On the Equivalence of the Bernoulli and Geometric CUSUM Charts

Szarka, John L.; Woodall, William H.

doi:10.1080/00224065.2012.11917881

Cited by 26 publications

(43 citation statements)

References 13 publications

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“…The random-shift model further complicates steady-state evaluation of the geometric CUSUM chart. For more information on the relationship between the geometric and Bernoulli CUSUM charts, see Szarka and Woodall 65 .…”

Section: The Relationship Between the Geometric And Bernoulli Cumulatmentioning

confidence: 99%

A Review and perspective on surveillance of Bernoulli processes

Szarka

Woodall

2011

Quality & Reliability Eng

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Bernoulli processes have been monitored using a wide variety of techniques in statistical process control. The data consist of information on successive items classified as conforming (nondefective) or nonconforming (defective). In some cases, the probability of obtaining a nonconforming item is very small; this is known as a high quality process. This area of statistical process control is also applied to health-related monitoring, where the incidence rate of a medical problem such as a congenital malformation is of interest. In these applications, standard Shewhart control charts based on the binomial distribution are no longer useful. In our expository paper, we review the methods implemented for these scenarios and present ideas for future work in this area. We offer advice to practitioners and present a comprehensive literature review for researchers.

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Section: The Relationship Between the Geometric And Bernoulli Cumulatmentioning

confidence: 99%

A Review and perspective on surveillance of Bernoulli processes

Szarka

Woodall

2011

Quality & Reliability Eng

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“…If p 1 is much less than p 0 , the waiting time until a nonconformity appears will be very long, not to mention r independent identical geometric counts. 5 CCC-r charts are very sensitive in detecting an upward shift in p 0 , which means process deterioration. 7 In practice, upper-sided shifts are more meaningful and practical in a manufacturing process.…”

Section: Ccc-r Chartmentioning

confidence: 99%

“…For instance, the nonconforming rate can be as small as 116 parts per million (ppm) for the thermo‐sonic wire bonding . Control charts based on Bernoulli data are highly recommended for its effectiveness in detecting shifts in p 0 , while charts based on variable data are costly and sometimes unavailable in monitoring a high‐quality process …”

Section: Introductionmentioning

confidence: 99%

“…When the nonconforming rate p is very small, there must be r nonconformities for the CCC‐ r chart to signal. If p 1 is much less than p 0 , the waiting time until a nonconformity appears will be very long, not to mention r independent identical geometric counts . CCC‐ r charts are very sensitive in detecting an upward shift in p 0 , which means process deterioration .…”

Section: Introductionmentioning

confidence: 99%

“…1,3 Control charts based on Bernoulli data are highly recommended for its effectiveness in detecting shifts in p 0 , while charts based on variable data are costly and sometimes unavailable in monitoring a high-quality process. 2,4,5 The optimality properties of various charts with Bernoulli data for high-quality processes have been reviewed extensively. 6 Among them, CCC-r chart, which is defined as the control chart based on the number of cumulative count of items until r nonconforming items are observed, is found to be effective in detecting process deterioration.…”

Section: Introductionmentioning

confidence: 99%

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CCC‐r charts' performance with estimated parameter for high‐quality process

Zhang

Hou

Hui

et al. 2018

Quality & Reliability Eng

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CCC‐r charts are effective in detecting process shifts in the nonconforming rate especially for a high‐quality process. The implementation of the CCC‐r charts is usually under the assumption that the in‐control nonconforming rate is known. However, the nonconforming rate is never known, and accurate estimation is difficult. We investigate the effect of estimation error on the CCC‐r charts' performances through the expected value of the average number of observations to signal (EANOS) as well as the standard deviation of the average number of observations to signal (SDANOS). By comparing the in‐control performance of the CCC‐r charts, the CCC‐r chart with a larger value of r is more susceptible to the effects of parameter estimation. Meanwhile, the performance of the CCC‐r charts can converge when detecting upward shifts in p of out‐of‐control processes. We recommend the use of the CCC‐4 chart when considering its effectiveness in detecting shifts as well as its easier construction in practice. Furthermore, it is investigated that the CCC‐4 chart is less sensitive to parameter estimation while being more effective in detecting different process shifts when compared with Geometric CUSUM chart and synthetic chart.

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Location‐scale monitoring of ordinal categorical processes

Bai

2021

Naval Research Logistics

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In many applications, process variables are measured by categorical data with some natural order among their attribute levels, such as “good,” “marginal,” and “bad.” This paper considers monitoring ordinal categorical factors, which are determined by their latent continuous variables. The monitoring considers shifts in the location or scale parameters of latent variables, but only the ordinal attribute levels are observable. To this end, univariate and multivariate location‐scale log‐linear (LSL2) models are first established to describe a single ordinal factor and multiple ones, respectively. LSL2 models are founded on the score tests with respect to the location and scale parameters of continuous variables, which transform the detection of latent location and scale shifts into testing the coefficients of LSL2 models. Based on this, univariate and multivariate location‐scale ordinal control charts are proposed for detecting shifts in the location and scale parameters of the latent continuous variable of a single ordinal factor, as well as shifts in the location, scale, and correlation parameters of the underlying continuous variables of multiple ordinal factors. Simulation results have demonstrated the power of the proposed methods under various types of latent continuous distributions.

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On the Equivalence of the Bernoulli and Geometric CUSUM Charts

Cited by 26 publications

References 13 publications

A Review and perspective on surveillance of Bernoulli processes

A Review and perspective on surveillance of Bernoulli processes

CCC‐r charts' performance with estimated parameter for high‐quality process

Location‐scale monitoring of ordinal categorical processes

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