Comparison of Pearson distribution system and response modeling methodology (RMM) as models for process capability analysis of skewed data

Shauly, Michal; Parmet, Yisrael

doi:10.1002/qre.1232

Cited by 12 publications

(14 citation statements)

References 19 publications

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“…Therefore, these models may also be used to model random variation. Cumulative experience have shown1,4–8 that these models, in particular model (8), deliver accurate representation to the quantile functions of diversely shaped distributions. To understand why this is so, probability density functions (pdfs) of four distributions are displayed in Figure 3(a).…”

Section: The Rmm Approach‐concepts Basic Model and Variationsmentioning

confidence: 99%

“…A condition for obtaining a proper pdf in the ML procedure is as follows8: â > 0 ,ĉ > 0. This condition desirably restricts the range where ML estimates for { a , c } should be searched.…”

Section: Rmm Modeling Of Random Variation–estimationmentioning

confidence: 99%

“…However, sample estimates of the third and fourth moments are notorious for their large standard errors. Fitting an RMM distribution to data generally results in better estimates of the end points of the underlying process distribution 7,8,10…”

Section: Applicationsmentioning

confidence: 99%

“…In a more recent comparison,8 based on sample data generated via Monte Carlo simulation, RMM and Pearson were fitted to simulated data, using ML procedures. The functional distances between the fitted pdf and the pdf of the true (data generating) distribution were then evaluated via the L 2 norm (minimal values of the L 2 norm are desired).…”

Section: Applicationsmentioning

confidence: 99%

“…Studies of the effectiveness of RMM as a general platform for modeling random variation have been described extensively 1,4–8,10…”

Section: Comparing Rmm To Other Approachesmentioning

confidence: 99%

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Solid organ transplantation and hepatitis B virus

Villamil¹,

Cairo²

2013

Clinical Liver Disease

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LiverIs There a Role for Hepatitis B Immunoglobulin? Is Antiviral Monotherapy Sufficient?. The risk of hepatitis B virus (HBV) recurrence following liver transplantation (LT) has progressively decreased from 75% in the late 1980s, when no prophylaxis was available, to <5% at the present time [1][2][3] (Fig. 1). Combination therapy with a nucleos(t)ide analogue (NUC) plus low-dose intramuscular hepatitis B immunoglobulin (HBIg) has become the standard of care worldwide. Most likely, entecavir (ETV) or tenofovir (TDF) will be increasingly used in combination with HBIg instead of lamivudine (LAM) or adefovir. Although experience is limited, recent studies showed complete absence of HBV recurrence when using low-dose HBIg þ ETV. HBIg requires parenteral administration, has limited availability, and is expensive. However, when used in combination therapy, high doses and indefinite administration are no longer required. Pre-and post-LT monotherapy with LAM resulted in high rates of recurrence (40%), mostly due to the emergence of YMDD mutations. Fung et al. 4 recently showed that among 80 patients who received ETV monoprophylaxis the cumulative rate of hepatitis B surface antigen (HBsAg) loss was 91% with 98.8% of patients achieving undetectable HBV DNA. However, 18 patients (22.5%) were HBsAg-positive at the time of their last follow-up (persistence in eight and reappearance in 10). Are these results ''good enough'' to recommend HBIg-free prophylaxis to all patients transplanted for hepatitis B? The answer to this important question mostly relies on the definition of HBV recurrence. For many years, recurrent infection has been defined as persistence or reappearance of HBsAg in serum after its initial disappearance following LT. Based on this definition, results of the study by Fung et al. are inferior to those obtained with combination therapy in which >95% of patients remain HBsAg-negative after LT. In contrast, if HBV recurrence is defined as detectable serum HBV DNA, then persistence or reappearance of HBsAg after LT in the absence of viral replication should not be regarded as an inferior outcome. In any case, longer follow-up is required to establish whether patients with an inactive post-LT HBV carrier state induced by ETV will eventually clear HBsAg or go on to develop breakthrough and elevated ALT, as described with LAM. Clearance of HBsAg from serum is the most desired endpoint of antiviral therapy in patients with chronic hepatitis B. It is now considered that levels of HBsAg in serum reflect the transcriptional activity of covalently closed circular DNA (ccc DNA) in the liver. Although the HBsAg secretory pathway is partially independent of HBV replication, it can provide an indirect measure of the number of infected hepatocytes. Therefore, HBsAg negativity after LT appears to be a desirable goal in addition to the absence of replication.Although the mechanisms by which HBIg prevents graft reinfection are not completely understood, it is known that it binds circulating virions and may also decrease the hor...

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Section: The Rmm Approach‐concepts Basic Model and Variationsmentioning

confidence: 99%

Section: Rmm Modeling Of Random Variation–estimationmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

Section: Applicationsmentioning

confidence: 99%

“…Studies of the effectiveness of RMM as a general platform for modeling random variation have been described extensively 1,4–8,10…”

Section: Comparing Rmm To Other Approachesmentioning

confidence: 99%

See 3 more Smart Citations

Solid organ transplantation and hepatitis B virus

Villamil¹,

Cairo²

2013

Clinical Liver Disease

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Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Shore

2013

Quality & Reliability Eng

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Statistical process control monitoring of nonlinear relationships (profiles) has been the subject of much research recently. While attention is primarily given to the statistical aspects of the monitoring techniques, little effort has been devoted to developing a general modeling approach that would introduce ‘uniformity of practice’ in modeling nonlinear profiles (analogously with the three‐sigma limits of Shewhart control charts). In this article, we use response modeling methodology (RMM) to demonstrate implementation of this approach to statistical process control monitoring of ecological relationships. Using 10 ecological models that have appeared in the literature, it is first shown that RMM models can replace (approximate) current ecological models with negligible loss in accuracy. Computer simulation is then used to demonstrate that estimated RMM models and estimated data generating ecological models achieve goodness‐of‐fit that is practically indistinguishable from one another. A regression‐adjusted control scheme, based on control charts for the predicted median and for residuals variation, is developed and demonstrated for three types of ‘out of control’ scenarios. Copyright © 2013 John Wiley & Sons, Ltd.

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Non-normal Capability Indices for the Weibull and Lognormal Distributions

Piña‐Monarrez

Ortiz-Yañez

Rodríguez-Borbón

2015

Qual. Reliab. Engng. Int.

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Because the normal process capability indices (PCIs) C p , C pu , C pl , and C pk represent the times that the process standard deviation is within the specification limits; then, based on and by using the direct relations among the parameters of the Weibull, Gumbel (minimum extreme value type I) and lognormal distributions, the Weibull and lognormal PCIs are derived in this paper. On the other hand, because the proposed PCIs P p , P pu , P pl , and P pk were derived as a function of the mean and standard deviation of the analyzed process, they have the same practical meaning with those of the normal distribution. Results show that the proposed PCIs could be used as the standard C p , C pu , C pl , and C pk if a short-term variance is analyzed. An application to a set of simulated data is presented.

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Comparison of Pearson distribution system and response modeling methodology (RMM) as models for process capability analysis of skewed data

Cited by 12 publications

References 19 publications

Solid organ transplantation and hepatitis B virus

Solid organ transplantation and hepatitis B virus

Modeling and Monitoring Ecological Systems—A Statistical Process Control Approach

Non-normal Capability Indices for the Weibull and Lognormal Distributions

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