Detecting improvement using Shewhart attribute control charts when the lower control limit is zero

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

doi:10.1080/07408170600692317

Cited by 22 publications

(18 citation statements)

References 22 publications

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“…Lucas et al recommended policies for detecting p 1 < p 0 based on

P (\hat{p} = 0)

for the p ‐chart given ( n , p 0 ). For high quality processes,

P (\hat{p} = 0)

for a moderate value of n will be large.…”

Section: The Traditional Shewhart P‐chartmentioning

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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“…Lucas et al recommended policies for detecting p 1 < p 0 based on

P (\hat{p} = 0)

for the p ‐chart given ( n , p 0 ). For high quality processes,

P (\hat{p} = 0)

for a moderate value of n will be large.…”

Section: The Traditional Shewhart P‐chartmentioning

confidence: 99%

A Review and perspective on surveillance of Bernoulli processes

Szarka

Woodall

2011

Quality & Reliability Eng

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“…For example, Lucas et al 36 propose a method based on run rules to detect process improvement when the lower limit of an np-chart is zero. When combined with the upper control limit of an np-chart, it can offer a two-sided feature.…”

Section: Literature Review To Select Methods On Monitoring a Fractionmentioning

confidence: 99%

“…We follow a convention found in Lucas et al 36 , Ryan and Schwertman 4 , and Quesenberry 8,30 in which a signal represents a sample falling outside the control limits, not on or within these limits. The numbers of runs in the simulations are determined such that the standard error of every estimated ARL is less than 2% of its estimated ARL.…”

Section: Comparison Of Easily Designed Methods For a Fractionmentioning

confidence: 99%

Monitoring a fraction with easy and reliable settings of the false alarm rate

Duran¹,

Albin²

2009

Quality & Reliability Eng

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Monitoring a fraction arises in many manufacturing applications and also in service applications. The traditional p-chart is easy to use and design but is difficult to achieve the desired false alarm rate. We propose a two-sided CUSUM Arcsine method that achieves both large and small desired false alarm rates for an in-control probability anywhere between 0 and 1. The parameters of the new method are calculated easily, without tables, simulation, or Markov chain analysis used by many of the existing methods. The proposed method detects increases and decreases and works for constant and Poisson distributed sample sizes. The CUSUM Arcsine also has a superior sensitivity compared with other easily designed existing methods for monitoring Binomial distributed data. This paper includes an extensive literature review and a taxonomy of the existing monitoring methods for a fraction.

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“…Since exponential distribution is highly right-skewed, the runs rule will be more effective in the monitoring of decreases in θ while the standard one-of-one rule will be applied in the monitoring of increases in θ (see also [16]). It is worth to mention that a similar runs-rule control scheme for attribute data, has been proposed by Lucas et al [24] Thus, the T 1 : k/m control chart gives an out-ofcontrol signal if (i) k of m consecutive points are plotted below LCL, separated by at most m − k points plotted between CL and LCL, or (ii) if a single point is plotted above UCL, whichever comes sooner.…”

Section: Two-sided T-charts With Runs Rulesmentioning

confidence: 98%

Monitoring exponential data using two-sided control charts with runs rules

Rakitzis

2015

Journal of Statistical Computation and Simulation

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In this article, new two-sided control charts with runs rules, suitable for the monitoring of exponential data, are proposed and studied. The proposed schemes are suitable to identify changes (upward or downward) in the mean of an exponential distribution. Also, they have the desired in-control performance as well as unbiased performance. Guidelines for the most effective scheme in practice are provided, along with comparisons with other competitive schemes. Finally, the practical application of the proposed schemes is also discussed.

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Detecting improvement using Shewhart attribute control charts when the lower control limit is zero

Cited by 22 publications

References 22 publications

A Review and perspective on surveillance of Bernoulli processes

A Review and perspective on surveillance of Bernoulli processes

Monitoring a fraction with easy and reliable settings of the false alarm rate

Monitoring exponential data using two-sided control charts with runs rules

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