X-bar Control Chart Research Articles

Integrated optimization for X-bar control chart, preventive maintenance and production rate

There are close relationships among statistical process control, maintenance, and production that have not fully explored in existing studies. In this study, we propose an economic model for jointly optimizing the X-bar control chart, preventive maintenance, and production rate. Unlike conventional studies relying on known failure rate functions, we employ a Gamma process to describe the system's deterioration. This approach allows us to consider not only the relationship between the production rate and the deterioration rate but also a broad range of deterioration scenarios and failure modes in the integrated optimization. After calculating the failure probability at each time point, we propose a recursive method to derive the production revenue, process control costs, and quality losses. This approach explores the close inner relationship between the production rate, deterioration, process monitoring and maintenance. Subsequently, we establish an optimization model aimed at maximizing the profit rate within a renewal cycle. The decision variables of this model include the production rate, control chart coefficient, sample size, length of the first sampling interval, and number of sampling intervals. Finally, we use a case study to illustrate the effectiveness and validity of our proposed model by identifying and explaining the interactions between production rate, deterioration, process control and maintenance.

Performance evaluation of cable-stayed bridge expansion joints based on Lasso dimensionality reduction and temperature-displacement-correlation model

Expansion joints play a crucial role in accommodating the longitudinal movement of the main beam, which is mainly caused by temperature variation. This paper establishes an accurate model that relates the temperature field of the main beam to the displacement of the expansion joint, enabling reliable performance prediction and early warning of the expansion joint. Firstly, three commonly used methods for characterizing the temperature field of the main beam are introduced, along with their advantages and disadvantages. Secondly, a novel method is proposed using the Lasso algorithm to calculate critical temperatures. The objective is to select temperature channels data that have significant impact on the longitudinal displacement of the main beam. The selected channels data is then linearly weighted based on feature importance to obtain critical temperature. Based on this, a precise relationship model between the main beam temperature and the expansion joint displacement is derived through regression. For the residual term in the model fitting, an expansion joint performance early warning procedure is developed based on the X-bar control chart. Finally, using one-year long-term monitoring data from a newly constructed cable-stayed bridge as an example, the proposed method demonstrates superior capability in predicting the predefined damage of the expansion joint compared to the other two commonly used methods.

Optimized repetitive sampling X-bar control chart: performance evaluation and comparison with Shewhart control chart

When initial sample information falls short of enabling industrial engineers to confidently make decisions about lot quality assessment, repetitive sampling emerges as a solution. In this study, we present an optimized repetitive sampling control chart for X-bar values. Through meticulous analysis, we determined the optimal control chart coefficients. Additionally, we established the control chart parameters for scenarios where the sample size equals the average sample number, encompassing both in-control and out-of-control processes. To underscore the effectiveness of our proposed chart compared to the traditional Shewhart control chart, we provide comprehensive tables across various sample sizes. By meticulously examining these tables alongside the corresponding control charts, the chart's efficacy in relation to the Shewhart alternative becomes evident.

Performance optimization of radiator engine parameters during hard conditions by control charts monitoring and evaluating

Recently, engine design and control systems have been developed using data-driven modeling techniques to specify the in-cylinder complicated combustion process. The cooling fan performance is highly influenced by several factors that are determined based on what is called (DOE) «design of experiments». These factors include blade tip clearance, pitch angle, distance from radiator. This work presents a method to improve a cooling fan performance of an engine by designing a Six Sigma technique using Control, Improve, Analyze, Measure, and Define (CIAMD). First, let’s assess the existing cooling fan performance and define its problem. Then, let’s specify the parameters that affect on fan performance to be optimized. Next, let’s conduct sensitivity analysis and evaluate manufacturing control of the developed cool Fan. The primary fan does not distribute air enough by the radiator to maintain the machine cool throughout hard circumstances. First, the work demonstrates how to develop an experiment to examine the influence of three performance elements: blade pitch angle, blade-tip clearance, and fan distance from the radiator. In order to improve the performance of the cooling fan, Box-Behnken design is adopted for testing quadratic (nonlinear) effects. It then indicates how to predict optimal quantities for every element, to produce a technique that makes airflows above the objective of 1486.6 m3/h when utilizing experimental measurements. Finally, it reveals how to operate simulations to confirm that this method creates airflow based on the specifications with more additional fans manufactured performance of 99.999 %. The results of S and X-bar control charts indicate that the manufacturing process is statistically under control

