Control Chart Limits Research Articles

Optimal design of time-between-event control charts with parameter estimation

The tr chart is a Shewhart-type control chart used to monitor the time between events, especially in high-quality processes. It has been shown to be more efficient than classical attribute control charts based on count data. In practical applications, the in-control process parameters are often unknown and need to be estimated from a Phase I reference sample. When the available Phase I data are small and the chart parameters have to be estimated, a popular approach is to adjust the control chart limits from a conditional perspective to avoid frequent false alarms using the exceedance probability criterion. However, this approach ignores the practitioner-to-practitioner (p-to-p) variation caused by the random Phase I reference samples, which results in getting different control limits and chart performance for each practitioner Large p-to-p variation makes practitioners to have a limited confidence on using their own estimated charts. Hence, in this article, we propose to optimize the tr chart via an exact method so that it has a minimum p-to-p variation. Comparisons between the optimal and conventionally adjusted charts are made in both the in- and out-of-control cases. The most important results are that the optimal chart has a far smaller p-to-p variation and its unconditional average run length values are closer to the desired ones compared to the conventional approach regardless of the in- or out-of-control cases. Finally, two real examples are presented to illustrate the implementation of the proposed chart.

Shift Detection Comparison For Sized Biased And Area Biased Exponential Distributions Based Control Charts

Probability distribution models are very helpful to solving many real-life problems. The development of new or extensions to an existing model is a very attractive area of research. Among many types of probability distribution models, weighted distributions are becoming more important for modeling data. Weighted distributions can help discover defects in manufacturing and outliers by weighting significant observations. Control charts are the most important tools to monitor process efficiency. In recent decades, researchers have focused on weighted distributions, especially those with size and area biased exponential distribution. This research introduces a novel control chart for a characteristic following a size-biased and area-biased exponential distribution to emphasize the relevance of weighted distributions. Charts are effectively determines size-biased and area-biased exponential distribution control chart limits also Monte Carlo simulations are used to assess different Average Run Length (ARL) values.

A New Sine-Based Distributional Method with Symmetrical and Asymmetrical Natures: Control Chart with Industrial Implication

Control charts are widely used in quality control and industrial sectors. Because of their important role, researchers are focusing on the development of new control charts. According to our study, there is no significant amount of published work on control charts using trigonometrically generated distribution methods. In this paper, we contribute to this interesting research gap by developing a new control chart using a sine-based distributional method. The proposed distributional method (or family of probability distributions) may be called a new modified sine-G family of distributions. Based on the new modified sine-G method, a novel modification of the Weibull distribution, namely, a new modified sine-Weibull distribution, is introduced. The new modified sine-Weibull distribution is flexible enough to capture symmetrical and asymmetrical behaviors of its density function. An industrial application is considered to show the importance and implacability of the proposed distribution in quality control. Based on the proposed model, an attribute control chart is developed under a truncated life test. The control chart limits (ARLs) are also computed for the proposed model. The ARLs of the proposed control chart are compared with the attribute control chart of the Weibull distribution. The results show that the developed chart is more efficient than the existing attribute control chart for the Weibull distribution.

Analysis of Quality Defects in Plastic Seed Products Using Statistical Process Control (SPC) Method

Plastic seed products are products made from recycled plastic materials such as raw materials for plastic bags and some screen printing plastics. UD. ABC is a company that produces PP (Polypropylene) plastic pellets. The existing problems include the discovery of instability in the production of plastic pellets which is in a negative direction for the company, namely there are product defects in plastic pellet products that exceed the standard defect tolerance limit of the company by 2%. Based on the Pareto diagram, it can show that the type of protrusion defect is 69.56% more dominant than the type of connecting defect, which is 30.44%. Based on the control chart based on the p-chart, it shows that some dates are outside the limits of the control chart, namely the sample lot number 3 (March) of 0.0352, 4 (April) 0.0273, 7 (July) 0, 0134, 8 (August) 0.271. The data that comes out of the control chart limits exceeds the upper control limit (BKA/UCL) of 0.02649 and the lower control limit (BKB/LCL) of 0.02395. So what must be done to repair the engine factor is to carry out periodic briefings on how the machine works starting from setting the temperature and changing the filter. Meanwhile, the human factors section, namely directing the replacement of machine filter workers with temperature operators so that workers do not get tired easily, conducting periodic supervision of each worker for the leader and providing guidance on knowledge about machine work systems, mixing raw materials and operating machine temperature controls regularly.

