Multivariate setup adjustment with fixed adjustment cost

For a discrete-part manufacturing process, adjustment is necessary to bring the process to target when the setup of the machine is improperly done. This paper investigates the adjustment scheme for a multivariate process with initial offset in the presence of fixed adjustment cost. The objective is to derive a solution for the case that the cost for different responses can be different. Based on the state process-control model, expressions of optimal adjustment scheme are derived by the dynamic programming and congruent transformation of quality loss matrix. This scheme belongs to a deadband form and calls for an adjustment only when the norm of the linear transformation of perceived process mean vector is at the outside of the deadband. A simulation study is conducted to compare the scheme proposed in this paper with two other schemes.