Inspection strategies for quality products with rewards in a multi-stage production

Abstract

In a multi-stage manufacturing system, defective components are generated due to deteriorating machine parts and failure to install the feed load. In these circumstances, the system requires inspection counters to distinguish imperfect items and takes a few discreet decisions to produce impeccable items. Whereas the prioritisation of employee appreciation and working on reward is one of the important policies to improve productivity. Here we look at the multi-stage manufacturing system as an M/PH/1 queue model and rewards are given for using certain inspection strategies to produce the quality items. A matrix analytical method is proposed to explain a continuous-time Markov process in which the reward points are given to the strategy of inspection in each state of the system. By constructing the value functions of this dynamic programming model, we derive the optimal policy and the optimal average reward of the entire system in the long run. In addition, we obtain the percentage of time spent on each system state for the probability of conformity and non-conformity of the product over the long term. The results of our computational experiments and case study suggest that the average reward increases due to the actions are taken at each decision epoch for rework and disposal of the non-conformity items.

Keywords:

• Sequential process
• infinitesimal operator
• Markov decision processes
• value function
• optimal policy
• optimal average reward

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

R. Satheesh Kumar

R. Satheesh Kumar is a mathematician and serves as a professor in Department of Mathematics, PSNA College of Engineering and Technology. His research interest are in the field of Production and Inventory Management, MDP in Reinforcement learning and Operational Research.

A. Nagarajan

A. Nagarajan is a mathematician and serves as a professor in Department of Mathematics, PSNA College of Engineering and Technology. His expertise are in Solid Transportation Problem and Production Management.