Setting process control chart limits for rounded-off measurements

Measurements can often be imprecise and subjected to rounding-off. Typically, this rounding-off is ignored and assumed to have little to no effect. However, when the measuring scale step is not negligible, it may affect statistical control tools such as X‾-chart. Designing statistical process controls without considering the effects of rounding leads to high exposure to false negative results. This study illustrates the effects of rounding on the X-chart and shows that the result may further deteriorate due to asymmetry (incompatibility of the process and the measuring device parameters). A new simple method to design control limits is proposed, based on maintaining the original characteristics of the chart as devised by Shewhart.

Bayesian inference in control charts using normal prior

The Control Chart is a method of quality control which utilizes statistical methods to monitor and manage processes and based on the sampling inspections and chart performance. This issue is currently being researched into the economic planning of control chart. The traditional approach to design control chart utilizes the traditional structure of control plot to determine the value of parameters of the chart, namely: The sample size, sample interval and control chart limits for achieving economic needs. Under Bayes estimate framework, focus on defining the optimal control policy based on posterior probabilities, thereby reducing total expected costs in the given finite time horizon or the expected average long-term costs.

Improved control chart performance using cautious parameter learning

Parameter estimation is an important topic in Statistical Process Monitoring, as inaccurate estimates may lead to undesirable control chart performance. Updating the control chart limits during the monitoring period reduces estimation uncertainty. However, when out-of-control situations remain undetected, using the corresponding samples to update the parameter estimates can deteriorate the control chart performance in terms of in-control and out-of-control run lengths. For this reason, updating parameter estimates should only occur when there is sufficient evidence of an in-control process state. In this article, we study the performance of a cautious updating scheme for the Shewhart, Cumulative Sum, and Exponentially Weighted Moving Average control charts. We propose simple rules for updating parameters that improve the out-of-control performance of the control charts. We show the added value of using these updating rules in practice through a case study using data from a truck manufacturer.

Designing Exponentially Weighted Moving Average Control Charts under Failure Censoring Reliability Tests

One of the most important quality characteristics in a production process is the product lifetime. The production of highly reliable products is a concern of manufacturers. Since it is time-consuming and costly to measure lifetime data, designing a control chart seems difficult. To solve the problem, lifetime tests are employed. In the present study, one-sided and two-sided EWMA control charts are designed under a type II censoring (failure censoring) life test. Product lifetime is a quality characteristic dealt with in this study. It is assumed to follow the Weibull distribution with a fixed shape parameter and a variable scale parameter. In order to design a control chart, first, the control chart limits are calculated for different parameters, and then the Average Run Length (ARL) in the out-of-control state is used to evaluate the performance of the proposed control chart. Next, a comprehensive sensitivity analysis is performed for the different parameters involved. The computational results show that the one-sided control chart has better performance to detect the shift of lifetime data than the two-sided control chart. The average run length curve of the two-sided control chart is biased, while that of the one-sided control chart is unbiased. A very effective parameter that increases the performance of a control chart is found to be the number of failures in the failure censoring process. Finally, simulated and real examples are provided to show the performance of the proposed control chart.

On the Use of Copula for Quality Control Based on an AR(1) Model

Manufacturing for a multitude of continuous processing applications in the era of automation and ‘Industry 4.0’ is focused on rapid throughput while producing products of acceptable quality that meet customer specifications. Monitoring the stability or statistical control of key process parameters using data acquired from online sensors is fundamental to successful automation in manufacturing applications. This study addresses the significant problem of positive autocorrelation in data collected from online sensors, which may impair assessment of statistical control. Sensor data collected at short time intervals typically have significant autocorrelation, and traditional statistical process control (SPC) techniques cannot be deployed. There is a plethora of literature on techniques for SPC in the presence of positive autocorrelation. This paper contributes to this area of study by investigating the performance of ‘Copula’ based control charts by assessing the average run length (ARL) when the subsequent observations are correlated and follow the AR(1) model. The conditional distribution of yt given yt−1 is used in deriving the control chart limits for three different categories of Copulas: Gaussian, Clayton, and Farlie-Gumbel-Morgenstern Copulas. Preliminary results suggest that the overall performance of the Clayton Copula and Farlie-Gumbel-Morgenstern Copula is better compared to other Archimedean Copulas. The Clayton Copula is the more robust with respect to changes in the process standard deviation as the correlation coefficient increases.

