A linear‐time method for computing the ANOS of Bernoulli and Poisson CUSUM charts

Pollard, Emma; Davis, Darwin J.; Saniga, Erwin M.; Lucas, James M.

doi:10.1002/qre.2277

Cited by 2 publications

(5 citation statements)

References 6 publications

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“…Additionally, 59 papers incorporated the ATS in their analysis. In contrast, the ANOS was discussed in only five papers 40,44,62,230,232 . The AEQL was introduced in four studies, 46,63,207,219 while another five papers examined the AND 64,215,216,245 .…”

Section: Resultsmentioning

confidence: 99%

“…59,61 It is defined as 𝐴𝑁𝑂𝑆 = 𝐴𝑅𝐿 × 𝑛. 62 • Overall performance indicators: When the performance of the control chart is measured over a wide range of shifts, then the performance metric is an overall measure of performance. The following are the most popular overall performance measures:…”

Section: Types Of Performance Indicatorsmentioning

confidence: 99%

“…In contrast, the ANOS was discussed in only five papers. 40,44,62,230,232 The AEQL was introduced in four studies, 46,63,207,219 while another five papers examined the AND. 64,215,216,245 Additionally, five studies focused exclusively on the EARL.…”

Section: Analysis Of the Literature According To The Performance Indi...mentioning

confidence: 99%

“… The average number of observations to signal ( ANOS ) measures the expected number of observations until a signal is emitted 59,61 . It is defined as

ANOS\ = \ ARL \times n

62 Overall performance indicators : When the performance of the control chart is measured over a wide range of shifts, then the performance metric is an overall measure of performance.…”

Section: Description Of the Classification Scheme And Answers To Rese...mentioning

confidence: 99%

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Optimization design of control charts: A systematic review

Haridy,

Maged,

Alherimi

et al. 2024

Quality & Reliability Eng

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In today's competitive landscape, fulfilling customer expectations and achieving a competitive edge are crucial for business success. These objectives can be attained by effective monitoring in both manufacturing and service sectors to enhance quality, reduce variation, and augment productivity. The control chart, a widely used tool for this purpose, has attracted significant attention from researchers for its ability to detect anomalies and manage out‐of‐control situations. The optimization of control charts, a central focus of this review, not only enhances the detection effectiveness but also maintains the desired false alarm rate, thus ensuring efficient process control without additional cost, complexity, or operational challenges for shop floor personnel. The optimization process involves adjusting charting parameters like the sample size, sampling interval, and control limits within a hypothesis testing framework, thereby achieving optimal system performance. Numerous optimization models have been developed to enhance control chart performance. This paper introduces a classification scheme to analyze and categorize the existing research on control chart optimization. By conducting a thorough review of more than 240 articles, the study pinpoints research gaps and offers valuable insights, thereby advancing the future research in this domain.

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Section: Resultsmentioning

confidence: 99%

Section: Types Of Performance Indicatorsmentioning

confidence: 99%

Section: Analysis Of the Literature According To The Performance Indi...mentioning

confidence: 99%

“… The average number of observations to signal ( ANOS ) measures the expected number of observations until a signal is emitted 59,61 . It is defined as

ANOS\ = \ ARL \times n

62 Overall performance indicators : When the performance of the control chart is measured over a wide range of shifts, then the performance metric is an overall measure of performance.…”

Section: Description Of the Classification Scheme And Answers To Rese...mentioning

confidence: 99%

See 2 more Smart Citations

Optimization design of control charts: A systematic review

Haridy,

Maged,

Alherimi

et al. 2024

Quality & Reliability Eng

View full text Add to dashboard Cite

show abstract

“…The R matrix for the Bernoulli CUSUM was given by Bourke 15 and Pollard et al, 28 and the R matrix for the version of the geometric CUSUM where the CRL does not include the final nonconforming item was given by Bourke. 6 For completeness, the R matrix for the geometric CUSUM where the observation, 𝑌 𝑗 , in equation ( 2) includes the final nonconforming item is given below:…”

Section: Appendix a Details Of The Markov Chain Approachmentioning

confidence: 99%

A closer look at the equivalence of Bernoulli and geometric CUSUM control charts

Saccucci

Lucas²,

Bourke

et al. 2022

Quality & Reliability Eng

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Some researchers have incorrectly concluded that the geometric CUSUM is superior to the Bernoulli CUSUM as a procedure for monitoring a repetitive process, even though the two procedures have been proved to be equivalent for detecting an upward shift in the proportion of nonconforming items. We use an exact Markov‐chain‐based methodology to re‐examine the relationship between geometric CUSUM and Bernoulli CUSUM control charts. Exact methods allow us to differentiate between similar but different‐valued quantities that have contributed to some misunderstandings in the literature. We show that for a random‐shift model, evaluations of steady‐state average number of inspected items until a signal (ANIs) are identical for both geometric CUSUMs and Bernoulli CUSUMs, provided the correct choices of return levels are made. We also show that a steady‐state geometric CUSUM based on a fixed‐shift model only uses the geometric CUSUM states, while a steady‐state geometric CUSUM based on a random‐shift model will reach the states of a Bernoulli CUSUM after a long series of zeros. We note that our conclusions are contrary to the published results of other researchers, and we examine these differences in detail. Layman's Abstract: Since, their introduction by Walter Shewhart in 1931, control charts such as the Shewhart p‐chart have had widespread application for monitoring the output quality from manufacturing processes, such as the proportion (p) in the stream of manufactured items that are nonconforming. But the Shewhart p‐chart is not very effective for monitoring processes when the proportion p is less than about 4 percent. Other charts, such as the geometric CUSUM (proposed in 1991) and the Bernoulli CUSUM (proposed in 1999) have been shown to be superior at identifying changes in p when p is small. Some researchers have relied on simulation‐based investigations to compare these two CUSUMs, and have incorrectly concluded that the geometric CUSUM is superior to the Bernoulli CUSUM, even though the two procedures have been proved to be equivalent for detecting an upward shift in the proportion p. Using exact, Markov‐chain‐based methodology, we re‐examine the relationship between the geometric CUSUM and the Bernoulli CUSUM control charts and demonstrate that these two charts are equivalent when evaluated correctly. Exact methods allow us to precisely compare these two monitoring schemes and correct some erroneous conclusions that have appeared in the literature.

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A linear‐time method for computing the ANOS of Bernoulli and Poisson CUSUM charts

Cited by 2 publications

References 6 publications

Optimization design of control charts: A systematic review

Optimization design of control charts: A systematic review

A closer look at the equivalence of Bernoulli and geometric CUSUM control charts

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