Designing of Single Sampling Plan by Attributes Under the Conditions of Borel Distribution

Acceptance sampling is one of the widely used methodologies in the industry to sentence about the quality of a lot or lots based on random samples. In this modern industrial era, the manufacturing process is well monitored, hence the occurrence of defects is rare. However, the lots formed from a process, in practice, have quality variations, which occur due to random fluctuations. Therefore, the proportion of nonconforming units in the lots cannot be eliminated completely. In this situation, the appropriate distribution to model the number of defects is the Borel distribution. This paper aims to develop a single sampling plan by attributes when the number of defects follows the Borel distribution. Further, the operating characteristic function (OC) of the sampling plan is derived and comprehensive analysis of the performance of the proposed sampling plan is described through its OC curves. The procedure for determining the plan parameters using unity values with operating ratio as a measure of discrimination is discussed. The methodology for obtaining an optimal plan is also presented through a numerical illustration. And a comparative study between SSP under Borel distribution and Zero Truncated Poisson distribution has been done.