The effect of measurement errors on the performance of the homogenously weighted moving average X¯ monitoring scheme with estimated parameters

ABSTRACT

Classical monitoring schemes are typically designed under the assumption of known process parameters, perfect measurements and normality. In real-life applications, these assumptions are often violated. Thus, their Phase II performances are negatively affected by both measurement errors and parameter estimation. In this paper, the performance of the homogenously weighted moving average (HWMA) scheme is investigated under the assumption of unknown process parameters with and without measurement errors using the characteristics of the run-length distribution through intensive simulations. The negative effect of measurement errors is reduced using multiple measurements sampling strategy. It is found that the negative effect of the measurement errors is higher as the smoothing parameter increases and the larger the Phase I sample size, the smaller the negative effect of measurement errors. An illustrative example is given to demonstrate the implementation in real-life applications.

KEYWORDS:

• Homogenously weighted moving average scheme
• linear covariate error model
• linearly increasing variance
• measurement error
• multiple measurements
• parameter estimation

Disclosure statement

No potential conflict of interest was reported by the author(s).