A new Bayesian acceptance sampling plan considering inspection errors

Abstract A sampling plan is a statement of criteria of acceptance applied to a batch, based on appropriate examination of a required number of sample units by specific methods. In this paper, a new acceptance sampling plan is introduced in which it is assumed that every defective item cannot be detected with complete certainty. To model the problem, the probability distribution function of the number of defective items in the batch is determined through Bayesian inference, and based on this probability density function, the probability of correct decisions in different actions is evaluated. An objective function is defined for each decision that minimizes the ratio of the system cost to the system correct decision probability, including the cost of rejecting the batch, and the cost of defectives items remaining in an accepted batch. Three numerical examples are provided to illustrate the applications of the proposed models.

[1]  Samuel Kotz,et al.  Errors in Inspection and Grading: Distributional Aspects of Screening and Hierarchal Screening. , 1982 .

[2]  Douglas G. Bonett.  Estimating the number of defects under imperfect inspection , 1988 .

[3]  Akhavan Niaki Seyed Taghi,et al.  A NEW ACCEPTANCE SAMPLING PLAN BASED ON CUMULATIVE SUMS OF CONFORMING RUN-LENGTHS , 2011 .

[4]  Eamonn Mullins,et al.  Probability and Statistics. 2nd edn. , 1988 .

[5]  M. S. Fallahnezhad,et al.  A NEW ACCEPTANCE SAMPLING DESIGN USING BAYESIAN MODELING AND BACKWARD INDUCTION , 2012 .

[6]  Young H. Chun,et al.  Bayesian inspection model with the negative binomial prior in the presence of inspection errors , 2007, Eur. J. Oper. Res..

[7]  Seyed Taghi Akhavan Niaki,et al.  Decision rule of repetitive acceptance sampling plans assuring percentile life , 2012 .

[8]  Wolfgang Stadje,et al.  Group testing procedures with incomplete identification and unreliable testing results , 2006 .

[9]  Fallah Nezhad Mohammad Saber,et al.  DESIGNING A SINGLE STAGE ACCEPTANCE SAMPLING PLAN BASED ON THE CONTROL THRESHOLD POLICY , 2011 .

[10]  Fallah Nezhad,et al.  A New Markov Chain Based Acceptance Sampling Policy via the Minimum Angle Method , 2012 .

[11]  S. Kotz,et al.  Faulty Inspection Distributions -- Some Generalizations. , 1981 .

[12]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[13]  Seyed Taghi Akhavan Niaki,et al.  A New Acceptance Sampling Policy Based on Number of Successive Conforming Items , 2013 .

[14]  Samuel Kotz,et al.  Effects of False and Incomplete Identification of Defective Items on the Reliability of Acceptance Sampling , 1984, Oper. Res..

[15]  Taraneh Eghlidos,et al.  Practical Next Bit Test for Evaluating Pseudorandom Sequences , 2009 .

[16]  Samuel Kotz,et al.  “Faulty inspeciton” distributions , 1980 .