Statistical Process Control Tools Research Articles

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.

Robustness of Moving Average-Exponential Weighted Moving Average Control Chart with the Light-Tailed Distribution

Control charts are the most significant statistical process control tools for ensuring industrial process reliability and efficiency. This research uses moving average – exponentially weighted moving average (MA-EWMA) control charts to investigate the dispersion characteristics. The control chart performance compares the arithmetic mean of run length (AMRL) and standard deviation of run length (SDRL) profiles of MA-EWMA and synthetic charts. Student's t-distributions are compared for dispersion processes. Finally, we present a case to show how essential control charts are in practice.

A time-adjusted control chart for monitoring surgical outcome variations.

Statistical Process Control (SPC) tools providing feedback to surgical teams can improve patient outcomes over time. However, the quality of routinely available hospital data used to build these tools does not permit full capture of the influence of patient case-mix. We aimed to demonstrate the value of considering time-related variables in addition to patient case-mix for detection of special cause variations when monitoring surgical outcomes with control charts. A retrospective analysis from the French nationwide hospital database of 151,588 patients aged 18 and older admitted for colorectal surgery between January 1st, 2014, and December 31st, 2018. GEE multilevel logistic regression models were fitted from the training dataset to predict surgical outcomes (in-patient mortality, intensive care stay and reoperation within 30-day of procedure) and applied on the testing dataset to build control charts. Surgical outcomes were adjusted on patient case-mix only for the classical chart, and additionally on secular (yearly) and seasonal (quarterly) trends for the enhanced control chart. The detection of special cause variations was compared between those charts using the Cohen's Kappa agreement statistic, as well as sensitivity and positive predictive value with the enhanced chart as the reference. Within the 5-years monitoring period, 18.9% (28/148) of hospitals detected at least one special cause variation using the classical chart and 19.6% (29/148) using the enhanced chart. 59 special cause variations were detected overall, among which 19 (32.2%) discordances were observed between classical and enhanced charts. The observed Kappa agreement between those charts was 0.89 (95% Confidence Interval [95% CI], 0.78 to 1.00) for detecting mortality variations, 0.83 (95% CI, 0.70 to 0.96) for intensive care stay and 0.67 (95% CI, 0.46 to 0.87) for reoperation. Depending on surgical outcomes, the sensitivity of classical versus enhanced charts in detecting special causes variations ranged from 0.75 to 0.89 and the positive predictive value from 0.60 to 0.89. Seasonal and secular trends can be controlled as potential confounders to improve signal detection in surgical outcomes monitoring over time.

Proactive Manufacturing Strategy for Managing the Multiproduct Production Plan

The case study focuses on a multi-product company in Indonesia that aims to develop a proactive manufacturing strategy to tackle production disruptions caused by process uncertainty. Data from 30 periods are analyzed to evaluate the company's weekly production plan performance, revealing consistent quantity fulfillment but significant discrepancies in the types of products produced compared to the plan. Process uncertainty, especially regarding quality, leads to disruptions such as uneven and inadequate material supplies. Statistical Process Control (SPC) tools, like Pareto analysis, are used to identify priority quality issues, forming the basis for Fault Tree Analysis (FTA) to trace root causes and determine intervention points. Each machine's limited set of valves and pipes poses challenges for thorough cleaning during downtime and quality management outside working hours. Introducing backup valves and pipes per machine can mitigate these issues and improve production efficiency. Companies can implement procurement strategies for pipes and valves to prevent dirty prints in the primary process, ensuring smooth material supply and minimizing disruptions. Although actual production plan achievement hasn't reached 100%, this strategy has the potential to increase product sales by 3.31% by reducing the rejection ratio of dirty prints. Ultimately, proactive procurement of spare pipes and valves is expected to increase production efficiency by 4%, indicating enhanced production schedule stability.

Bayesian and classical inference of the process capability index under progressive type-II censoring scheme

This article uses the maximum likelihood technique, the bootstrap method, and the Markov chain Monte Carlo method to estimate the process capability index (C py ) for the generalised inverted exponential distribution. These methods are all based on the progressive Type-II censoring scheme. In reliability analysis, the generalised inverted exponential distribution is a frequently used distribution, and the C py is a critical tool in statistical process control. The manuscript proposes a comparative study of the three methods for estimating C py , and their performance is evaluated using simulation studies. Furthermore, three examples of real data is examined to show all the estimation approaches. The results demonstrate that all three methods can provide accurate estimates of C py , with the Markov chain Monte Carlo method having an advantage in providing more information on the uncertainty of the estimates. The manuscript concludes that the proposed methods can be useful in practice for estimating C py for the generalised inverted exponential distribution based on progressive Type-II censoring scheme, providing an objective measure of process performance and helping organizations to optimize their production processes.