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

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

An Integrated Model of Maintenance Policies and Economic Design of X-bar Control Chart Under Burr XII Shock Model

The combination of different methods of maintenance and economic design of control charts has received much attention from researchers in recent years. These maintenance policies increase the reliability of a system. So far, only a small number of failure distributions, with fixed or increasing hazard rates, have been used as a shock model in the integrated model of maintenance and economic design of X-bar control chart. A proper alternative for this situation may be the Burr distribution, in which the hazard rate has general form. In this paper, for the economic design of the X-bar control chart under the Burr XII shock model, we have presented an integrated model using preventive maintenance and incomplete maintenance. The obtained integrated model has been implemented using a numerical example and its sensitivity analysis has been performed. The results show that, the use of higher maintenance levels causes further reduction of the average cost per unit time of the quality cycle. The results of sensitivity analysis also show that our proposed model is not sensitive to the misspecification of the Burr XII distribution parameters.

Anomaly diagnosis of stay cables based on vehicle-induced cable force sums

Stay cables are one of the most critical load-carrying components for cable-stayed bridges. Cable damage or performance degradation can affect the normal operation of bridges. Therefore, it is essential to evaluate the service performance of cables in real time to ensure bridge safety. In this paper, an anomaly diagnosis method for stay cables based on vehicle-induced cable force sums (VICFS) of cable pairs (defined as two symmetric cables upstream and downstream) is proposed. First, the theoretical relationship between the vehicle load and VICFS was derived through mechanical analysis. Second, a new anomaly-sensitive warning index was established based on the above derivation, and the anomaly diagnosis for stay cables was achieved by combining it with the X-bar control chart. Then, according to finite element simulation, the variations in VICFS in different cases were analyzed to verify the rationality of the theoretical derivation and the established warning index. Finally, an engineering application to an in-service cable-stayed bridge was carried out to validate the feasibility and effectiveness of the anomaly diagnosis method. The results show that the proposed method can accurately detect and locate damaged cables, which can be successfully applied to monitor the long-term performance of stay cables.

Ensemble Classifier for Recognition of Small Variation in X-Bar Control Chart Patterns

Manufacturing processes have become highly accurate and precise in recent years, particularly in the chemical, aerospace, and electronics industries. This has attracted researchers to investigate improved procedures for monitoring and detection of small process variations to remain in line with such advances. Among these techniques, statistical process controls (SPC), in particular the control chart pattern (CCP), have become a popular choice for monitoring process variance, being utilized in numerous industrial and manufacturing applications. This study provides an improved control chart pattern recognition (CCPR) method focusing on X-bar chart patterns of small process variations using an ensemble classifier comprised of five complementing algorithms: decision tree, artificial neural network, linear support vector machine, Gaussian support vector machine, and k-nearest neighbours. Before advancing to the classification step, Nelson’s Rus Rules were utilized as a monitoring rule to distinguish between stable and unstable processes. The study’s findings indicate that the proposed method improves classification performance for patterns with mean changes of less than 1.5 sigma, and confirm that the performance of the ensemble classifier is superior to that of the individual classifier. The ensemble classifier can distinguish unstable pattern types with a classification accuracy of 99.55% and an ARL1 of 11.94.

Monitoring Using X-Bar Control Chart Using Neutrosophic-Based Generalized Multiple Dependent State Sampling with Application

In this article, an enhanced X-bar control chart using generalized multiple dependent state (GMDS) sampling under neutrosophic statistics is presented. The joint advantages of GMDS sampling and the neutrosophic statistics have been recycled for the efficient monitoring of the average quality characteristic of any production process. The efficiency of the proposed chart has been evaluated using the average run length values under different ranges of the parameters under study. The comparison of the proposed chart with the existing control chart has been discussed. The comparison shows that the proposed chart is better than the existing chart. Results reveal the superiority of the proposed neutrosophic-based GMDS sampling chart. In addition, an example has also been included for the practical implementation of the proposed methodology.

