Assessing the effect of estimation error on risk-adjusted CUSUM chart performance

Jones, Mark; Steiner, Stefan H.

doi:10.1093/intqhc/mzr082

Cited by 105 publications

(112 citation statements)

References 5 publications

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“…The effect of ignoring estimation of baseline parameters from historical data sets, has been well-examined in recent literature. For instance, Jones and Steiner (2012) …”

Section: Accepted Manuscriptmentioning

confidence: 99%

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

Hussein

Kasem

Nkurunziza

et al. 2016

Communications in Statistics - Simulation and Computation

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Monitoring health care performance outcomes such as post-operative mortality rates has recently become more common, spurring new statistical methodologies designed for this purpose. One such methodology is the Risk-adjusted Cumulative Sum chart (RA-CUSUM) for monitoring binary outcomes such as mortality after cardiac surgery. When building RA-CUSUMs, independence and model correctness are assumed. We carry out a simulation study to examine the effect of violating these two assumptions on the chart's performance

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“…The effect of ignoring estimation of baseline parameters from historical data sets, has been well-examined in recent literature. For instance, Jones and Steiner (2012) …”

Section: Accepted Manuscriptmentioning

confidence: 99%

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

Hussein

Kasem

Nkurunziza

et al. 2016

Communications in Statistics - Simulation and Computation

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“…According to the previous literature, this procedure is very promising and don't have a severe adverse effect on the out‐of‐control performance of the control chart as shown in several studies (see Aly et al ., and Saleh et al ., for example). Following the same approach of Jones and Steiner and Gandy and Kvaløy's, the practitioner can use the following algorithm to adjust the control limit of the MAEWMA chart: 1Using the available m Phase I samples, each of size n , the practitioner first calculates

\overset{θ}{true} = ((), {\overset{μ}{true}}_{bold0}, {\overset{Σ}{true}}_{0})

; where

{\overset{true^}{boldμ}}_{0} = \overset{\overset{true¯}{boldx}}{true}

{\overset{true^}{boldΣ}}_{0} = \overset{S}{true}

for the sub‐grouped MAEWMA chart and

{\overset{true^}{boldμ}}_{0} = \overset{x}{true}

{\overset{true^}{boldΣ}}_{0} = boldS

for the individual MAEWMA chart. 2Assuming the true in‐control distribution is N p ( μ 0 , Σ 0 ), generate B bootstrap samples from

N_{p} ((), {\overset{μ}{true}}_{bold0}, {\overset{Σ}{true}}_{0})

and calculate the corresponding bootstrap estimates

{\overset{true^}{θ}}_{i}^{*} = ((),, {\overset{μ}{true}}_{bold0}^{bold*}, {\overset{Σ}{true}}_{0}^{*})

; i = 1, 2,...., B ; where B is a large number, say 1000. 3Search for the MAEWMA control limit

L_{i}^{*}

; i =1,2....., B that satisfies the desired in‐control ARL; where the Phase II data are generated from

N_{p} ((), {\overset{μ}{true}}_{bold0}, {\overset{Σ}{true}}_{0})

and the MAEWMA chart statistics are computed using

…”

Section: A Bootstrap Algorithm To Adjust the Control Limit Of The Maementioning

confidence: 99%

“…This metric accounts for the practitioner‐to‐practitioner variation that occurs due to using different Phase I datasets by different practitioners. This metric was proposed by Jones and Steiner to study the performance of control charts with estimated parameters. They used it to study the effect of parameter estimation on the performance of the risk‐adjusted CUSUM chart.…”

Section: Introductionmentioning

confidence: 99%

“…Gandy and Kvaløy used a bootstrap design procedure suggested by Jones and Steiner to overcome the low in‐control ARL values that frequently occur in the case of estimated parameters. Their procedure adjusts the control limits of a control chart so that the in‐control ARL is greater than or equal to a desired value with a specific probability based on a bootstrap technique.…”

Section: Introductionmentioning

confidence: 99%

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The Performance of the Multivariate Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

Aly

Mahmoud

Hamed

2015

Quality & Reliability Eng

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The multivariate adaptive exponentially weighted moving average control chart (MAEWMA) can detect shifts of different sizes while diminishing the inertia problem to a large extent. Although it has several advantages compared to various multivariate charts, previous literature has not considered its performance when the parameters are estimated. In this study, the performance of the MAEWMA chart with estimated parameters is studied while considering the practitioner-topractitioner variation. This kind of variation occurs due to using different Phase I samples by different practitioners in estimating the unknown parameters. The simulation results in this paper show that estimating the parameters results in extensively excessive false alarms and as a result a large number of Phase I samples is needed to achieve the desired incontrol performance. Using small number of Phase I samples in estimating the parameters may result in an in-control ARL distribution that almost completely lies below the desired value. To handle this problem, we strongly recommend the use of a bootstrap-based algorithm to adjust the control limit of the MAEWMA chart. This algorithm enables practitioners to achieve, with a certain probability, an in-control ARL that is greater than or equal to the desired value while using the available number of Phase I samples.

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“…This metric is important because it takes into account the practitioner‐to‐practitioner variation that arises because of the use of different phase I datasets by different practitioners. Jones and Steiner proposed the SDARL metric to evaluate the performance of control charts with estimated parameters and used it to study the effect of estimation on the performance of the risk‐adjusted Bernoulli CUSUM chart. Moreover, Zhang et al .…”

Section: Introductionmentioning

confidence: 99%

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

Aly

Saleh

Mahmoud

et al. 2014

Quality & Reliability Eng

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The performance of control charts can be adversely affected when based on parameter estimates instead of known in‐control parameters. Several studies have shown that a large number of phase I observations may be needed to achieve the desired in‐control statistical performance. However, practitioners use different phase I samples and thus different parameter estimates to construct their control limits. As a consequence, there would be in‐control average run length (ARL) variation between different practitioners. This kind of variation is important to consider when studying the performance of control charts with estimated parameters. Most of the previous literature has relied primarily on the expected value of the ARL (AARL) metric in studying the performance of control charts with estimated parameters. Some recent studies, however, considered the standard deviation of the ARL metric to study the performance of control charts. In this paper, the standard deviation of the ARL metric is used to study the in‐control and out‐of‐control performance of the adaptive exponentially weighted moving average (AEWMA) control chart. The performance of the AEWMA chart is then compared with that of the Shewhart trueX¯ and EWMA control charts. The simulation results show that the AEWMA chart might represent a good solution for practitioners to achieve a reasonable amount of ARL variation from the desired in‐control ARL performance. In addition, we apply a bootstrap‐based design approach that provides protection against frequent false alarms without deteriorating too much the out‐of‐control performance. Copyright © 2014 John Wiley & Sons, Ltd.

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Assessing the effect of estimation error on risk-adjusted CUSUM chart performance

Cited by 105 publications

References 5 publications

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

Performance of risk-adjusted cumulative sum charts when some assumptions are not met

The Performance of the Multivariate Adaptive Exponentially Weighted Moving Average Control Chart with Estimated Parameters

A Reevaluation of the Adaptive Exponentially Weighted Moving Average Control Chart When Parameters are Estimated

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