CPV Monitoring - Optimization of Control Chart Design by Reducing the False Alarm Rate and Nuisance Signal

The Food and Drug Administration’s 2011 Process Validation Guidance and International Council for Harmonization Quality Guidelines recommend continued process verification (CPV) as a mandatory requirement for pharmaceutical, biopharmaceutical, and other regulated industries. As a part of product life cycle management, after process characterization in stage 1 and process qualification and validation in stage-2, CPV is performed as stage-3 validation during commercial manufacturing. CPV ensures that the process continues to remain within a validated state. CPV requires the collection and analysis of data related to critical quality attributes, critical material attributes, and critical process parameters on a minimum basis. Data is then used to elucidate process control regarding the capability to meet predefined specifications and stability via statistical process control (SPC) tools. In SPC, the control charts and Nelson rules are commonly used throughout the industry to monitor and trend data to ensure that a process remains in control. However, basic control charts are susceptible to false alarms and nuisance alarms. Therefore, it is imperative to understand the assumptions behind control charts and the inherent false alarm rates for different Nelson rules. In this article, the authors have detailed the assumptions behind the usage of control charts, the rate of false alarms for different Nelson rules, the impact of skewness and kurtosis of a data distribution on the false alarm rate, and methods for optimizing control chart design by reducing false alarm rates and nuisance signals.

Efficient Monitoring of Autoregressive and Moving Average Process using HWMA Control Chart

Quality control is an essential process for manufacturing and industry because it enhances product quality, consumer satisfaction, and overall profitability. Among many other statistical process control tools, quality practitioners typically employ control charts to monitor the industrial process and detect production changes. Control charts are widely used to detect flaws in many applications, such as distributed circuits and systems, electronic devices, and systems and signals. In this study, we derived an explicit formula for Average Run Length (ARL) of the Homogenously Weighted Moving Average control chart (HWMA) under the ARMA (p,q) process. The accuracy was checked using the numerical integral equation (NIE) technique. The finding showed that the explicit formulas and numerical solutions presented an outstanding level of agreement. However, the computational time for the explicit formulas was approximately one second, which was less than that required for the NIE. Moreover, the performance efficiency of the HWMA control chart is compared with the cumulative sum control chart for ARMA (p, q) processes including ARMA (2,1), ARMA (2,3), and ARMA (1,1) processes. The results found that the HWMA control chart performance is found to be preferable to the CUSUM control chart performance. Additionally, the explicit formula of the HWMA control chart was implemented in a practical application of the count of nonconformities in printed circuit boards (PCBs).

STATISTICAL PROCESS CONTROL AS A TOOL FOR QUALITY IMPROVEMENT: A CASE STUDY IN DENIM PANT PRODUCTION

In this study, after defining the concepts of quality and quality control, the concept of statistical process control tools is examined. As a result of the data obtained from denim pants produced by a textile company operating in the ready-to-wear sector, defects were analyzed using statistical process control techniques. In this study, flowchart, control charts, pareto analysis, p-control diagram, cause-effect diagram, and grouping techniques were used. With the use of basic statistical process control tools, the most recurring defects were, and these defects were divided into subheadings for more detailed analysis. In this way, it was tried to prevent the repetition of defects by going down to the root causes of the detected defects. The causes of possible defects that may occur during production and solution suggestions were categorized. By going down to the basic causes of the detected defects and categorized them, defects were prevented by presenting and implementing solution suggestions. It is expected that the study with this different perspective will be an example of the sector and related fields as an alternative method. The aim of this study is to examine quality control practices in the garment industry, contribute to statistical control methods and problem-solving procedures, produce suggestions for problem-solving approaches, and disseminate improvement studies.

