Determination of Single Sampling Plans by Attributes Under the Conditions of Zero-Inflated Poisson Distribution

When the manufacturing process is well monitored, occurrence of nondefects would be a frequent event in sampling inspection. The appropriate probability distribution of the number of defects is a zero-inflated Poisson (ZIP) distribution. In this article, determination of single sampling plans (SSPs) by attributes using unity values is considered, when the number of defects follows a ZIP distribution. The operating characteristic (OC) function of the sampling plan is derived. Plan parameters are obtained for some sets of values of (p1, α, p2, β). Numerical illustrations are given to describe the determination of SSP under ZIP distribution and to study its performance in comparison with Poisson SSP.

[1]  Daniel Gianola,et al.  A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep , 2008, Genetics Selection Evolution.

[2]  N. Jansakul,et al.  Score Tests for Extra-Zero Models in Zero-Inflated Negative Binomial Models , 2008, Commun. Stat. Simul. Comput..

[3]  José R. Berrendero,et al.  Tests for zero-inflation and overdispersion: A new approach based on the stochastic convex order , 2009, Comput. Stat. Data Anal..

[4]  G. B. Wetherill,et al.  Quality Control and Industrial Statistics , 1975 .

[5]  Yan Yang,et al.  Unified computational methods for regression analysis of zero-inflated and bound-inflated data , 2010, Comput. Stat. Data Anal..

[6]  Zhao Yang,et al.  Score tests for overdispersion in zero-inflated Poisson mixed models , 2010, Comput. Stat. Data Anal..

[7]  Liming Xiang,et al.  A Note on Tests for Zero-Inflation in Correlated Count Data , 2011, Commun. Stat. Simul. Comput..

[8]  Feng-Chang Xie,et al.  Score tests for zero-inflated generalized Poisson mixed regression models , 2009, Comput. Stat. Data Anal..

[9]  Chin-Shang Li,et al.  Testing the Lack-of-Fit of Zero-Inflated Poisson Regression Models , 2011, Commun. Stat. Simul. Comput..

[10]  M. H. Lim,et al.  Attribute Charts for Zero-Inflated Processes , 2008, Commun. Stat. Simul. Comput..

[11]  Thong Ngee Goh,et al.  Zero-inflated Poisson model in statistical process control , 2002 .

[12]  John Hinde,et al.  Models for count data with many zeros , 1998 .

[13]  K. Govindaraju,et al.  Inspection Error Adjustment in the Design of Single Sampling Attributes Plan , 2007 .

[14]  Dean V. Neubauer,et al.  Acceptance Sampling in Quality Control , 1983 .

[15]  Dankmar Böhning,et al.  The zero‐inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology , 1999 .

[16]  Cheryl L. Addy,et al.  Score Tests for Zero-Inflation in Overdispersed Count Data , 2010 .

[17]  J. Hardin,et al.  Some Remarks on Testing Overdispersion in Zero-Inflated Poisson and Binomial Regression Models , 2010 .

[18]  Kenneth S. Stephens,et al.  The Handbook Of Applied Acceptance Sampling: Plans, Procedures And Principles , 2001 .

[19]  Diane Lambert,et al.  Zero-inflacted Poisson regression, with an application to defects in manufacturing , 1992 .

[20]  Gary Sneddon,et al.  Zero-Inflated Poisson Regression for Longitudinal Data , 2009, Commun. Stat. Simul. Comput..

[21]  Abbas Moghimbeigi,et al.  A score test for zero-inflation in multilevel count data , 2009, Comput. Stat. Data Anal..

[22]  M. Xie,et al.  Outlier identification and robust parameter estimation in a zero-inflated Poisson model , 2011 .

[23]  Geoffrey J. McLachlan,et al.  Finite Mixture Models , 2019, Annual Review of Statistics and Its Application.