Adjusting Quality Control Chart Limits for WBC, RBC, Hb, and PLT Counts to Reduce Daily Control Risks in Hospital Laboratory.

BackgroundTo continuously improve medical quality and provide clinicians with more accurate blood test reports, this study collected blood quality control data in 2017 from a medical examination laboratory in a teaching level hospital located in Taoyuan City, Taiwan.Material and MethodsThe quality control data were arranged and analyzed from daily complete blood count (CBC), including white blood cells (WBC), red blood cells (RBC), hemoglobin (Hb), and platelets (PLT) recorded by a laboratory blood analyzer. Using the empirical Bayesian method, we estimated the variation of concentrations of the last and current batches to establish a novel control chart with adjusted upper and lower limits for the current batch, and then compared results with the traditional Shewhart method. The average run length (ARL) and sensitivity of the empirical Bayesian method were explored.ResultsThe study found that ARL showed a qualified capability for the four blood routine tests when using the empirical Bayesian method. Compared to the Levey–Jennings control chart, the novel control chart presents an alert earlier when a deviation occurs and shows a fake alert later when there is no deviation.ConclusionThe parallel tests showed that the longer the time is, the better the test’s proficiency. We concluded that the empirical Bayesian method could be applied effectively to improve the capability of daily control in CBC laboratory tests.

Emergency department length of stay following discontinuation of routine oral contrast material.

To determine the effect of discontinuing routine oral contrast material on emergency department (ED) length of stay (LOS), time from order to CT completion, and preliminary report turnaround time (TAT). A HIPAA-compliant, IRB-waived, single-institution, retrospective cohort study was conducted on adult patients presenting with abdominal pain to the ED from October 2015 to April 2019. Routine oral contrast material was administered prior to July 2018 and discontinued thereafter. CT workflow (ED LOS, exam completion time, report TAT) data were analyzed in a univariate analysis before and after discontinuation of oral contrast. Pre- versus post-policy data were compared with 2-sided t tests. The primary outcome was ED LOS. Data were analyzed on a process control chart and confidence limits were adjusted using established criteria. There were 5020 included abdominopelvic CTs. After routine oral contrast material was discontinued, ED LOS (13.4h vs 10.7h, p < 0.001) and time from CT order to CT completion (2.7h vs 2.1h, p < 0.001) declined. However, control chart analysis revealed improvement in overall LOS preceded the policy change by 9months, while improvement in time to CT completion coincided with the policy change. Preliminary report TAT increased by 4min after the policy change (29min vs. 33min, p < 0.001). Discontinuation of routine oral contrast material in the ED accelerated time to CT completion but had a minor non-significant effect on overall ED LOS. Much of the reduction in overall LOS likely was due to unrelated process improvements.

Joint design of control chart, production and maintenance policy for unreliable manufacturing systems

PurposeThe purpose of this study is to develop a joint production, maintenance and quality control strategy involving a periodic preventive maintenance policy.Design/methodology/approachThe proposed integrated policy is defined and modeled mathematically.FindingsThe paper focuses on finding simultaneously the optimal values of the preventive maintenance period, the buffer stock size, the sample size, the sampling interval and the control chart limits, such that the expected total cost per time unit is minimized.Practical implicationsThe paper attempts to integrate in a single model the three main aspects of any manufacturing system: production, maintenance and quality. The considered system consists of one machine subject to a degradation process that directly affects the quality of products. The process and product quality control is carried out using an “x-bar” control chart. In the proposed model, a preventive maintenance action is performed every inspections of product quality in order to reduce the shift rate to the “out-of-control” state. A corrective maintenance action is undertaken once the control limits are exceeded. In order to palliate perturbations caused by the stopping of the machine to undergo maintenance actions, a buffer stock is built up to ensure the continuous supply of the subsequent machine. The main goal of this work is to develop a model that captures the underlying link between the preventive maintenance policy, the buffer stock size and the parameters of an “x-bar” control chart used to control the quality of the product. Numerical experiments and a study of the effects of the input parameters variation on the obtained results are performed.Originality/valueThe existing models that simultaneously consider maintenance, inventory and control charts consist of a condition-based maintenance (CBM) policy. Periodic preventive maintenance (PM) has not been considered in such models. The proposed integrated model is original, in that it links production through buffer stocks, quality through a control chart and maintenance through periodic preventive maintenance (different practical settings and modeling approach than when CBM is used). Hence, this paper addresses practical situations where, for economic or technical reasons, only systematic periodic preventive maintenance is possible.