Using DMAIC for in-plant logistic activities improvement

Goal: In-plant logistics activities are important for increasing the performance of the supply chains, so our research aims to study the application of Six Sigma tools for in-plant logistics activities in the cement industry. Our research contributes to the literature by developing a real case study that provides insights into the practical implementation of continuous improvement programs. Design / Methodology / Approach: This study uses the Industrial Case Study in a large cement plant, a branch of a multinational business group, in Brazil’s Middle-west region. This research applies Define, Measure, Analyze, Improve, Control (DMAIC) guidelines with Statistical Process Control tools for solving a real problem for out-control processes. From this, we propose an improvement plan to correct flaws in the in-plant cement loading and unloading process (in-plant logistics). Results: The results suggest that based on the control chart, the studied in-plant logistics activities were out of control. These processes exhibit a high variability, between 3σ and 5σ, presenting 26 problems with causes related to machine, measure, and human resources. An out-control action plan was proposed aiming for improvements to solve these problems. Limitations of the investigation: On the out-control action plan, this study presents an improvement proposal. The action plan does not fully develop the control step for DMAIC. Practical implications: Managers in the cement industry can use our case for insights and learning about improvement programs, especially for the in-plant logistics activities addressing processing-based manufacturing environments. Originality / Value: Our research contributes a real case study that applies the DMAIC methodology, with a specific focus on in-plant logistics activities. By developing the application of improvement programs within the cement industry, our study offers practical insights into how processing industries can effectively implement such programs.

Monitoring urea concentration at different slope angles in drip fertigation

The use of statistical process control tools in irrigation is becoming widespread as it allows for quick and effective investigation and detection of possible problems with drippers, especially when fertilizer is used in irrigation water and different slopes. Therefore, the research used statistical quality control charts to monitor urea concentration at different inclinations of the lateral line. The experiment was conducted in a protected environment at the Irrigation and Fertigation Laboratory - LIF) in the city of Cascavel, Paraná State, Brazil. It followed a randomized block design, in a 4x3 factorial arrangement, in which fertilizer concentrations were evaluated at three slope angles. Experimental plots were divided into two factors. The first is the type of water (clean water from an artesian well and water with a nitrogen fertilizer at 44% N) subdivided into four subplots, representing concentrations of urea (0, 2, 4, and 6 g L-1). The second factor was slope angle and represented the sub-plots: uphill (2%), level (0%), and downhill (2%). The results show that Shewhart's statistical control charts were sensitive in observing the change in uniformity due to the increase in fertilizer concentration. Water with fertilizer (4 gL-1) affected uniformity at all studied slope levels. The results also show that high concentrations of fertilizers change the pH of the water. The lowest urea concentrations showed the best distribution uniformity results.
 Keywords: control charts, drip irrigation, Shewhart, uniformity.

Performance Analysis of Interval Type-2 Fuzzy X¯ and R Control Charts

Statistical process control (SPC) is one of the most powerful techniques for improving quality, as it is able to detect special causes of problems in processes, products and services with a remarkable degree of accuracy. Among SPC tools, X¯ and R control charts are widely employed in process monitoring. However, scenarios involving vague, imprecise and even subjective data require a type-2 fuzzy set approach. Thus, X¯ and R control charts should be coupled with interval type-2 triangular fuzzy numbers (IT2TFN) in order to add further information to traditional control charts. This paper proposes a performance analysis of IT2TFN and X¯ and R control charts by means of average run length (ARL), standard deviation of the run length (SDRL) and RL percentile. Computer simulations were carried out considering 10,000 runs to obtain ARL, SDRL and the 5th, 25th, 50th, 75th and 95th RL percentiles. Simulation results reveal that the proposed control charts increased fault detection capability (speed of response) and slightly reduced the number of false alarms in processes under control. Moreover, it was observed that, in addition to superior performance, IT2TFN X¯-R control charts proved to be more robust and flexible when compared to traditional control charts.

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.

Measuring and Evaluating the Services of Kumasi Technical University Restaurant by Employing Statistical Process Control Tools

The study measures and evaluates Kumasi Technical University (KsTU) Restaurant’s services using statistical process control tools. Two categories of respondents (members of staff and students) were engaged in the study. Data was collected from 100 members of staff and 223 students using questionnaires. Statistical tools such as mean, pareto charts and factor analysis were used in the analysis. The results shows that respondents are highly satisfied with the services provided by the restaurant. The survey also found that consumers consider two factors, namely atmosphere and food quality, while evaluating the services offered by a restaurant.

