding behavior and rumen temperature response variables. These results indicate that Shewhart procedures can effectively identify deviations in feeding behavior and rumen temperature patterns to enable subclinical detection of BRD in beef cattle.

Constructing a Control Chart Using Functional Data

This study proposes a control chart based on functional data to detect anomalies and estimate the normal output of industrial processes and services such as those related to the energy efficiency domain. Companies providing statistical consultancy services in the fields of energy efficiency; heating, ventilation and air conditioning (HVAC); installation and control; and big data for buildings, have been striving to solve the problem of automatic anomaly detection in buildings controlled by sensors. Given the functional nature of the critical to quality (CTQ) variables, this study proposed a new functional data analysis (FDA) control chart method based on the concept of data depth. Specifically, it developed a control methodology, including the Phase I and II control charts. It is based on the calculation of the depth of functional data, the identification of outliers by smooth bootstrap resampling and the customization of nonparametric rank control charts. A comprehensive simulation study, comprising scenarios defined with different degrees of dependence between curves, was conducted to evaluate the control procedure. The proposed statistical process control procedure was also applied to detect energy efficiency anomalies in the stores of a textile company in the Panama City. In this case, energy consumption has been defined as the CTQ variable of the HVAC system. Briefly, the proposed methodology, which combines FDA and multivariate techniques, adapts the concept of the control chart based on a specific case of functional data and thereby presents a novel alternative for controlling facilities in which the data are obtained by continuous monitoring, as is the case with a great deal of process in the framework of Industry 4.0.

CEP ONLINE: A WEB-ORIENTED EXPERT SYSTEM FOR STATISTICAL PROCESS CONTROL

ABSTRACT In this paper, a new software for Statistical Process Control (SPC) is proposed. The system, the so-called CEP Online, was developed based on statistical computing resources of well-known free softwares, such as HTML, PHP, R and MySQL under an online server with operating system Linux Ubuntu. The main uni and multivariate SPC tools are available for monitoring and evaluation of manufacturing and non-manufacturing production processes over time. Some advantages of the new software are: (i) low operational cost, since it is cloud-based, only needing a computer connected to the Internet; (ii) easy to use with great interaction with the user; (iii) it does not require investment in any specific hardware or software; (iv) real time reports generation on process condition monitoring and process capability. Thus, the CEP Online offers for SPC practitioners fast, efficient and accurate SPC procedures. Therefore, CEP Online becomes an important resource for those who have no access to non-free softwares, such as SAS, SPSS, Minitab and STATISTICA. To the best of our knowledge, the CEP Online is unique with respect to its characteristics.

Statistical process control procedures for functional data with systematic local variations

ABSTRACTMany engineering studies for manufacturing processes, such as for quality monitoring and fault detection, consist of complicated functional data with sharp changes. That is, the data curves in these studies exhibit large local variations. This article proposes a wavelet-based local random-effect model that characterizes the variations within multiple curves in certain local regions. An integrated mean and variance thresholding procedure is developed to address the large number of parameters in both the mean and variance models and keep the model simple and fit the data curves well. Guidelines are provided to select the regularization parameters in the penalized wavelet-likelihood method used for the parameter estimations. The proposed mean and variance thresholding procedure is used to develop new statistical procedures for process monitoring with complicated functional data. A real-life case study shows that the proposed procedure is much more effective in detecting local variations than existing techniques extended from methods based on a single data curve.

036 Evaluation of statistical process control procedures to monitor feeding behavior and ruminal temperature changes associated with experimental inoculation of Mannheimia haemolytica

036 Evaluation of statistical process control procedures to monitor feeding behavior and ruminal temperature changes associated with experimental inoculation of Mannheimia haemolytica

043 Evaluation of Statistical Process Control Procedures to Monitor Feeding Behavior Patterns and Detect Onset of Bovine Respiratory Disease in Growing Bulls