Guaranteed conditional performance of the median run length based EWMA chart with unknown process parameters

Exponentially weighted moving average (EWMA) type charts are very popular and efficient in monitoring various kind of statistics. Much researches have been done on the EWMA chart with known process parameters. But, in practice, the process parameters used to set the control chart limits are often unknown and they need to be estimated from different Phase I samples. Moreover, because the shape of the run length distribution for the EWMA chart changes with the mean shift, the median run length (MRL) can serve as a good alternative to evaluate the performance of the EWMA chart. In this article, we will investigate the conditional properties of the EWMA chart with unknown process parameters based on the MRL metric. In order to investigate the chart’s properties, the average MRL (AMRL) and the standard deviation of MRL (SDMRL) will be used together when the process parameters are unknown. To prevent too many lower in-control MRL values, the adjusted control limits of the MRL based EWMA chart are obtained by using a bootstrap type approach and the results show that the adjusted control limits can give a good tradeoff between the in-control and out-of-control MRL performances.

The effect of continuously updating control chart limits on control chart performance

AbstractAn open topic within statistical process monitoring is the effect on control chart properties of updating the control chart limits during the monitoring period. The challenge is to use the correct data for updating the control limits as in‐control data could be incorrectly classified as out of control and therefore not used for re‐estimating the parameters, and out‐of‐control data could be classified as in control and therefore used for re‐estimating. In the present article, we study the effect of updating the Shewhart, cumulative sum, and exponentially weighted moving average control chart limits. We simulate different scenarios: the monitoring data could be in or out of control, and the practitioner may or may not be able to find out whether the process is indeed out of control when the control chart gives a signal. The results reveal that the variation in the performance of the conditional control charts decreases significantly as a result of updating the control chart limits when the updating data are in control and also when the updating data are out of control and the practitioner is able to classify correctly data samples that produce a signal. However, when a practitioner is not able to classify a signal correctly, the advisability of updating depends on the type of control chart and the level of data contamination.

Guaranteed in‐control performance of the EWMA chart for monitoring the mean

AbstractResearch on the performance evaluation and the design of the Phase II EWMA control chart for monitoring the mean, when parameters are estimated, have mainly focused on the marginal in‐control average run‐length (ARLIN). Recent research has highlighted the high variability in the in‐control performance of these charts. This has led to the recommendation of studying of the conditional in‐control average run‐length (CARLIN) distribution. We study the performance and the design of the Phase II EWMA chart for the mean, using the CARLIN distribution and the exceedance probability criterion (EPC). The CARLIN distribution is approximated by the Markov Chain method and Monte Carlo simulations. Our results show that in‐order to design charts that guarantee a specified EPC, more Phase I data are needed than previously recommended in the literature. A method for adjusting the Phase II EWMA control chart limits, to achieve a specified EPC, for the available amount of data at hand, is presented. This method does not involve bootstrapping and produces results that are about the same as some existing results. Tables and graphs of the adjusted constants are provided. An in‐control and out‐of‐control performance evaluation of the adjusted limits EWMA chart is presented. Results show that, for moderate to large shifts, the performance of the adjusted limits EWMA chart is quite satisfactory. For small shifts, an in‐control and out‐of‐control performance tradeoff can be made to improve performance.

Understanding Seasonal Changes to Improve Good Practices in Livestock Management.