Efficient Monitoring of a Parameter of Non-Normal Process Using a Robust Efficient Control Chart: A Comparative Study

The control chart is a fundamental tool in statistical process control (SPC), widely employed in manufacturing and construction industries for process monitoring with the primary objective of maintaining quality standards and improving operational efficiency. Control charts play a crucial role in identifying special cause variations and guiding the process back to statistical control. While Shewhart control charts excel at detecting significant shifts, EWMA and CUSUM charts are better suited for detecting smaller to moderate shifts. However, the effectiveness of all these control charts is compromised when the underlying distribution deviates from normality. In response to this challenge, this study introduces a robust mixed EWMA-CUSUM control chart tailored for monitoring processes characterized via symmetric but non-normal distributions. The key innovation of the proposed approach lies in the integration of a robust estimator, based on order statistics, that leverages the generalized least square (GLS) technique developed by Lloyd. This integration enhances the chart’s robustness and minimizes estimator variance, even in the presence of non-normality. To demonstrate the effectiveness of the proposed control chart, a comprehensive comparison is conducted with several well-known control charts. Results of the study clearly show that the proposed chart exhibits superior sensitivity to small and moderate shifts in process parameters when compared to its predecessors. Through a compelling illustrative example, a real-life application of the enhanced performance of the proposed control chart is provided in comparison to existing alternatives.

ARL Evaluation of a DEWMA Control Chart for Autocorrelated Data: A Case Study on Prices of Major Industrial Commodities

The double exponentially weighted moving average (DEWMA) control chart, an extension of the EWMA control chart, is a useful statistical process control tool for detecting small shift sizes in the mean of processes with either independent or autocorrelated observations. In this study, we derived explicit formulas to compute the average run length (ARL) for a moving average of order q (MA(q)) process with exponential white noise running on a DEWMA control chart and verified their accuracy by comparison with the numerical integral equation (NIE) method. The results for both were in good agreement with the actual ARL. To investigate the efficiency of the proposed procedure on the DEWMA control chart, a performance comparison between it and the standard and modified EWMA control charts was also conducted to determine which provided the smallest out-of-control ARL value for several scenarios involving MA(q) processes. It was found that the DEWMA control chart provided the lowest out-of-control ARL for all cases of varying the exponential smoothing parameter and shift size values. To illustrate the efficacy of the proposed methodology, the presented approach was applied to datasets of the prices of several major industrial commodities in Thailand. The findings show that the DEWMA procedure performed well in almost all of the scenarios tested. Doi: 10.28991/ESJ-2023-07-05-020 Full Text: PDF

Enhanced performance of mixed HWMA-CUSUM charts using auxiliary information.

Quality control (QC) is a systematic approach to ensuring that products and services meet customer requirements. It is an essential part of manufacturing and industry, as it helps to improve product quality, customer satisfaction, and profitability. Quality practitioners generally apply control charts to monitor the industrial process, among many other statistical process control tools, and to detect changes. New developments in control charting schemes for high-quality monitoring are the need of the hour. In this paper, we have enhanced the performance of the mixed homogeneously weighted moving average (HWMA)-cumulative sum (CUSUM) control chart by using the auxiliary information-based (AIB) regression estimator and named it MHCAIB. The proposed MHCAIB chart provided an unbiased and more efficient estimator of the process location. The various measures of the run length are used to judge the performance of the proposed MHCAIB and to compare it with existing AIB charts like CUSUMAIB, EWMAAIB, MECAIB (mixed AIB EWMA-CUSUM), and HWMAAIB. The Run length (RL) based performance comparisons indicate that the MHCAIB chart performs relatively better in monitoring small to moderate shifts over its competitor's charts. It is shown that the chart's performance improves with the increase in correlation between the study variable and the auxiliary variable. An illustrative application of the proposed MHCAIB chart is also provided to show its implementation in practical situations.

Single and multiple fault diagnosis based on PCA with relative variation of contribution strategy

Data-driven methods have been recognized as an efficient tool for multivariate statistical process control. Contribution plots are also well known as a popular tool in principal component analysis, which is used for isolating sensor faults without the need for any prior information. However, studies carried out in the literature have unified contribution plots in three general approaches. Furthermore, they demonstrated that correct diagnosis based on contribution plots is not guaranteed for either single or multiple sensor faults. Therefore, to deal with this issue, the present paper highlights a new contribution formula called relative variation of contribution. Simulation results show that the proposed method of contribution can successfully perform the fault isolation task, in comparison with partial decomposition contribution and its relative version (rPDC) based on their fault isolation rate.

A nonparametric EWMA control chart for monitoring mixed continuous and count data

ABSTRACT Conventional statistical process control tools monitor either continuous or count data but rarely both simultaneously. While process data are becoming increasingly complex, there will be more data points containing both continuous and count information. In the case of mixed continuous and count data with unknown distributions, the traditional parameter control chart cannot be used to monitor them. It is proposed in this paper a novel nonparametric EWMA control chart to monitor mixed continuous and count data. The mixed continuous and count data are first transformed into categorical data, and then a log-linear model is utilized to analyze correlations between variables, followed by the construction of an EWMA statistic that is used to monitor mixed continuous and count data. Next, the proposed control chart is compared with several improved control charts for monitoring mixed continuous and count data. Based on the numerical simulation results, the control chart presented in this paper provides a superior method of detecting alarm signals in the process compared to some improved control charts. Finally, the proposed control chart is demonstrated to be effective and applicable using the semiconductor manufacturing process dataset from the UC Irvine Machine Learning Repository.

