Performance evaluation of moving average-based EWMA chart for exponentially distributed process

ABSTRACT

The moving average (MA), exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are popular control charts to detect small shifts quickly in process parameters. In this study, we evaluate the performance of the EWMA chart for monitoring exponentially distributed quality characteristics based on moving average statistics. The average run length and some other associated characteristics are used as performance measures of the chart. The concept of using the probability of detection for the performance assessment of this chart has been criticized in this study. A real-life application is also provided for practical consideration.

KEYWORDS:

• EWMA chart
• exponential distribution
• moving average
• Monte Carlo simulation
• probability of detection
• run length

Nomenclature

ARL	=	Average run length
ARL1	=	In-control ARL
ARL0	=	Out-of-control ARL
CUSUM	=	Cumulative sum
DEWMA	=	Double exponentially weighted moving average
DMA	=	Double moving average
dMEWMA	=	Double multivariate exponentially weighted moving average
EWMA	=	Exponentially weighted moving average
LCL	=	Lower control limit
MDRL	=	Median run length
MA	=	Moving average
MEWMA	=	Multivariate exponentially weighted moving average
$P_{in}^0$	=	Probability of the in-control process
$P_{in}^1$	=	Probability of the out-of-control process
RL	=	Run length
SDRL	=	Standard deviation of run length
SPC	=	Statistical process control
UCL	=	Upper control limit
${\theta }_1$	=	Amount of shift
${\theta }_0$	=	Target value
$\lambda$	=	Smoothing constant

Disclosure statement

No potential conflict of interest was reported by the authors.