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.

Assessment of multiple choice question exams quality using graphical methods

Exams should be valid, reliable, and discriminative. Multiple informative methods are used for exam analysis. Displaying analysis results numerically, however, may not be easily comprehended. Using graphical analysis tools could be better for the perception of analysis results. Two such methods were employed: standardized x-bar control charts with standard error of measurement as control limits and receiver operator characteristic curves. Exams of two medical classes were analyzed. For each exam, the mean, standard deviation, reliability, and standard error of measurement were calculated. The means were standardized and plotted against the reference lines of the control chart. The means were chosen as cut-off points to calculate sensitivity and specificity. The receiver operator characteristic curve was plotted and area under the curve determined. Standardized control charts allowed clear, simultaneous comparison of multiple exams. Calculating the control limits from the standard error of measurement created acceptable limits of variability in which the standard deviation and reliability were incorporated. The receiver operator characteristic curve graphically showed the discriminative power of the exam. Observations made with the graphical and classical methods were consistent. Using graphical methods to analyse exams could make their interpretation more accessible and the identification of exams that required further investigation easier.

Analisis Pengendalian Mutu pada Asam Lemak Bebas Minyak Kelapa Sawit Menggunakan Metode SQC

PT. Socfindo Indonesia Seunagan Plantation is a company that produces palm oil and palm kernel (PKO). This observation aims to determine the parameters of free fatty acids in PT. Socfindo Indonesia Seunagan Plantation. Is it within the quality control limits based on the Xbar and Rbar control charts, as well as investigations into the causes of improving the quality of palm oil with Free Fatty Acid (FFA) parameters. Based on the results of the Crude Palm Oil (CPO) quality control chart, the number of samples for free fatty acid levels, according to the control chart Xbar = 2.1375 and Rbar = 1.2308, there are some data that are out of the control limit UCL = 2.7323, CL = 2.1375 LCL = 1.5427 after modification of Xbar and Rbar control chart. Based on the results of observations, interviews and fieldwork, there are five factors that affect the quality of Crude Palm Oil (CPO). The factors themselves are raw materials, work environment, people, machines and work methods and techniques. This case study was conducted on a company that produces palm oil and palm kernel (PKO). This observation aims to determine the parameters of free fatty acids in this company. Observe whether it is within the quality control limits based on Xbar and Rbar control charts. Then, investigate the cause of the increase in the quality of palm oil with the Free Fatty Acid (FFA) parameter. Based on the results of the Crude Palm Oil (CPO) quality control chart, the number of samples for free fatty acid levels, according to the control chart Xbar = 2.1375 and Rbar = 1.2308, there are some data that are out of the control limit UCL = 2.7323, CL = 2.1375 LCL = 1.5427 after modification of Xbar and Rbar control chart. The results of observations show that in interviews and in the field there are five factors that affect the quality of Crude Palm Oil (CPO). The factors themselves are raw materials, work environment, people, machines and work methods and techniques.

Process Improvement in Surgery

Process improvement is a skill all physicians need to be familiar with. This is particularly true for surgeons, who work in complex systems requiring multidisciplinary care in the health care system’s most expensive location: the operating room. Surgical leaders need to be familiar with the techniques and themes of process improvement. The current literature suggests that formal process improvement programs can be effective in improving clinical, operational, and financial performance of hospitals. This review outlines a general approach to process improvement, in addition to providing evidence for the efficacy of process improvement in health care, a definition of processes, and the history of process improvement. Tables outline forms of waste applied to health care and heuristic approaches to project improvement. Figures include a project charter, control chart, X-bar control chart, Pareto table and chart, Fishbone cause-and-effect diagram, diagrams of the Plan-Do-Study-Act process and cost/payoff matrix, statistical software control charts, and process flow maps. This review contains 10 figures, 3 tables, and 22 references Keywords: Operating room, surgery, surgical leader, multidisciplinary team, waste, project carter, control chart, Pareto table, health care improvement

