An adaptive EWMA scheme‐based CUSUM accumulation error for efficient monitoring of process location

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Random causes are vital part of every process in manufacturing and nonmanufacturing environments, and these do not affect the product features. Special causes, on the other hand, come because of some burden(s) in a process and requires special attention; otherwise, it ruins the products excellence. Special causes are categorized into small, moderate, and large shifts and are handled by statistical quality control charts. The Shewhart control chart is well known for large shifts, while the cumulative sum and exponentially weighted moving average are more effective in detecting small to moderate shifts. However, in practice, many processes require the simultaneous monitoring of both the small to the large shifts. In this study, we have designed an adaptive EWMA for dispersion parameter in connection with Huber and Tukey's bisquare functions. The performance measures used in this study include average run length, extra quadratic loss, relative average run length, and performancecomparison index. We have observed that the study proposals are good competitors to the other counter parts for an efficient monitoring of shifts of varying amounts. An illustrative example using real data is given to demonstrate the implementation of the study proposal.

“…The time‐varying upper control limit (UCL) and lower control limit (LCL) for the proposed schemes AEWMAT, AEWMAJ, and AEWMAV as follows:

\begin{matrix} true \\ {italicUCL}_{i} = μ_{F} (n) + L_{F} σ_{F} (n) \sqrt{\frac{λ}{((), 2 - λ)} [1 - {((), 1 - λ)}^{2 i}]} \\ {italicLCL}_{i} = μ_{F} (n) - L_{F} σ_{F} (n) \sqrt{\frac{λ}{((), 2 - λ)} [1 - {((), 1 - λ)}^{2 i}]} \end{matrix},

Section: Related Literature Transformations and Design Structure Ofmentioning

confidence: 99%

An adaptive approach to EWMA dispersion chart using Huber and Tukey functions

Zaman

Lee

Riaz

et al. 2019

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“…A comprehensive literature review on adaptive control charts can be studies in Psarakis 21 work. The AEWMA C

({AEWMA}_{false(1 false)}^{C} and {AEWMA}_{false(2 false)}^{C})

control charts based classical CUSUM control chart accumulation error for efficient monitoring of process location shift proposed by Zaman et al 22 . More details about recent development in control charts with new techniques can be studied in Bilal et al., 23 Shafqat et al., 24 Naveed et al., 25 Shah et al., 26 Ali et al., 27 and references therein.…”

Section: Introductionmentioning

confidence: 99%

Efficient adaptive CUSUM control charts based on generalized likelihood ratio test to monitor process dispersion shift

Zaman

2021

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In practice, a shift in the process parameters (location and/or dispersion) is unknown in prior and cannot be diagnosed precisely with the classical cumulative sum (CUSUM) control chart. To overcome this issue, this study proposed two adaptive CUSUM (ACUSUM) control charts. The proposed control charts utilized linear weighted function that is inspired by generalized likelihood ration test (GLRT) to monitor small and certain range of shift in the process dispersion. In more details, the proposed control charts methodologies are based on GLRT, exponentially weight moving average statistic, and score functions. To obtain the run length of the proposed control charts for performance assessment, algorithms are designed in MATLAB based on Monte Carlo simulation technique. Further, average run length (ARL) is used as a performance measure tool to compare the control charts performance for a single shift. For certain range of shift, extra quadratic loss function, relative ARL, and performance comparison index performance measures based on ARL are calculated. Some existing control charts are used for comparison purpose. The proposed control charts show outstanding capability to detect out‐of‐control signal against these control charts. Moreover, real‐life data of inside diameter of cylinder bore in an engine block are used to reveal the practicality and worth of the proposed control charts relative to other control charts.

“…Due to the remarkable adaptability of this AEWMA scheme, it has been investigated by several researchers, see, for instance, Refs. [4–12].…”

Section: Introductionmentioning

confidence: 99%

Optimal one‐ and two‐sided adaptive EWMA scheme for monitoring Poisson count data

Tang

Castagliola

et al. 2021

The Poisson distribution assumption often arises in several industrial applications for modeling defects or nonconformities. In this work, we investigate the one‐ and two‐sided performance of a new adaptive EWMA (exponentially weighted moving average)‐type chart for monitoring Poisson count data. An appropriate discrete‐state Markov chain technique is provided to compute the exact ARL (average run length) properties. Moreover, comparative studies are conducted to demonstrate the higher sensitivity of the proposed chart in the detection of shifts with various magnitudes. Advices on how to select the appropriate chart parameters are provided and an illustrative numerical example is proposed.