The design of a new repetitive sampling control chart based on process capability index

The implementation of Statistical Quality Control (SQC) has been tracked in various areas, such as agriculture, environment, industry, and health services. The employment of SQC methodologies is frequently employed for monitoring and identification of process irregularities across various fields. This research proposes and implements a novel SQC methodology in agricultural areas. A control chart is one of the SQC tools that facilitates real-time monitoring of multiple activities, including agricultural yield, industrial yield, and hospital outcomes. Advanced control charts with symmetrical data are being subjected to the new SQC method, which is suitable for this purpose. This research aims to develop a novel hybrid exponentially weighted moving average control chart for detecting the coefficient of variation (CV) using a repetitive sampling method called the HEWMARS-CV control chart. It is an effective tool for monitoring the mean and variance of a process simultaneously. The HEWMARS-CV control chart used the repetitive sampling scheme to generate two pairs of control limits to enhance the performance of the control chart. The proposed control chart is compared with the classical HEWMA and Shewhart control charts regarding the average run length (ARL) when the data has a normal distribution. The Monte Carlo simulation method is utilized to approximate the ARL values of the proposed control charts to determine their performance. The proposed control chart detects small shifts in CV values more effectively than the existing control chart. An illustrative application related to monitor the wheat yield at Rothamsted Experimental Station in Great Britain is also incorporated to demonstrate the efficiency of the proposed control chart. The efficiency of the proposed HEWMARS-CV control chart on the real data shows that the proposed control chart can detect a shift in the CV of the process, and it is superior to the existing control chart in terms of the average run length.

A new exponentially weighted moving average sign chart using repetitive sampling

ABSTRACTA new process capability index (PCI) control chart for monitoring the process mean using repetitive sampling is presented. The design of the proposed control chart is based on an unbiased estimator of the process standard deviation for a normally distributed quality characteristic. The formulae for the in-control and out-of-control average run length and the standard deviation of the run length (SDRL) are derived. Tables of in-control and out-of-control average run length (ARL) and SDRL for various shifts, δ are presented. The proposed control chart outperforms existing control chart in detecting relatively small process mean shifts in terms of ARLs and SDRLs. Numerical example is presented to demonstrate the application of the proposed chart.

Non-normal processes are common in practice. In this paper, we propose a novel approach to defining bootstrap process capability index (PCI) control charts to monitor the performance of in-control skew normal processes. We use a bootstrap method to calculate phase I control limits of the corresponding PCI control charts. The β-risk curves of the associated PCI control charts will be used to assess the performance of the PCI control charts. We use Monte-Carlo simulation to evaluate the performance of the proposed PCI control charts. A numerical example to illustrate the implementation of the proposed control charts.

Measurement error is a usually met distortion factor in real-world applications that influences the outcome of a process. The performance of the control charts can be affected in the presence of measurement error which also leads to erroneous conclusions regarding the average run length. In this paper, we proposed regression estimator-based mixed exponentially weighted moving average-cumulative sum (MxEMCUS) control chart to monitor the process mean and investigate the effect of measurement error on shift detection ability of the proposed control chart. The performance of MxEMCUS control chart is evaluated in the cases of mean shift with and without measurement error. The linear covariate model is used to evaluate the control chart in the presence of measurement error. The case of multiple measurements and linear increasing variance is also investigated in the presence of measurement error. The average run length and standard deviation of run length are used as the performance measuring tool. Based on simulation results, it is concluded that in the presence of measurement error, proposed chart has better performance as compared to other existing charts. An example with real data set is given to demonstrate the implementation of MxEMCUS control chart.

Enhancing the ability of control charts for detecting shifts of small magnitude in the process parameter is desirable. In this paper, a double moving average control chart based on the sample standard deviation is proposed for detecting shifts in the process variability. The performance of the proposed control chart is investigated in terms of average run length and compared with existing control charts. The results show that the proposed control chart performs better than the existing control charts. A numerical example based on simulated and real-life data is provided to demonstrate the application of the proposed chart.

ABSTRACTCompared to the grid search approach to optimal design of control charts, the gradient-based approach is more computationally efficient as the gradient information indicates the direction to search the optimal design parameters. However, the optimal parameters of multivariate exponentially weighted moving average (MEWMA) control charts are often obtained by using grid search in the existing literature. Note that the average run length (ARL) performance of the MEWMA chart can be calculated based on a Markov chain model, making it feasible to estimate the ARL gradient from it. Motivated by this, this paper develops an ARL gradient-based approach for the optimal design and sensitivity analysis of MEWMA control charts. It is shown that the proposed method is able to provide a fast, accurate, and easy-to-implement algorithm for the design and analysis of MEWMA charts, as compared to the conventional design approach based on grid search.