Process Improvement in Surgery

Process improvement is a skill all physicians need to be familiar with. This is particularly true for surgeons, who work in complex systems requiring multidisciplinary care in the health care system’s most expensive location: the operating room. Surgical leaders need to be familiar with the techniques and themes of process improvement. The current literature suggests that formal process improvement programs can be effective in improving clinical, operational, and financial performance of hospitals. This review outlines a general approach to process improvement, in addition to providing evidence for the efficacy of process improvement in health care, a definition of processes, and the history of process improvement. Tables outline forms of waste applied to health care and heuristic approaches to project improvement. Figures include a project charter, control chart, X-bar control chart, Pareto table and chart, Fishbone cause-and-effect diagram, diagrams of the Plan-Do-Study-Act process and cost/payoff matrix, statistical software control charts, and process flow maps. This review contains 10 figures, 3 tables, and 22 references Keywords: Operating room, surgery, surgical leader, multidisciplinary team, waste, project carter, control chart, Pareto table, health care improvement

Process Improvement in Surgery

Process improvement is a skill all physicians need to be familiar with. This is particularly true for surgeons, who work in complex systems requiring multidisciplinary care in the health care system’s most expensive location: the operating room. Surgical leaders need to be familiar with the techniques and themes of process improvement. The current literature suggests that formal process improvement programs can be effective in improving clinical, operational, and financial performance of hospitals. This review outlines a general approach to process improvement, in addition to providing evidence for the efficacy of process improvement in health care, a definition of processes, and the history of process improvement. Tables outline forms of waste applied to health care and heuristic approaches to project improvement. Figures include a project charter, control chart, X-bar control chart, Pareto table and chart, Fishbone cause-and-effect diagram, diagrams of the Plan-Do-Study-Act process and cost/payoff matrix, statistical software control charts, and process flow maps. This review contains 10 figures, 3 tables, and 22 references Keywords: Operating room, surgery, surgical leader, multidisciplinary team, waste, project carter, control chart, Pareto table, health care improvement

A New X-bar Control Chart for Multiple Dependent State Sampling Using Neutrosophic Exponentially Weighted Moving Average Statistics with Application to Monitoring Road Accidents and Road Injuries

In this article, an efficient mean chart for symmetric data have been presented for multiple dependent state (MDS) sampling using neutrosophic exponentially weighted moving average (NEWMA) statistics. The existing neutrosophic exponentially weighted moving average charts are not capable of seizure the unusual changes threatened to the manufacturing processes. The control chart coefficients have been estimated using the symmetry property of the Gaussian distribution for the uncertain environment. The neutrosophic Monte Carlo simulation methodology has been developed to check the efficiency and performance of the proposed chart by calculating the neutrosophic average run lengths and neutrosophic standard deviations. The proposed chart has been compared with the counterpart charts for confirmation of the proposed technique and found to be a robust chart.

Reducing length of stay for patients with acute myeloid leukemia receiving inpatient high-dose cytarabine consolidation chemotherapy.

