Some theoretical comments regarding the run-length properties of the synthetic and runs-rules <i>  X¯  </i> monitoring schemes – part 1: zero-state

Shongwe, Sandile Charles; Graham, Marien Alet

doi:10.1080/16843703.2017.1389141

Cited by 10 publications

(7 citation statements)

References 25 publications

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“…Due to space restrictions, the readers are referred to Shongwe and Graham for the TPMs of the S2, S3, and S4, whereas the TPMs of the IS2, IS3, and IS4 are given in Shongwe and Graham . Also, M (in Equation ) is some specified positive integer that depends on the control limit H of the CRL subchart.…”

Section: Design Of the Shewhart Synthetic Chartsmentioning

confidence: 99%

An overview of synthetic‐type control charts: Techniques and methodology

Rakitzis

Chakraborti

Shongwe

et al. 2019

Quality & Reliability Eng

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In this paper, we provide an overview of a class of control charts called the synthetic charts. Synthetic charts are a combination of a traditional chart (such as a Shewhart, CUSUM, or EWMA chart) and a conforming run‐length (CRL) chart. These charts have been considered in order to maintain the simplicity and improve the performance of small and medium‐sized shift detection of the traditional Shewhart charts. We distinguish between different types of synthetic‐type charts currently available in the literature and highlight how each is designed and implemented in practice. More than 100 publications on univariate and multivariate synthetic‐type charts are reviewed here. We end with some concluding remarks and a list of some future research ideas.

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Section: Design Of the Shewhart Synthetic Chartsmentioning

confidence: 99%

An overview of synthetic‐type control charts: Techniques and methodology

Rakitzis

Chakraborti

Shongwe

et al. 2019

Quality & Reliability Eng

Self Cite

View full text Add to dashboard Cite

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“…In this Appendix, we follow a similar line of argument in deriving general TPMs and closed-form expressions as that done for the synthetic charts as well as 2-of-(H+1) runs-rules (with H a positive integer greater than 0) in Shongwe and Graham [43][44][45] using Markov chain design approach. In Section A, we discuss the theoretical run-length properties of the w-of-w upper or lower one-sided as well as the twosided NSS monitoring schemes based on the SRR and IRR designs.…”

Section: Appendixmentioning

confidence: 99%

One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

Shongwe

Malela‐Majika

Rapoo

2019

Journal of Probability and Statistics

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The one-sided and two-sided Shewhart w-of-w standard and improved runs-rules monitoring schemes to monitor the mean of normally distributed observations from independent and identically distributed (iid) samples are investigated from an overall performance perspective, i.e., the expected weighted run-length (EWRL), for every possible positive integer value of w. The main objective of this work is to use the Markov chain methodology to formulate a theoretical unified approach of designing and evaluating Shewhart w-of-w standard and improved runs-rules for one-sided and two-sided X- schemes in both the zero-state and steady-state modes. Consequently, the main findings of this paper are as follows: (i) the zero-state and steady-state ARL and initial probability vectors of some of the one-sided and two-sided Shewhart w-of-w standard and improved runs-rules schemes are theoretically similar in design; however, their empirical performances are different and (ii) unlike previous studies that use ARL only, we base our recommendations using the zero-state and steady-state EWRL metrics and we observe that the steady-state improved runs-rules schemes tend to yield better performance than the other considered competing schemes, separately, for one-sided and two-sided schemes. Finally, the zero-state and steady-state unified approach run-length equations derived here can easily be used to evaluate other monitoring schemes based on a variety of parametric and nonparametric distributions.

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“…en, run rules combined with control charts were studied by many researchers, such as Divoky and Taylor [2]; Champ and Woodall [3]; Klein [4]; Fu et al [5]; and so on. More recent works on control charts integrated with run rule schemes can be found in Hu and Castagliola [6]; Chew et al [7]; Shongwe and Graham [8]; Shongwe and Graham [8]; Shongwe et al [9]; Khaw and Chew [10]; Chew et al [11]; Shongwe [12]; Malela-Majika and Rapoo [13]; Malela-Majika et al [14]; Hu et al [15]; and Ali et al [16]. All these existing research studies focused on how to improve the chart's performance by incorporating run rules.…”

Section: Introductionmentioning

confidence: 99%

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart $\bar{X}$ Chart

Shan

Huang

2021

Mathematical Problems in Engineering

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In modern quality control applications, there often exist significant measurement errors because observations are measured quickly in time order. As a result, the errors influence the power of a control chart to detect a given change in the process parameter(s) of a quality characteristic. In this paper, by using a covariate error model, the properties of the Shewhart X ¯ chart integrated with run rules are investigated when errors exist in the measurement of quality characteristic. Two metrics, the average run length and 95% quantile of the run length, are adopted to evaluate the chart’s performance for different mean shifts and sample sizes. Numerous simulations are conducted, and the results indicate that the errors in the measurement significantly affect the performance of the run rule X ¯ chart, especially when the errors are large. To reduce this negative effect on the run rule X ¯ chart, measuring more times of each item in each subgroup and increasing the coefficient in the covariate error model are shown to be good choices for practitioners.

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Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes – part 1: zero-state

Cited by 10 publications

References 25 publications

An overview of synthetic‐type control charts: Techniques and methodology

An overview of synthetic‐type control charts: Techniques and methodology

One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart $\bar{X}$ Chart

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Some theoretical comments regarding the run-length properties of the synthetic and runs-rules X¯ monitoring schemes – part 1: zero-state

Cited by 10 publications

References 25 publications

An overview of synthetic‐type control charts: Techniques and methodology

An overview of synthetic‐type control charts: Techniques and methodology

One-Sided and Two-Sided w-of-w Runs-Rules Schemes: An Overall Performance Perspective and the Unified Run-Length Derivations

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart X ¯ Chart

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Product

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About

Treating Measurement Errors in the Run Rule Schemes Integrated with Shewhart $\bar{X}$ Chart