Understanding the Effect of Large Subgroup Sizes on Overdispersion and Using Laney’s P’ Chart to Monitor Overdispersed Data

Background The traditional Shewhart’s P chart is an important statistical process control tool that’s used to monitor processes that yield binary data. However, it has been known for showing a high rate of false alarms (i.e. overdispersion) when handling data with large subgroup sizes. Large subgroup sizes were usually considered to be the cause of overdispersion while no solid evidence actually exists to support this believe. In an effort to manage overdispersion Laney’s P’ chart was proposed in 2002 as a superior alternative to the traditional P chart. And the P chart diagnostic test was also introduced in some software packages to detect any overdispersion in the data and to recommend the suitable chart. Aim In this study we aimed at exploring the effect of large subgroup sizes on the overdispersion of data and we also attempted to test Laney’s P’ chart and the P chart diagnostic test in detecting and handling overdispersed data. Method An Experimental study was conducted using a single set of real data in addition to nine sets of simulated data with variable characteristics. All data sets were used to perform the P chart diagnostic test and to plot Shewhart P chart and Laney’s P’ chart. Results Large subgroup sizes proved to have no effect on binomially distributed data but if the data is not truly binomial, increasing the subgroup sizes will exaggerate overdispersion. In this case using Laney’s P’ chart will successfully resolve the problem. Conclusion The problem of overdispersion is not due to large subgroup sizes rather than it’s due to the false assumption that the data follows a binomial distribution when it frequently doesn’t. An ideal remedy for this problem is to discover a better fitting distribution for the data. Till then Laney’s P’ chart is a practical and capable remedy. Recommendations The P chart diagnostic tool should be used to detect any overdispersion before using Shewhart’s P chart. And if overdispersion is detected Laney’s P’ chart is a recommended alternative. We also recommend Further study of the performance of Laney’s P’ chart and other suggested distributions that can outperform the binomial distribution as a basis for the P chart.

The Optimal Control Chart Selection for Monitoring COVID-19 Phases: A Case Study of Daily Deaths in the USA.

Epidemiologists frequently adopt statistical process control tools, like control charts, to detect changes in the incidence or prevalence of a specific disease in real time, thereby protecting against outbreaks and emergent health concerns. Control charts have proven essential in instantly identifying fluctuations in infection rates, spotting emerging patterns, and enabling timely reaction measures in the context of COVID-19 monitoring. This study aims to review and select an optimal control chart in epidemiology to monitor variations in COVID-19 deaths and understand pandemic mortality patterns. An essential aspect of the present study is selecting an appropriate monitoring technique for distinct deaths in the USA in 7 phases, including pre-growth, growth, and post-growth phases. Stage-1 evaluated control chart applications in epidemiology departments of 12 countries between 2000 and 2022. The study assessed various control charts and identified the optimal one based on maximum shift detection using sample data. This study considered at Shewhart (Javid Shabbir2, ) control charts and exponentially weighted moving average (EWMA) control chart with smoothing parameters were all investigated in this study. In Stage-2, we applied the EWMA control chart for monitoring because of its outstanding shift detection capabilities and compatibility with the present data. Daily deaths have been monitored from March 2020 to February 2023. Control charts in epidemiology show growing use, with the United States leading at 42% applications among top countries. During the application on COVID-19 deaths, the EWMA chart accurately depicted mortality dynamics from March 2020 to February 2022, indicating six distinct stages of death. The third and fifth waves were extremely catastrophic, resulting in a considerable loss of life. Significantly, a persistent sixth wave appeared from March 2022 to February 2023. The EWMA map effectively determined the peaks associated with each wave by thoroughly examining the time and amount of deaths, providing vital insights into the pandemic's progression. The severity of each wave was measured by the average number of deaths. The United States entered a seventh phase (6th wave) from March 2022 to February 2023, marked by fewer deaths. While reassuring, it remains crucial to maintain vaccinations and pandemic control measures. Control charts enable early detection of daily COVID-19 deaths, providing a systematic strategy for government and medical staff. Incorporating the EWMA chart for monitoring immunizations, cases, and deaths is recommended.