Background and Aim: Food quality control techniques based on process control methods are increasingly adopted in livestock production systems to fulfill increasing market's expectations toward competitiveness and issues linked to One Health pillars (environment, animal, and human health). Control Charts allow monitoring and systematic investigation of sources of variability in dairy production parameters. These parameters, however, may be affected by seasonal variations that render impractical, biased or ineffective the use statistical control charts. A possible approach to this problem is to adapt seasonal adjustment methods used for the analysis of economic and demographic seasonal time series. The aim of the present work is to evaluate a seasonal decomposition technique called X-11 on milk parameters routinely collected also in small farms (fat, protein, and lactose content, solids-not-fat, freezing point, somatic cell count, total bacterial count) and to test the efficacy of different seasonal removal methods to improve the effectiveness of statistical control charting.Method: Data collection was carried out for 3 years on routinely monitored bulk tank milk parameters of a small farm. Seasonality presence was statistically assessed on milk parameters and, for those parameters showing seasonality, control charts for individuals were applied on raw data, on X-11 seasonally adjusted data, and on data smoothed with a symmetric moving average filter. Correlation of seasonally influenced parameters with daily mean temperature was investigated.Results: Presence of seasonality in milk parameters was statistically assessed for fat, protein, and solids-non-fat components. The X-11 seasonally-adjusted control charts showed a reduced number of violations (false alarms) with respect to non-seasonally adjusted control chart (from 5 to 1 violation for fat, from 17 to 1 violation for protein, and from 9 to none violation for solids-non-fat.). This result was achieved despite stricter control chart limits: with respect to raw data charts, the interval of control chart allowed variation (UCL–LCL) was reduced by 43% for fat, by 33.1% for protein, and by 14.3% for solids-not-fat.Conclusions: X-11 deseasonalization of routinely collected milk parameters was found to be an effective method to improve control chart application effectiveness in farms and milk collecting centers.

Conditional design of the EWMA median chart with estimated parameters

ABSTRACTThe exponentially weighted moving average (EWMA) chart is often designed assuming the process parameters are known. In practice, the parameters are rarely known and need to be estimated from Phase I samples. Different Phase I samples are used when practitioners construct their own control chart's limits, which leads to the “Phase I between-practitioners” variability in the in-control average run length (ARL) of control charts. The standard deviation of the ARL (SDARL) is a good alternative to quantify this variability in control charts. Based on the SDARL metric, the performance of the EWMA median chart with estimated parameters is investigated in this paper. Some recommendations are given based on the SDARL metric. The results show that the EWMA median chart requires a much larger amount of Phase I data in order to reduce the variation in the in-control ARL up to a reasonable level. Due to the limitation of the amount of the Phase I data, the suggested EWMA median chart is designed with the bootstrap method which provides a good balance between the in-control and out-of-control ARL values.

Penerapan Bagan Kendali Multivariat Robust Pada Data Produksi Pupuk ZK PT Petrokimia Gresik

PT Petrokimia Gresik is the most complete fertilizer producer in Indonesia and one of its production is ZK fertilizer. There are five measurable chemicals that correlate to form ZK fertilizer ie H 2 O, H 2 SO 4 , K 2 O, SO 3 and Cl - . ZK fertilizer monitoring process has not been statistically done by PT Petrokimia Gresik, either univariat or multivariate. Since ZK fertilizer is composed of five chemicals that correlate each other, a multivariate control chart is used. RMCD is one of the robust parameter estimation methods for outlier data. The average vector and variance-covariance matrix derived from the RMCD method is used to calculate the statistics on the multivariate control chart. Therefore, the robust control chart is more sensitive to detecting a shift in production processes compared to the classical ones. The data used in Phase I is daily data per January 1 - April 30, 2017, while Phase II data used is daily data as of May 1 - July 15, 2017. The results of the control chart analysis in Phase I shows that the production process has not been controlled statistically analysis of cause-effect diagrams. Furthermore, the control chart limits in Phase I that have been stable after the repair are used for Phase II production data. The result of the control chart analysis in Phase II shows that the production process has shifted. This can be known by the number of points that out of control.

Variable Control Charts - Linear Failure Rate Distribution

The well known Linear Failure Rate Distribution (LFRD) is considered. A process variate following LFRD is thought of in order to develop control charts for subgroup mean and subgroup range. In view of the limitations on LFRD the theoretical control limits are obtained through some approximations and the resulting control chart limits are worked out. Comparisons with the control limits of similar variable control charts is also presented.

Process capability indices and X ¯ $$ \overline{X} $$ , R control chart limit adjustments by taking into account measurement system errors

This paper investigates the effects of measurement system variability arising from evaluations of process capabilities. In this work, relationships between true process capability indices, C p,True and C pm,True, and their corresponding observed indices, C p,Obs and C pm,Obs, are developed depending on the levels of type I and II errors. Moreover, the method for adjusting control chart limits used to monitor the process is proposed based on measurement system variability. An industrial case study is used to highlight the findings of this investigation and to discuss the adjustment levels that should be conducted depending on the values of type I and type II errors.