Statistics and decision making as applied to printing conformity assessment

Conformity assessment, a relatively new activity in the printing industry, is an attestation that specified requirements relating to a product or process have been fulfilled. Printing certification bodies assess printing conformity according to sampling, aim points, tolerances, and decision-making rules that are stipulated by printing standards. However, do we know if: sampling is too large or too small; normative requirements are too many or too few; tolerances are set too tightly or too loosely; and the pass/fail criterion is too stringent or too relaxed? Moreover, how do these factors impact the passing probability of a sample, a job, and the database as a whole? To study inter-dependencies of these factors in production variation conformity, this research assumes that the number of jobs to be assessed for printing conformity is very large and that samples selected from a job are random. Statistical theory is used to study the relation between the passing probabilities of a printing job, a single sheet within each job, and each normative requirement. In our theoretical frame, given the tolerance levels of certain normative requirements, we can determine the passing probabilities of the criteria, the passing probability of a single sheet, and the overall passing probability of a printing job. Given the passing probability of a printing job, we can also determine the tolerance level of each normative requirement by reversing the procedure. This research uses a real-life printing dataset and simulation techniques to determine the passing probabilities of a job as a function of sampling, tolerances, and the pass/fail criterion of a job. This research offers two meaningful inferences: (1) the printing standards development community, i.e., ISO/TC 130, needs to be aware that sampling requirements, the number of normative requirements and their associated tolerances, and the pass/fail criteria impact the passing probability of a job; and (2) printers who are seeking printing certification need to know that, although sampling is random, the passing probability of a job ultimately depends on the process calibration and the effectiveness of local process control