The objective of this study was to evaluate the effectiveness and accuracy of monitoring feeding behavior patterns using cumulative summation (CUSUM) procedures to predict the onset of bovine respiratory disease (BRD). Growing bulls (N = 231) consigned from independent producers for the purpose of evaluating growth efficiency during a 70-d trial were used in this study. Within a 10-d period, 30 bulls were treated for BRD based on observed clinical symptoms and elevated rectal temperature (> 39.5 C); all remaining bulls (n = 201) were deemed to be healthy. The clinically ill and healthy bulls were used to evaluate the sensitivity and specificity of CUSUM models, respectively. Frequency and duration of bunk visit (BV) events, head down (HD) duration and DMI were continuously monitored during the trial. All data were standardized prior to generating CUSUM charts in a daily accumulative manner. CUSUM charts were constructed with PROC CUSUM (SAS 9.4). Accuracies (average of sensitivity and specificity) of these single-trait CUSUM models for detection of BRD were 81.6, 80.3, 82.8 and 80.2%, respectively, and average day of detection prior (P < 0.05) to observed symptoms of BRD were 4.4, 3.5, 4.5 and 2.6 d, respectively. In addition, factors derived from a principal component analysis (PCA) of all 4 traits were monitored using similar CUSUM procedures. This 4-trait PCA-based model was more accurate (84.7 %) than any of the 4 single traits and signaled (P < 0.05) 3.7 d prior to observed symptoms of BRD. When DMI was removed from the full PCA model, accuracy of prediction (84.3% vs. 84.7%) and signal day prior to observed symptoms of BRD (3.3 vs. 3.7 d) were minimally altered, demonstrating the validity of monitoring feeding behavior traits for early BRD detection. These results demonstrate that the use of PCA-derived factors in CUSUM charts was more accurate compared to single-trait CUSUM charts. Moreover, due to the multivariate aspect of PCA, the use of PCA-based CUSUM charts to monitor feeding behavior patterns should be more robust in applications for preclinical detection of BRD. Results from this study demonstrate the potential value of using CUSUM procedures to monitor electronic feeding-behavior systems to enable more accurate preclinical detection of BRD in feedlot cattle.

On first-order integer-valued autoregressive process with Katz family innovations

ABSTRACTThis paper considers the first-order integer-valued autoregressive (INAR) process with Katz family innovations. This family of INAR processes includes a broad class of INAR(1) processes with Poisson, negative binomial, and binomial innovations, respectively, featuring equi-, over-, and under-dispersion. Its probabilistic properties such as ergodicity and stationarity are investigated and the formula of the marginal mean and variance is provided. Further, a statistical process control procedure based on the cumulative sum control chart is considered to monitor autocorrelated count processes. A simulation and real data analysis are conducted for illustration.

Control charts for flexible and multi-variety production systems

This study presents two new proposals of self-start statistical process control procedures for implementing quality control charts in mass customized production environments. Mass customization is characterized by high variety and/or low production volumes, or by current production strategies that increase the necessity of flexibility. The proposed approaches consider that the quality characteristic under monitoring is the same among the items, allowing the possibility of different averages and standard deviations for different products into the series. Analysis of the proposed approaches include assumption violations and the comparison of the new approaches to a Phase I–Phase II residual control chart, as benchmark. Simulation results show that one of the proposed approaches ties in performance with the benchmark, and the other can produce faster detection of deviations from the process mean, both without the need of a Phase I – retrospective analysis, thus increasing suitability for application in real environments. Also, the proposed approaches are made to handle with unitary production lots as well. Analysis performed in an extensive simulation procedure presents that normality assumption violation (with higher asymmetry) has the most degenerative effect on all tested control charts. The study also shown decreasing in performance on scenarios that violated the independence of the observations assumption.

의사결정나무를 이용한 다변량 공정관리 절차

현대의 제조공정은 컴퓨터의 발전과 통신 및 네트워크의 발달로 컴퓨터통합제조가 가능해졌다. 이로 인해 고품질 제품의 고속 생산공정이 확대되고, 공정에서 실시간으로 전송되는 다양한 품질변수들의 데이터 축적 또한 가능하게 되었다. 이를 관리하기 위해서는 다변량 통계적 공정관리 절차가 필요하다. 전통적으로 사용하는 다변량 관리도는 이상상태 발생시 이상신호를 주지만, 이상원인이 어떠한 변수에 어떠한 영향을 주는지에 대한 정보를 제공하지 않는다는 단점이 있다. 이를 보완하기 위해 데이터마이닝과 기계학습 기법을 이용할 수 있다. 이 논문에서는 의사결정나무 학습 기법을 이용한 다변량 공정관리 절차를 소개하고, 이변량인 경우 모의실험을 통하여 그 효율을 살펴보았다. 모의실험 결과를 살펴볼 때, 상관계수에 따라 이상상태 탐지 능력은 비슷한 것으로 나타났고, 이상상태에 대한 분류 정확도는 상관계수와 이상원인의 형태에 따라 차이가 있지만 기존의 다변량 관리도에서는 제공하지 않는 이상원인의 정보를 제공하는 장점이 있음을 알 수 있다. In today's manufacturing environment, the process data can be easily measured and transferred to a computer for analysis in a real-time mode. As a result, it is possible to monitor several correlated quality variables simultaneously. Various multivariate statistical process control (MSPC) procedures have been presented to detect an out-of-control event. Although the classical MSPC procedures give the out-of-control signal, it is difficult to determine which variable has caused the signal. In order to solve this problem, data mining and machine learning techniques can be considered. In this paper, we applied the technique of decision tree learning to the MSPC, and we did simulation for MSPC procedures to monitor the bivariate normal process means. The results of simulation show that the overall performance of the MSPC procedure using decision tree learning technique is similar for several values of correlation coefficient, and the accurate classification rates for out-of-control are different depending on the values of correlation coefficient and the shift magnitude. The introduced procedure has the advantage that it provides the information about assignable causes, which can be required by practitioners.

