Quality control by the optimal control of a discrete-state stochastic process

This paper provides a stochastic control approach to quality control. Results and numerical examples are used to assess the mutual effects of the costs of inspection sampling and the failure of units that have been sold. The approach is an extension of classical statistical quality-control procedures. Firstly, the time dimension in production is explicitly considered and secondly, non-constants, such as variations in production output, production reliability, etc., with lines, are used in formulating the problems. These problems are then resolved analytically for linear inspection and failure costs and numerically for non-linear costs.