Proposed α-cut CUSUM and EWMA Control Charts for Fuzzy Response Observations

2020 ◽  
pp. 2150012 ◽  
Author(s):  
Abbas Al-Refaie ◽  
Ghaleb Abbasi ◽  
Dina Ghanim
Keyword(s):  
Fuzzy Logic ◽  
Control Charts ◽  
Moving Average ◽  
Mean Shift ◽  
Process Condition ◽  
Quality Characteristic ◽  
Business Applications ◽  
Wide Range ◽  
Triangular Membership Function ◽  
Cusum Control Charts

This research proposesalpha ([Formula: see text]-cut Exponentially Weighted Moving Average (EWMA) and Cumulative Sum (CUSUM) control charts with fuzzy response observations in a manufacturing process under the existence of mean shift utilizing the fuzzy logic. In this research, the replicate’s observation is a fuzzy number represented by a triangular membership function, with the lower, average, and upper observation values. The fuzzy numbers are then normalized and assigned as input to the fuzzy logic, while a common output measure (COM) value is the output. Finally, the original values of the COM values are employed in developing the EWMA and CUSUM control charts with different [Formula: see text]-cut values. Three real case studies are adopted to illustrate the proposed EWMA and CUSUM control charts; including piston inside diameter, cap’s angel, and tablet weight. Results showed that the proposed EWMA and CUSUM control charts efficiently monitor fuzzy observations and detect the shift in process means. Moreover, the amount mean shift and [Formula: see text]-cut values affect the decision on process condition. In conclusion, the proposed approach is found effective in monitoring quality characteristic of fuzzy observations under mean shift which can be applied in a wide range of business applications.

Drift Change Point Estimation in Multistage Processes Using MLE

2015 ◽  
Vol 22 (05) ◽  
pp. 1550025 ◽  
Author(s):  
Alireza Safaeipour ◽  
Seyed Taghi Akhavan Niaki
Keyword(s):  
Change Point ◽  
Control Charts ◽  
Moving Average ◽  
Location Parameter ◽  
Point Estimation ◽  
Quality Characteristic ◽  
Multistage Process ◽  
Sample Number ◽  
Multistage Processes ◽  
Exact Time

Usually the time a control chart shows an out-of-control signal is not the exact time at which a change happens; instead, the change has started before this time. The exact time the change starts is called the change point. Although many manufacturing processes are of a multistage type, most of change point estimations in the literature focused on processes with a single stage. In this research, a multistage process with a single quality characteristic monitored in each stage is first modeled using both a first-order autoregressive (AR(1)) and an autoregressive moving average (ARMA(1, 1)) model. Then, a maximum likelihood estimator is derived to estimate the change points, i.e., the sample number and the stage number, at which a drift change occurs in the location parameter of the multistage processes. To monitor the process, cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts are used and the performance of the proposed estimator is compared with the ones of CUSUM and EWMA approach in terms of the average and the standard deviation of the sample number and the number of wrong stages. The results of several simulation experiments indicate that the MLE estimator has a good performance to estimate drift change-point in multistage process.

Dynamic Response of Residuals of a Controlled Cutting Process to Shifts in the Process Mean

1998 ◽  
Vol 05 (02) ◽  
pp. 157-168
Author(s):  
Jiangbin Yang ◽  
Viliam Makis
Keyword(s):  
Control Charts ◽  
Moving Average ◽  
Cutting Process ◽  
Process Mean ◽  
Autocorrelated Process ◽  
Recursive Procedures ◽  
Statistical Behavior ◽  
Run Lengths ◽  
Cusum Control Charts ◽  
Weighted Moving Average

A usual approach to monitoring an autocorrelated process is to apply a control chart to the process residuals. In this paper, we study the statistical behavior of the residuals of a controlled second-order autoregressive (AR(2)) cutting process when a special-cause shift occurs to the process mean. Shewhart, exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are applied to the residuals to monitor the cutting process. Formulas, integral equations and recursive procedures for computing the average run lengths (ARLs) of the charts are derived. Numerical results are presented and the relative performance of the charts is investigated.

scholarly journals Fuzzy Logic and Back-Propagation Neural Networks for Optimal Performance

2019 ◽  
Vol 13 (2) ◽  
pp. 157
Author(s):  
Abbas Al-Refaie ◽  
Rami Fouad ◽  
Raed Athamneh
Keyword(s):  
Neural Networks ◽  
Fuzzy Logic ◽  
Back Propagation ◽  
Dynamic Environment ◽  
Fuzzy Model ◽  
Research Quality ◽  
Business Applications ◽  
Wide Range ◽  
Backward Propagation ◽  
Full Factorial

