Optimal design of exponentially weighted moving average– chart for the mean with estimated process parameters

ABSTRACT

This paper proposes an optimal design of the exponentially weighted moving average (EWMA)– chart with estimated process parameters in terms of average run length (ARL) and standard deviation of the run length (SDRL), using a Markov chain. An optimal design enables the EWMA– chart with estimated process parameters to be optimally designed by minimizing the out-of-control ARL, in order to overcome the current limitation, where only the EWMA– chart with known process parameters is optimally designed. With the proposed procedure, the EWMA– chart with estimated process parameters can be designed to have a similar in-control performance on average to its known process parameters counterpart.

KEYWORDS:

• Exponentially weighted moving average
• Individual measurements
• Markov chain
• Optimization design
• Process parameter estimation
• Subgroup data

MATHEMATICS SUBJECT CLASSIFICATION:

• 60J10
• 62P30

Funding

This research is supported by the Universiti Sains Malaysia (USM) through research university grant (number 1001/PMATHS/811263).