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Journal ArticleDOI

Monitoring of time between events with a double generally weighted moving average control chart

About: This article is published in Quality and Reliability Engineering International.The article was published on 2019-03-01. It has received 31 citations till now. The article focuses on the topics: Robustness (computer science) & Moving average.
Citations
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Journal ArticleDOI
TL;DR: Overall, performance study indicates that the Max-EWMA chart outperforms its existing counterparts with the same objective of detecting small shifts in process parameters and competes strongly in detecting large shifts.

35 citations

Journal ArticleDOI
TL;DR: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided in this article, where a number of possible future GWMA-related schemes are documented and categorized in such a manner that it is easy to identify research gaps.
Abstract: An overview of monitoring schemes from a class called generally weighted moving average (GWMA) is provided. A GWMA scheme is an extended version of the exponentially weighted moving average (EWMA) scheme with an additional adjustment parameter that introduces more flexibility in the GWMA model as it adjusts the kurtosis of the weighting function so that the GWMA scheme can be designed such that it has an advantage over the corresponding EWMA scheme in the detection of certain shift values efficiently. The parametric and distribution-free GWMA schemes to monitor various quality characteristics and its existing enhanced versions (i.e. double GWMA, composite Shewhart-GWMA, mixed GWMA-CUSUM and mixed CUSUM-GWMA) have better performance than their corresponding EWMA counterparts in many situations; hence, all such existing research works discussing GWMA-related schemes (i.e. 61 publications in total) are documented and categorized in such a manner that it is easy to identify research gaps. Finally, a number of possible future research ideas are provided.

20 citations

Journal ArticleDOI
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

References
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Journal ArticleDOI
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


"Monitoring of time between events w..." refers background or methods in this paper

  • ...Moreover, a Kolmogorov-Smirnov test and the Cramér-von Misser criterion confirm the goodness-of-fit of the data to Gamma(1, 615) distribution....

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  • ...f (x; k, θ) = x k−1 Γ (k) θk exp ( − x θ ) , x > 0, k > 0, θ > 0, (1)...

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  • ...We note that when β = 1, the Weibull(1, 1) distribution reduces to the exponential distribution....

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Journal Article
TL;DR: The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done.

1,624 citations

Journal ArticleDOI
TL;DR: In this article, the authors evaluate the properties of an exponentially weighted moving average (EWMA) control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value.
Abstract: Roberts (1959) first introduced the exponentially weighted moving average (EWMA) control scheme. Using simulation to evaluate its properties, he showed that the EWMA is useful for detecting small shifts in the mean of a process. The recognition that an EWMA control scheme can be represented as a Markov chain allows its properties to be evaluated more easily and completely than has previously been done. In this article, we evaluate the properties of an EWMA control scheme used to monitor the mean of a normally distributed process that may experience shifts away from the target value. A design procedure for EWMA control schemes is given. Parameter values not commonly used in the literature are shown to be useful for detecting small shifts in a process. In addition, several enhancements to EWMA control schemes are considered. These include a fast initial response feature that makes the EWMA control scheme more sensitive to start-up problems, a combined Shewhart EWMA that provides protection against both larg...

1,380 citations

Journal ArticleDOI
TL;DR: Design and implementation procedures for counted data CUSUM's (these are sometimes called C USUM's for attributes) are described, which are easy to design and implement and can be used to detect both increases and decreases in the count level.
Abstract: Cumulative Sum (CUSUM) control schemes are widely used in industry for process and measurement control. Most CUSUM applications have been for continuous variables. There have been fewer uses of CUSUM control schemes when the response is a count such as the number of defects per unit or the occurrence of an accident. This article describes design and implementation procedures for counted data CUSUM's (these are sometimes called CUSUM's for attributes). These CUSUM's are easy to design and implement; they can be used to detect both increases and decreases in the count level. Enhancements to the CUSUM scheme, including the fast initial response (FIR) feature and the robust CUSUM are discussed. These enhancements speed up the detection of changes in the count level and guard against the effects of atypical or outlier observations.

372 citations

Journal ArticleDOI
TL;DR: A recent control scheme based on the cumulative quantity between observations of defects has been proposed which can be easily adopted to monitor the failure process for exponentially distributed inter-failure time and can detect process improvement even in a high-reliability environment.

249 citations


Additional excerpts

  • ...UCL∕LCL = kθ0±L √ Qkθ2 0 ,CL = kθ0, (8)...

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