scholarly journals Statistical Design for Monitoring Process Mean of a Modified EWMA Control Chart based on Autocorrelated Data

2021 ◽  
Vol 18 (12) ◽  
Author(s):  
Yadpirun SUPHARAKONSAKUN
Keyword(s):  
Explicit Formula ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Series Data ◽  
Run Length ◽  
Ewma Control Chart ◽  
Autocorrelated Observations ◽  
Normally Distributed

From the principles of statistical process control, the observations are assumed to be identically and independently normally distributed, although this assumption is frequently untrue in practice. Therefore, control charts have been developed for monitoring and detecting data which are autocorrelated. Recently, a modified exponentially weighted moving average (EWMA) control chart has been introduced that is a correction of the EWMA statistic and is very effective for detecting small and abrupt changes in independent normally distributed or autocorrelated observations. In this study, the performance of a modified EWMA chart is investigated by examining the 2 sides of the exact average run length based on an explicit formula when the observations are from a general-order moving average process with exponential white noise. A performance comparison of the EWMA and the modified EWMA control charts is also presented. In addition, the performance of the modified and EWMA control charts is contrasted using Dow Jones composite average from a real-life dataset. The findings suggest that the modified EWMA control chart is more sensitive than the EWMA control chart for almost every case of the studied smoothing parameter and constant values of the control chart. HIGHLIGHTS Autocorrelation data is frequency untrue of assumption practice in time series data Modified EWMA is a new control chart that is effective for detecting change in independent normal distribution and autocorrelated observations The efficiency of the control chart is measured by average run length Explicit formula is easy to derive and provides the exact value of the average run length

An EWMA control chart based on the Wilcoxon rank-sum statistic using repetitive sampling

2018 ◽  
Vol 35 (3) ◽  
pp. 711-728 ◽  
Author(s):  
Jean-Claude Malela-Majika ◽  
Olatunde Adebayo Adeoti ◽  
Eeva Rapoo
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Location Parameter ◽  
Process Mean ◽  
Content Type ◽  
Underlying Process ◽  
Run Length ◽  
Design And Implementation ◽  
Ewma Control Chart

Purpose The purpose of this paper is to develop an exponentially weighted moving average (EWMA) control chart based on the Wilcoxon rank-sum (WRS) statistic using repetitive sampling to improve the sensitivity of the EWMA control chart to process mean shifts regardless of the prior knowledge of the underlying process distribution. Design/methodology/approach The proposed chart is developed without any distributional assumption of the underlying quality process for monitoring the location parameter. The authors developed formulae as well as algorithms to facilitate the design and implementation of the proposed chart. The performance of the proposed chart is investigated in terms of the average run-length, standard deviation of the run-length (RL), average sample size and percentiles of the RL distribution. Numerical examples are given as illustration of the design and implementation of the proposed chart. Findings The proposed control chart presents very attractive RL properties and outperforms the existing nonparametric EWMA control chart based on the WRS in the detection of the mean process shifts in many situations. However, the performance of the proposed chart relatively deteriorates for small phase I sample sizes. Originality/value This study develops a new control chart for monitoring the process mean using a two-sample test regardless of the nature of the underlying process distribution. The proposed control chart does not require any assumption on the type (or nature) of the process distribution. It requires a small number of subgroups in order to reach stability in the phase II performance.

scholarly journals Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling

2021 ◽  
Author(s):  
Wasif Yasin ◽  
Muhammad Tayyab ◽  
Muhammad Hanif
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Practical Utilization ◽  
Run Length ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Shift Detection

It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.

scholarly journals Moving Average control charts for Burr X and Inverse Gaussian distributions

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Ambreen Shafqat ◽  
Muhammad Aslam ◽  
Mohammed Albassam
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Inverse Gaussian ◽  
Life Test ◽  
Run Length ◽  
Truncated Life Test ◽  
Average Control ◽  
Better Than

The Burr X and Inverse Gaussian (IG) distributions are considered in this paper to design an attribute control chart for time truncated life test with Moving Average (MA) scheme w. The presentation of the MA control chart is estimated in terms of average run length (ARL) by using the Monte Carlo simulation. The ARL is decided for different values of sample sizes, MA statistics size, parameters’ values, and specified average run length. The performance of this new MA attribute control chart is compared with the usual time truncated control chart for Burr X and IG distributions. The performance of a new control chart is better than the existing control chart.