Robust algorithms for economic designing of a nonparametric control chart for abrupt shift in location

The existing statistical process control procedures typically rely on the fundamental assumption of a parametric distribution of the quality characteristic. However, when there is a lack of knowledge about the underlying distribution (as full knowledge is not available in practice), the performance of these parametric charts is very likely to be heavily degraded. Motivated by this problem, a one-sided nonparametric monitoring procedure using the single sample sign statistic is proposed for detecting a shift in the location parameter of a continuous distribution. An economic model of the control chart is developed to optimize the sample size, sampling interval, and control limits. Three data-dependent estimation approaches for the unknown parameter are evaluated and discussed. Simulation results exhibit that our proposed procedure generally performs well under a great variety of continuous distributions and hence it is recommended as an alternative scheme especially when the knowledge of the underlying distribution is imperfect. Furthermore, beneficial recommendations of estimation approach selection are provided for practical implementation of the control chart.

Economic Robustness Analysis of Adaptive Chart Schemes for Monitoring the Total Nonconformities Number in Inspection Units

In recent years, a variety of enhanced schemes for the c chart have been developed aimed at the effectiveness improving of the related statistical process control (SPC) procedures. However, the performance of such chart schemes can be very sensitive to values assumed for some operating and cost parameters, in particular to the considered process shift magnitude arising from out-of-control conditions. In such a circumstance, the effectiveness of such chart schemes can be subjected to substantial reductions when they are implemented in operative contexts given that, in practice, such value is unknown and it can be very difficult to accurately estimate. For this reason, in the present paper it is developed an economic optimization approach able to find out the optimal configurations of the main adaptive c chart schemes. Subsequently, economic performances of such configurations are compared in order to derive information on their relative economic robustness, considering the difference between the estimated process shift magnitude and the actual one as influential factor and costs arising from the related SPC operations as performance comparison index. In addition, also a sensitivity analysis based on a [Formula: see text] fractional factorial design scheme, to investigate on influence of several operating and cost parameters on charts economic robustness, is carried out and the related considerations are given. The obtained results show that the parameters having the most impact on economic robustness, when the out-of-control process shift is not accurately estimated, are the cost associated with the production of non-conforming parts and the failure rate of the manufacturing system.

Economic design of Shewhart control charts for monitoring autocorrelated data with skip sampling strategies

On-line monitoring of process variability is strategic to achieve high standards of quality and maintain at acceptable levels the number of nonconforming items. Shewhart control charts are the simplest Statistical Process Control (SPC) procedure to achieve this goal. An efficient implementation of a control chart requires the optimal selection of its design parameters. They can be selected according to an economic-statistical objective: an expected total cost per unit of time incurred during production is minimized subject to a statistical constraint limiting the number of false alarms issued by the control chart. This paper investigates the economic-statistical design of Shewhart control charts implementing skip sampling strategies for constructing subgroups and monitoring autocorrelated AR(1) processes. Implementing skip sampling strategies within a rational subgroup reduces the negative effects of autocorrelation on the statistical performance of the Shewhart control chart. A wide benchmark of examples has been generated as a screening experimental design to study the process and cost factors influencing the selection of the sampling strategy. Regression models have been fitted to the results to help practitioners in the selection of the most convenient sampling strategy. Finally, a sensitivity analysis has been performed to evaluate how the parameters misspecification biases the evaluation of the optimal cost per unit of time.