The optimal choice of negative binomial charts for monitoring high-quality processes

Albers, Willem

doi:10.1016/j.jspi.2009.07.005

Cited by 29 publications

(41 citation statements)

References 17 publications

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“…The emphasis now is on the relative overdispersion increase (r + 1)τ , for which we let the values range from 0 (homogeneous case) to 1 (upper limit in Lemma 2.2). The value of p (as long as it is at most 0.01) fortunately has no impact on the approximation quality, which allows us to summarize the results in terms of n τ p andñ τ p. In Albers (2010) it was concluded that the approximation performs quite well over the region considered. Fortunately, Table 1 shows that this conclusion can be extended to the case of positive (r + 1)τ , all the way to the upper limit 1.…”

Section: Overdispersionmentioning

confidence: 95%

“…The range of values of interest for θ obviously remains the same as in Albers (2010). Just as in that paper, we are interested in the quality of the approximation provided, but now the focus is on the behavior with respect to τ .…”

Section: The Ooc Situationmentioning

confidence: 99%

“…Most of the authors quoted above [and also Bourke (1991Bourke ( , 2006] therefore suggest as a remedy to essentially use a negative binomial chart: postpone the decision whether to stop until r > 1 failures have occurred. Some guidance on how to choose r in practice can be found in Ohta et al (2001), but a systematic treatment of this issue was given in Albers (2010), resulting in a simple rule of thumb for choosing the optimal r as a function of the desired false alarm rate (F AR) and the supposed degree of increase of p compared to its value during In-Control (I C). As expected, the larger the increase one has in mind, the smaller r should be, with again the geometric chart (r = 1) as the ultimate result.…”

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confidence: 99%

“…The second problem addressed in Albers (2010) concerns the estimation step involved. Note the general nature of this issue: typically, control charts have one or more unknown parameters which first have to be estimated on the basis of a so-called Phase I sample.…”

mentioning

confidence: 99%

“…Hence as a rule, such effects have to be taken into account and, if possible, corrections should be applied to the control limits to neutralize these. This program is indeed carried out in Albers (2010) for the negative binomial charts when p is unknown, and the result is a chart which is both simple to understand and to apply.…”

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confidence: 99%

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Control charts for health care monitoring under overdispersion

Albers

2009

Metrika

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An attractive way to control attribute data from high quality processes is to wait till r ≥ 1 failures have occurred. The choice of r in such negative binomial charts is dictated by how much the failure rate is supposed to change during Outof-Control. However, these results have been derived for the case of homogeneous data. Especially in health care monitoring, (groups of) patients will often show large heterogeneity. In the present paper we will show how such overdispersion can be taken into account. In practice, typically neither the average failure rate, nor the overdispersion parameter(s), will be known. Hence we shall also derive and analyze the estimated version of the new chart.

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Section: Overdispersionmentioning

confidence: 95%

Section: The Ooc Situationmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Control charts for health care monitoring under overdispersion

Albers

2009

Metrika

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Cumulative conformance count chart with variable sampling intervals and control limits

Chen

Chiou

2011

Appl Stoch Models Bus & Ind

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The cumulative conformance count (CCC) chart has been used for monitoring processes with very low fraction of nonconforming items. Typically, the items produced from the process were examined using 100% inspection for generating the CCC chart. However, this would be costly when taking the inspection cost and time into consideration and thus limit its application. Instead of inspecting the items one by one, this study takes sample from them, and regards the time between two successive samples as the sampling interval. In order to increase the sensitivity of the CCC chart to process change, the sampling interval and control limits are allowed to vary in this study. The average time to signal process change of the modified CCC chart (called the variable sampling interval and control limit (VSI/VCL) CCC chart) is derived by the Markov chain approach and taken as the performance measure to evaluate its statistical efficiency. With some minor changes, this chart can be reduced to the VSI CCC chart, the VCL CCC chart, and the standard CCC chart. In addition, comparisons among them are made and discussed.

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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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The optimal choice of negative binomial charts for monitoring high-quality processes

Cited by 29 publications

References 17 publications

Control charts for health care monitoring under overdispersion

Control charts for health care monitoring under overdispersion

Cumulative conformance count chart with variable sampling intervals and control limits

A Review and perspective on surveillance of Bernoulli processes

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