Thus far, the Taguchi technique is found only efficient in obtaining the combination of optimal factor settings when a single product/process response is considered. In today’s dynamic environment, customers are interested in multiple quality responses. This research, therefore, utilizes fuzzy logic and backward-propagation neural networks (BPNNs) to optimize process performance for products of multiple quality responses. In this research, quality characteristics are transformed to signal to noise (S/N) ratios, which are then used as inputs to a fuzzy model to obtain a single common output measure (COM). Next, BPNNs are employed to obtain full-factorial experimental data. Finally, the combination of factor levels that maximizes the average COM value is chosen as the optimal combination. Three case studies are provided for illustration; in all of which the proposed approach provided the largest total anticipated improvement. This indicates that the proposed approach is more efficient than Taguchi-fuzzy, grey-Taguchi, and Taguchi-utility methods. In conclusion, the fuzzy-BPNN approach may greatly assist process/product engineers in optimizing performance with multiple responses in a wide range of business applications.

scholarly journals Penerapan Peta Kendali Neutrosophic Exponentially Weighted Moving Average (NEWMA) X dalam Monitoring Rata-Rata Proses Ketebalan Kaca

2022 ◽  
Vol 4 (1) ◽  
Author(s):  
Wibawati Wibawati ◽  
Widya Amalia Rahma ◽  
Muhammad Ahsan ◽  
Wilda Melia Udiatami
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Quality Characteristic ◽  
Average Process ◽  
Exponentially Weighted Moving Average ◽  
Ewma Control Chart ◽  
Control Limits ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In the industrial sector, the measurement results of a quality characteristic often involve an uncertainty interval (interval indeterminacy). This causes the classical control chart to be less suitable for monitoring quality. Currently, a control chart with a neutrosophic approach has been developed. The neutrosophic control chart was developed based on the concept of neutrosophic numbers with control charts. One of the control charts that have been developed to monitor the mean process is the Neutrosophic Exponentially Weighted Moving Average (NEWMA) X control chart. This control chart is a combination of neutrosophic with classical EWMA control chart.  The neutrosophic control chart consists of two control charts, namely lower and upper, each of which consists of upper and lower control limits. Therefore, NEWMA X is more sensitive to detect out-of-control observations. In this research, the NEWMA X control chart will be used to monitor the average process of the thickness of the panasap dark grey 5mm glass produced by a glass industry. Through the analysis in this research, it was found that by using weighting λN [0, 10; 0, 10] and constant value kN [2, 565; 2, 675], the average process of the thickness of panasap dark grey 5mm glass has not beet controlled statistically because 21 observations were identified that were outside the control limits (out of control). When compared with the classical EWMA control chart with the same weighting λ, 17 observations were detected out of control. This proves that the NEWMA X control chart is more sensitive in detecting observations that are out of control because the determination of the in-control state is based on two values, lower and upper, both at the lower and upper control limits.

scholarly journals A comparison of multivariate control charts for skewed distributions using weighted standard deviations

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Michael B.C. Khoo ◽  
Sin Yin Teh ◽  
May Yin Eng
Keyword(s):  
False Alarm ◽  
Process Monitoring ◽  
Control Charts ◽  
Moving Average ◽  
Quality Characteristic ◽  
Skewed Distributions ◽  
Underlying Process ◽  
Multivariate Control Charts ◽  
Multivariate Quality Control ◽  
Multivariate Control

The quality of a manufacturing process usually depends on more than one quality characteristic. Thus, most process monitoring data are multivariate in nature. The assumption that the underlying process follows a multivariate normal distribution is usually required by most multivariate quality control charts. However, in most process monitoring situations, the multivariate normality assumption is often violated. Multivariate control charts for skewed distributions have been suggested to enable process monitoring to be made when the underlying process distribution is skewed. Among the recent heuristic multivariate charts for skewed distributions suggested in the literature are those based on the weighted standard deviation (WSD) approach. This paper compares the performances of three multivariate charts for skewed distributions incorporating the WSD method, namely, the WSD T 2 , WSD multivariate cumulative sum (WSD MCUSUM) and WSD multivariate exponentially weighted moving average (WSD MEWMA) charts. These heuristic charts are compared based on the multivariate lognormal, gamma and Weibull distributions. The charts’ performances are evaluated using the false alarm rates, computed via a Monte-carlo simulation. The chart with the lowest false alarm rate for most of the skewness levels and sample sizes will be identified as the chart having the best performance.