A simulation approach to multivariate quality control

Design of X-bar control chart based on Inverse Rayleigh Distribution under repetitive group sampling

Traditional control charts assume independence of observations obtained from the monitored process. However, if the observations are autocorrelated, these charts often do not perform as intended by the design requirements. Recently, several control charts have been proposed to deal with autocorrelated observations. The residual chart, modified Shewhart chart, EWMAST chart, and ARMA chart are such charts widely used for monitoring the occurrence of assignable causes in a process when the process exhibits inherent autocorrelation. Besides autocorrelation, one other issue is the unknown values of true process parameters to be used in the control chart design, which are often estimated from a reference sample of in-control observations. Performances of the above-mentioned control charts for autocorrelated processes are significantly affected by the sample size used in a Phase I study to estimate the control chart parameters. In this study, we investigate the effect of Phase I sample size on the run length performance of these four charts for monitoring the changes in the mean of an autocorrelated process, namely an AR(1) process. A discussion of the practical implications of the results and suggestions on the sample size requirements for effective process monitoring are provided.

Part 1 Statistical process control: development of SPC what SPC is and is not online SPC methods off-line process control SPC methodolgy other factors affecting the success of SPC. Part 2 Some basic distributions: attribute data countable data geometric distribution the Normal distribution distributions derived from the Normal distribution application of results testing for normality the Normal approximation to the binomial distribution Normal approximation to the Poisson distribution. Part 3 Process variation: reasons for process variation types of process variation some models for process variation sampling error and measurement error. Part 5 Basic Shewhart control charts for continuous variables: control charts for average level charts for control of (within group) process spread the average run length (ARL) special problems some theoretical results for Shewhart charts charts for control of process spread. Part 6 Extensions to Shewhart charts for one-at-a-time data: one-at-a-time sampling estimation of sigma for one-at-a-time data details of further control charts for control of process average level control of process spread choice of charting method practical use of Shewhart and moving average charts properties of EWMA and MA charts. Part 7 Cumulative sum techniques for continuous variables: CuSum charts - for control of average level, for control of process spread nomogram for CuSums. Part 8 Further theoretical results on control charts for continuous variables: the effect of departures from assumption on moments of x and s(2) Shewhart charts - Markov chain approach cumulative Sum charts charts for control of process spread. Part 9 The design of control charts for specification limits: single specification limits - chart for means double specification limits - high capability processes, an alternative approach. Part 10 Control of discrete data processes: Shewhart charts - for countable data (c and u), for attribute data (np and p) CuSum charts for countable data, for attribute data comparison of Shewhart and CuSum schemes. Part 11 Sampling inspection: classification of inspection plans some properties of sampling plans methods of using sampling plans for attributes. Part 12 Inspection by variables: single specification limit - sigma known, sigma unknown estimation of fraction non-conforming, single specification limit double specification limit - sigma known, sigma unknown multivariate sampling plans. Part 13 Standard sampling systems: statement of method for inspection by attributes inspection by variables International Standards for process and quality control. Part 14 Adaptive sampling plans: CSP-1 and the AOQL criterion theory of CSP-1 the AEDL criterion. (Part contents).

The multivariate and discrete data are commonly used to monitor product defects and epidemic diseases. It is difficult to model their complex structure and design a suitable control chart to monitor them in the area of statistical process control. To monitor the tri-variate Poisson process, this paper establishes a one-parameter copula function to describe the spatial correlation and designs a control chart based on the log-likelihood ratio test. The Markov chain is employed to approximate the average run length and to measure the performance of the control chart. Simulation results show that the proposed chart is efficient for detecting upward shifts and can achieve better monitoring performances when the target mean shift in control chart design is equal to a true mean shift. Compared with D chart, the proposed chart achieves a better performance when the correlation level is high.

This research suggests a Distance Weighted Mean (DWM) based control chart under normal distribution implementing Simple Random Sampling (SRS). The control limits are calculated using the quantile point method. The control chart's performance is assessed using the Average Run Length (ARL) statistic. The numerical findings are illustrated using samples of sizes 3 and 5. The ARL1 values are determined using Monte Carlo Simulation for increasing and decreasing shifts in the location parameter ranging from 5% to 30%. Using the ARL1 measurement, the proposed DWM control charts are compared to the existing Shewhart control charts. According to the comparison analysis, the suggested DWM control chart surpasses the competing Shewhart control chart. The real-life application of the proposed DWM control chart is also shown by using the lifetime of the light bulb (in hours). The results suggest that the proposed DWM control chart can be a useful tool for monitoring process mean shifts, especially when the sample size is large, and the magnitude of the shift is significant.

Statistical process control (SPC) charts play a very important role in the determination of process capability. It is important that SPC be achieved via the use of appropriate control charts before process capability indices are calculated, so that the indices reflect the long‐term capability of a process to produce product within specification. A significant portion of the theoretical research dedicated to process capability indices has focused on those index estimators that utilize a pooled estimator of process variance, but data collected in subsamples from an in‐control SPC chart, most likely an X − R or X − s chart, is preferred in practice for index estimation to insure process stability. This article is focused on the significant work published to date on process capability indices estimated using subsamples, including confidence bounds and hypothesis testing procedures for the primary indices C p , C pk , and C pm .

This paper deals with the statistical design of control charts and describes a methodology to identify control schemes with action and warning limits that, for a fixed in-control average run length (ARL), minimize the ARL at a given out-of-control situation as measured by a shift in the process mean. This methodology allows the design of control charts with improved ARL performance for moderate shifts without degrading the in-control ARL as typically happens when run rules are applied to a conventional control chart. These optimal control schemes significantly reduce the out-of-control average run length compared with nonoptimal schemes.