A nonparametric triple exponentially weighted moving average sign control chart
01 Jun 2021-Quality and Reliability Engineering International (John Wiley & Sons, Ltd)-Vol. 37, Iss: 4, pp 1504-1523
About: This article is published in Quality and Reliability Engineering International.The article was published on 2021-06-01. It has received 22 citations till now. The article focuses on the topics: Sign (mathematics).
Citations
More filters
DOI•
TL;DR: The Journal is indexed by Academic Search (EBSCO Publishing), Academic Search Alumni Edition (AALE), EBSCO publishing, Advanced Technologies & Aerospace Database (ProQuest), COMPENDEX (Elsevier), Current
Abstract: ing and Indexi g The Journal is indexed by Academic Search (EBSCO Publishing), Academic Search Alumni Edition (EBSCO Publishing), Advanced Technologies & Aerospace Database (ProQuest), COMPENDEX (Elsevier), Current
44 citations
TL;DR: Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart as mentioned in this paper , usually to put greater emphasis on past data and less weight on current and recent data.
Abstract: Many extensions and modifications have been made to standard process monitoring methods such as the exponentially weighted moving average (EWMA) chart and the cumulative sum (CUSUM) chart. In addition, new schemes have been proposed based on alternative weighting of past data, usually to put greater emphasis on past data and less weight on current and recent data. In other cases, the output of one process monitoring method, such as the EWMA statistic, is used as the input to another method, such as the CUSUM chart. Often the recursive formula for a control chart statistic is itself used recursively to form a new control chart statistic. We find the use of these ad hoc methods to be unjustified. Statistical performance comparisons justifying the use of these methods have been either flawed by focusing only on zero-state run length metrics or by making comparisons to an unnecessarily weak competitor.
15 citations
14 citations
Journal Article•
TL;DR: An extensive simulation study is done on the performance of the two-sided NPEWMA-SR chart including a detailed comparison with a number of existing control charts, including the traditional EWMA chart for subgroup averages and some nonparametric charts i.e. runs-rules enhanced Shewhart-type SR charts.
Abstract: Nonparametric control charts can provide a robust alternative in practice to the data analyst when there is a lack of knowledge about the underlying distribution. A nonparametric exponentially weighted moving average (NPEWMA) control chart combines the advantages of a nonparametric control chart with the better shift detection properties of a traditional EWMA chart. A NPEWMA chart for the median of a symmetric continuous distribution was introduced by Amin and Searcy (1991) using the Wilcoxon signed-rank statistic (see Gibbons and Chakraborti, 2003). This is called the nonparametric exponentially weighted moving average Signed-Rank (NPEWMA-SR) chart. However, important questions remained unanswered regarding the practical implementation as well as the performance of this chart. In this paper we address these issues with a more in-depth study of the two-sided NPEWMA-SR chart. A Markov chain approach is used to compute the run-length distribution and the associated performance characteristics. Detailed guidelines and recommendations for selecting the chart's design parameters for practical implementation are provided along with illustrative examples. An extensive simulation study is done on the performance of the chart including a detailed comparison with a number of existing control charts, including the traditional EWMA chart for subgroup averages and some nonparametric charts i.e. runs-rules enhanced Shewhart-type SR charts and the NPEWMA chart based on signs. Results show that the NPEWMA-SR chart performs just as well as and in some cases better than the competitors. A summary and some concluding remarks are given.
11 citations
TL;DR: In this paper, the authors designed an advanced form of NP TEWMA Wilcoxon signed-rank based on RSS, denoted as control chart to identify a shift in the process location parameter.
Abstract: The nonparametric (NP) control charts are famous for detecting a shift in the process parameters (location and/or dispersion) when the underlying process characteristic does not follow the distributional assumptions. Similarly, when the cost of estimations is very high and the ranking of observational is relatively simple, the ranked set sampling (RSS) technique is preferred over the simple random sampling (SRS) technique. On the other hand, the NP triple exponentially weighted moving average (EWMA) control chart based on SRS is superior to the NP EWMA and NP double EWMA (NP DEWMA) based on the SRS technique to detect a shift in the process location. This study designed an advanced form of NP TEWMA Wilcoxon signed-rank based on RSS, denoted as control chart to identify a shift in the process location parameter. The Monte Carlo simulation method is used to assess the performance of the proposed control chart along with SRS-based NP TEWMA (TEWMA-SR), SRS-based NP TEWMA sign (TEWMA-SN), SRS-based , and RSS-based NP DEWMA-SR control charts. The study shows that the proposed control chart is more efficient in identifying shifts (especially in small shifts) in the process location than the existing control charts. Finally, a real-life application is also provided for the practical implementation of the proposed control chart.
8 citations
References
More filters
4,805 citations
TL;DR: There are valuable points here; they are, however, generally too hard to find and some of them are undercut by the author’s misguided attempt to be “fair.”
Abstract: (2007). Introduction to Statistical Quality Control. Technometrics: Vol. 49, No. 1, pp. 108-109.
3,358 citations
1,264 citations
TL;DR: An overview of the literature on nonparametric or distribution-free control charts for univariate variables data is presented and connections to some areas of active research are made, such as sequential analysis, that are relevant to process control.
Abstract: The literature on nonparametric or distribution-free control charts for univariate variables data is examined. The advantages of these charts have over more traditional distribution-based control charts are demonstrated. Constructive criticism of the li..
331 citations
TL;DR: In this article, a nonparametric control chart is presented for detecting changes in the process median (or mean), or changes in process variability when samples are taken at regular time intervals.
Abstract: Nonparametric control chart are presented for the problem of detecting changes in the process median (or mean), or changes in the process variability when samples are taken at regular time intervals. The proposed procedures are based on sign-test statistics computed for each sample, and are used in Shewhart and cumulative sum control charts. When the process is in control the run length distributions for the proposed nonparametric control charts do not depend on the distribution of the observations. An additional advantage of the non-parametric control charts is that the variance of the process does not need to be established in order to set up a control chart for the mean. Comparisons with the corresponding parametric control charts are presented. It is also shown that curtailed sampling plans can considerably reduce the expected number of observations used in the Shewhart control schemes based on the sign statistic.
170 citations
"A nonparametric triple exponentiall..." refers methods in this paper
...Step 3: Calculate theWt statistics using Equation (6)....
[...]
...Step 2: For a pre-specified value of ARL0, specify the design parameters 𝜆 and 𝐿. Step 3: Calculate the𝑊𝑡 statistics using Equation (6)....
[...]
...(5) Combining Equation (3) to (5), the statistic𝑊𝑡 is written as 𝑊𝑡 = 𝜆3 2 𝑡∑ 𝑗=1 (1 − 𝜆)𝑡−𝑗(𝑡 − 𝑗 + 1)(𝑡 − 𝑗 + 2)𝑁𝑗 + ( (1 − 𝜆)𝑡 2 ) [𝜆𝑡(𝜆𝑡 + 𝜆 + 2) + 2] 𝑛 2 ....
[...]
...Step 4: Calculate the control limits given by Equation (8) and compare each statistic𝑊𝑡 with them....
[...]