257 Background: For patients receiving high dose cytarabine (HiDAC) at University of Virginia (UVA) Health between 10/2019 and 10/2020, median length of stay (LOS) from time of clinic appointment to hospital discharge was 119.35 hours. Standard treatment time should be 112 hours from premedication to end of chemotherapy. There are no national standards for duration of inpatient stay for planned chemotherapy, but only 50% of these patients were discharged after noon (over 3 hours post-chemotherapy completion). LOS that extends beyond the standard treatment time results in increased cost, overutilization of hospital resources, delayed admissions for future patients, and patient dissatisfaction. Methods: A multidisciplinary team comprised of licensed providers, pharmacists, and nurses was formed. The team focused on percentage of patients discharged by noon as a surrogate marker for LOS due to inconsistency of admission times; the aim was to increase patients discharged by noon to 65%. Reviewing the baseline data revealed an unstable process with a 3-sigma X-bar statistical process control chart. The team developed current and ideal process state maps, a Pareto chart, and a priority matrix to determine an action plan. The most common identified causes for delay in discharge included: lack of standardized discharge checklist, discharge order placed after 10 am, medications dispensed from the outpatient pharmacy after 11 am, licensed providers not prioritizing discharge patients, and medication reconciliation not completed prior to day of discharge. Results: From 10/2020 to 5/2021, the first PDSA cycle focused on standardizing the discharge process to correct the instability in the process. A discharge checklist was created based on the ideal process map, which allowed the providers to have a consistent process at discharge. 3-sigma Xbar chart demonstrated a now stable process and an increase of patients discharged by noon to 58%. During the second PDSA cycle starting in 6/2021, providers completed medication reconciliation the day before discharge, prioritized HiDAC discharges first during rounds, and ensured discharge orders were placed by completion of the last chemotherapy bag. Data collection is ongoing, and will be analyzed by August 2021. Future tests of change are planned to focus on the pharmacy medication delivery service. Hospital LOS has also decreased after the first PDSA cycle. Conclusions: Using quality improvement methodology, a multidisciplinary team developed an action plan for patients receiving HiDAC which to date has increased the percentage of patients discharging by noon and decreased length of stay. This outcome may lead to reduce hospitalization costs and increase bed availability for other oncology patients. Further PDSA cycles are scheduled and continuous evaluation of the process is ongoing.

Optimum evaluation performance of adaptive X-bar control charts

ABSTRACT Control charts are useful tools to regulate processes. Thereby the quality of products and services is enhanced which makes them more attractive to the customers. While fixed-parameter X-bar charts have been regularly utilized in manufacturing systems since 1931, their incompetent effectiveness in the discovery of small-to-moderate shifts in mean has proven to be a major limitation. A systematic study providing in-depth information on the effectiveness of adaptive X-bar control charts at optimal points within the response space was needed to resolve this issue. While previous research used a forward perspective, evaluating the effectiveness of adaptive models for a specified range of design parameters, we utilized a reverse viewpoint to investigate all feasible sets of design parameters. It allowed obtaining the minimum values for three different performance measures using single-objective and multi-objective optimizations. The guideline provides quality engineers with an in-depth awareness on optimal points to select an appropriate adaptive model.

Practical application of product and process parameters under the specified process capability value

In 2018, Chen and Chou proposed a jointly design model with manufacturing quantity, specification limits, process mean, and the parameters of X-bar control chart based on the specified process capability index Cpm or Cpmk value. This integrated model is a generalization of economic manufacturing quantity (EMQ) model with statistical quality control chart. In this study, the author presents the practical application of Chen and Chou’s model for the manufacturer. The manufacturer can apply these parameters in the design of a variable single rectifying inspection plan for the output product before shipping to the customer and the determination of the stock quantity for shipment to the customer in the newsvendor problem.

Many-objective x-bar control chart using hybrid NSGA-III and DEA

The present study aimed to find the optimal design of the x-bar control chart which optimises quadruple objectives. The objectives are the average run length, the detection power, the average time to signal, and the expected cost per hour. In this study, a many-objective mathematical model was developed to find the optimal design and solved it using three different variations of the third version of the non-dominated sorting genetic algorithm, named NSGA-III, θ-NSGA-III, and NSDGA-III. The third one is the contribution of this paper which hybridised the NSGA-III with data envelopment analysis (DEA) and technique for order of preference by similarity to ideal solution (TOPSIS). The performances of the three algorithms were tested using a numerical example. The results revealed that the developed NSDGA-III is well defined to explore the search area and in each generation, it is always the best one in choosing solutions that have higher efficiency. Therefore, it is superior in comparing with other algorithms to find better solutions. Hence, the new hybrid algorithm can outperform NSGA-III and θ-NSGA-III. It can be used in all processes with variation due to an assignable cause.