scholarly journals A New Generalized Range Control Chart for the Weibull Distribution

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Osama H. Arif ◽  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Comparison Study ◽  
Exponentially Weighted Moving Average ◽  
Run Length ◽  
Weighted Moving Average ◽  
Exponentially Weighted

In this study, a generalized range control chart is designed for the Weibull distribution using generally weighted moving average statistics. The proposed chart is based on minimum generally weighted moving average statistic and maximum generally weighted moving average statistics. We utilize the inverse erf function to transform the Weibull data to normal data. The necessary measures are given to assess the performance of the proposed control chart. The comparison study shows that the proposed control chart outperforms the existing control charts based on exponentially weighted moving average statistic in terms of the average run length. A real example is given for applying the proposed chart in the industry.

ZIB-EWMA CONTROL CHART FOR MONITORING RARE HEALTH EVENTS

2011 ◽  
Vol 11 (04) ◽  
pp. 881-895 ◽  
Author(s):  
RASSOUL NOOROSSANA ◽  
AMIR AFSHIN FATAHI ◽  
PERSHANG DOKOUHAKI ◽  
MASSOUD BABAKHANI
Keyword(s):  
Control Chart ◽  
Control Charts ◽  
Average Run Length ◽  
Moving Average ◽  
Cusum Chart ◽  
Health Events ◽  
Ewma Chart ◽  
Ewma Control Chart ◽  
Significant Public Health ◽  
Health Related

Monitoring rare health events, as a significant public health subject, has been considered recently by different authors. In this regard, different statistical methods such as g-type control chart, Poisson CUSUM control chart, sets-based methods, and Bernoulli CUSUM chart have been developed. Zero-inflated binomial (ZIB) distribution, due to its structure, can also be considered to develop methods for monitoring rare health-related events. If zero inflation is considered in the sampling data, and the sampling subgroup size is mandatory greater than 1, then the data best fits the ZIB distribution and the aforementioned control charts cannot be applied. ZIB distribution assumes that random shocks, corresponding to rare health events, occur and then number of failures in each subgroup fits a binomial distribution. In this paper, an exponentially weighted moving average (EWMA) control chart is applied for ZIB data to develop a ZIB-EWMA chart. Since ZIB-EWMA statistic values are not independent, Markov chain approach is considered to evaluate the performance of the proposed control chart in terms of average run length (ARL). According to the ARL measure, this ZIB-EWMA chart has a better performance in comparison with the methods available in the literature. In addition, a real case study related to rare infections in a hospital is investigated to show the applicability of the proposed control chart.

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.

scholarly journals Average Run Length on CUSUM Control Chart for Seasonal and Non-Seasonal Moving Average Processes with Exogenous Variables

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 173
Author(s):  
Rapin Sunthornwat ◽  
Yupaporn Areepong
Keyword(s):  
Control Chart ◽  
Average Run Length ◽  
Moving Average ◽  
Optimal Parameters ◽  
Exogenous Variables ◽  
Explicit Formulas ◽  
Run Length ◽  
Ewma Control Chart ◽  
Cusum Control Chart ◽  
Moving Average Processes

The aim of this study was to derive explicit formulas of the average run length (ARL) of a cumulative sum (CUSUM) control chart for seasonal and non-seasonal moving average processes with exogenous variables, and then evaluate it against the numerical integral equation (NIE) method. Both methods had similarly excellent agreement, with an absolute percentage error of less than 0.50%. When compared to other methods, the explicit formula method is extremely useful for finding optimal parameters when other methods cannot. In this work, the procedure for obtaining optimal parameters—which are the reference value ( a ) and control limit ( h )—for designing a CUSUM chart with a minimum out-of-control ARL is presented. In addition, the explicit formulas for the CUSUM control chart were applied with the practical data of a stock price from the stock exchange of Thailand, and the resulting performance efficiency is compared with an exponentially weighted moving average (EWMA) control chart. This comparison showed that the CUSUM control chart efficiently detected a small shift size in the process, whereas the EWMA control chart was more efficient for moderate to large shift sizes.

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