Economical process adjustment with measurement error

Abstract

Srivastava and Wu (1997) considered a random walk model with sampling interval and measurement error which was assumed to be white noise. In this paper, we consider the situation in which the measurement error is also a random walk. It is assumed that there is a sampling cost and an adjustment cost. The cost of deviating from the target value is assumed to be proportional to the square of the deviations. The long-run average cost rate is evaluated exactly in terms of the first four moments of a randomly stopped random walk. Using approximations of those moments, optimum, values of the control parameters are given.

Keywords:

• Adjustment cost
• inspection cost
• random walk
• optimum control of parameters