On-line quality control procedures for a random walk model with measurement error

Abstract

An economical on-line quality control procedure is given for cases where measurement error u present.The unobservable quality characteristic procw is assumed to follow a normal random walk.model independent of the measurement error which is white noise. The off-target loss function used is proportional to the squared deviation from the target value.The procw is inspected at regular intervals of m time units and adjusted at the end of a cycle when the process goes out of the control limit d.The limning long-run average cost rate is evaluated.The optimum value of the control parameters,the inspection interval m,and the control limit d are obtained by minimlzlng the long-run average cost rate.When m is small and d is large, explicit expressions for the control parameters are given.