Investigating the effect of learning on setup cost in imperfect production systems using two-way inspection plan for rework under screening constraints

In the modern industrial environment, there is a continuous need for the advancement and improvement of the organization’s operations. Learning is an inherent property which is time-dependent and comes with experience. In view of this, the present framework considers the process of learning for an imperfect production system which aids in reducing the setup cost with the level of maturity gained, hence, providing positive results for the organization. Because of machine disturbances/ malfunctions, defectives are manufactured with a known probability density function. To satisfy the demand with good products only, the manufacturer invests in a two-way inspection process with multiple screening constraints. The first inspection misclassifies some of the items and delivers inaccuracies, viz., Type-I and Type–II. The loss due to inspection at the first stage is managed efficiently through a second inspection which is presumed to be free from errors. The study mutually optimizes the production and backordering quantities in order to maximize the expected total profit per unit time. Numerical analysis and detailed sensitivity analysis is carried out to validate the hypothesis and further cater to some valuable implications.