Explicit Formulas of ARL on Double Moving Average Control Chart for Monitoring Process Mean of ZIPINAR(1) Model with an Excessive Number of Zeros

2021 ◽  
Author(s):  
Kobkun Raweesawat ◽  
Saowanit Sukparungsee
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Mean Shift ◽  
Process Mean ◽  
Explicit Formulas ◽  
Run Length ◽  
Number Of Zeros ◽  
Excessive Number

Usually, the performance of control charts are widely measured by average run length (ARL). In this paper, the derivative explicit formulas of the ARL for double moving average (DMA) control chart are proposed for monitoring the process mean of zero-inflated Poisson integer-valued autoregressive first-order (ZIPINAR(1)) model. This model is fit when there are an excessive number of zeros in the count data. The performance of the DMA control chart is compared with the results of moving average and Shewhart control charts by considering from out of control average run length (ARL1). The numerical results found that the DMA control chart performed better than other control charts in order to detect mean shift in the process. In addition, the real-world application of the DMA control chart for ZIPINAR(1) process is addressed.

On control chart for monitoring exponentially distributed quality characteristic

2019 ◽  
Vol 42 (2) ◽  
pp. 295-305 ◽  
Author(s):  
Olatunde A Adeoti
Keyword(s):  
Exponential Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Real Life ◽  
Quality Characteristic ◽  
Exponentially Weighted Moving Average ◽  
Run Lengths ◽  
Weighted Moving Average ◽  
Exponentially Weighted

The double exponentially weighted moving average (DEWMA) control chart has been observed to be more sensitive than the exponentially weighted moving average (EWMA) control chart for process monitoring assuming that the quality characteristic follows the normal distribution. In this paper, the DEWMA control chart is proposed for monitoring quality characteristics that follow the exponential distribution using variable transformation technique. The in-control and out-of-control average run lengths (ARLs) of the proposed control chart is obtained for equal and unequal smoothing constants. The performance of the proposed control chart with equal and unequal smoothing constants was investigated and compared with recent existing control charts in terms of the out-of-control average run lengths. Real life example is given to demonstrate the application of the proposed chart. The findings show that the performance of the proposed control chart outweighs existing control charts in the monitoring of process parameter when the quality variable follows exponential distribution for all shift sizes.

scholarly journals Monitoring of mechanical sugarcane harvesting through control charts

2015 ◽  
Vol 35 (6) ◽  
pp. 1079-1092 ◽  
Author(s):  
Murilo A. Voltarelli ◽  
Rouverson P. da Silva ◽  
Cristiano Zerbato ◽  
Carla S. S. Paixão ◽  
Tiago de O. Tavares
Keyword(s):  
Process Control ◽  
Statistical Process Control ◽  
Control Chart ◽  
Control Charts ◽  
Moving Average ◽  
Grinding Wheel ◽  
Individual Values ◽  
Statistical Process ◽  
Minas Gerais State ◽  
Weighted Moving Average

ABSTRACT Statistical process control in mechanized farming is a new way to assess operation quality. In this sense, we aimed to compare three statistical process control tools applied to losses in sugarcane mechanical harvesting to determine the best control chart template for this quality indicator. Losses were daily monitored in farms located within Triângulo Mineiro region, in Minas Gerais state, Brazil. They were carried over a period of 70 days in the 2014 harvest. At the end of the evaluation period, 194 samples were collected in total for each type of loss. The control charts used were individual values chart, moving average and exponentially weighted moving average. The quality indicators assessed during sugarcane harvest were the following loss types: full grinding wheel, stumps, fixed piece, whole cane, chips, loose piece and total losses. The control chart of individual values is the best option for monitoring losses in sugarcane mechanical harvesting, as it is of easier result interpretation, in comparison to the others.

Process Mean Shift Detection Using Prediction Error Analysis

1998 ◽  
Vol 120 (3) ◽  
pp. 489-495 ◽  
Author(s):  
S. J. Hu ◽  
Y. G. Liu
Keyword(s):  
Error Analysis ◽  
Prediction Error ◽  
Control Charts ◽  
Mean Shift ◽  
Measurement Data ◽  
Step Function ◽  
False Alarms ◽  
Prediction Errors ◽  
Function Type ◽  
Shift Detection

Autocorrelation in 100 percent measurement data results in false alarms when the traditional control charts, such as X and R charts, are applied in process monitoring. A popular approach proposed in the literature is based on prediction error analysis (PEA), i.e., using time series models to remove the autocorrelation, and then applying the control charts to the residuals, or prediction errors. This paper uses a step function type mean shift as an example to investigate the effect of prediction error analysis on the speed of mean shift detection. The use of PEA results in two changes in the 100 percent measurement data: (1) change in the variance, and (2) change in the magnitude of the mean shift. Both changes affect the speed of mean shift detection. These effects are model parameter dependent and are obtained quantitatively for AR(1) and ARMA(2,1) models. Simulations and examples from automobile body assembly processes are used to demonstrate these effects. It is shown that depending on the parameters of the AMRA models, the speed of detection could be increased or decreased significantly.

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