Sampling plans for the zero-inflated negative binomial distribution in the food industry

In this paper, we propose 3 new sampling plans, including resubmitted single sampling plan (RSSP), repetitive group sampling (RGS) plan, and multiple dependent state (MDS) sampling plan to study the zero-inflated negative binomial distribution in microbiological food safety and quality assurance practices. The unity value approach is used to find optimal plan parameters. The proposed plans are compared with the single sampling plan (SSP). We found that degree of clustering and excess of zeros counts affect the performance of all sampling plans. The MDS plan outperforms the SSP, RSSP, and RGS plans with respect to minimum average sample number in most cases. Both RGS and MDS plans show a comparable performance. The average run length is calculated to evaluate the rejection capability of the plans and signal the deterioration of the quality of lots. An example from 9 Irish abattoirs is used to illustrate the application of the proposed methods.