On the performance of combinedEWMAschemes forμandσ: a markovian approach

Abstract

Key Words and Phrases: two-dimensional Markov chain, average run length, run length percentage points, probability of a misleading signal. ABSTRACTChanges 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 X, S2 ( ) 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.2

Statistical Surveillance. Optimality and Methods

“…Saniga (1989) and Morais and Pacheco (2000). In the latter the probability of signaling in the wrong chart is evaluated.…”

Evaluations of some Exponentially Weighted Moving Average methods

“…The case of a shift in the variance was studied by Chang and Gan (1994), Crowder and Hamilton (1992) and Morais and Pacheco (1998). The case of a simultaneous shift in both the mean and the variance has been studied by Domangue and Patch (1991), Gan (1995) and Morais and Pacheco (2000). Also shifts in other types of processes have been studied.…”

A comparative study of the median run length (MRL) performance of the Max-DEWMA and SS-DEWMA control charts

“…This has led to the development of a single EWMA-type chart. Many researchers have contributed to the development of single EWMA-type charts (see [2][3][4][5][6][7][8][9][10][11]). A comprehensive review of single EWMA-type control charts has been discussed in Cheng and Thaga [12] and Khoo et al [13].…”