On the performance of combined EWMA schemes for μ and σ: a markovian approach

Abstract

Changes in the process mean (μ) or in the process standard deviation (σ) ought to be regarded as an indication that a production process is out of control.

This paper considers the problem of the joint monitoring of these two parameters — when the quality characteristic follows a normal distribution —, using a combined Exponentially Weighted Moving Average (CEWMA) scheme.

Three performance measures of this joint control scheme are investigated under shifts in the process mean or inflations of the process standard deviation, and under the adoption of head starts: the average run length, the run length percentage points and the probability of a misleading signal.

Approximations to these three performance indicators will be obtained considering a two-dimensional Markov chain. The independence between the horizontal and vertical transitions of this approximating two-dimensional Markov chain plays an important role in providing simple expressions to those performance measures which avoid the computation of a probability transition matrix with unusual dimensions.

A numerical comparison between these three performance measures and the corresponding ones of the matched combined Shewhart (CShewhart) scheme will be also presented, leading to the conclusion that the substituition of this combined scheme by the CEWMA scheme can improve the joint monitoring of the process mean and standard deviation.

Keywords:

• two-dimensional Markov chain
• average run length
• run length percentage points
• probability of a misleading signal