Question

Equivalence of moving average and exponentially weighted moving average control charts. Show that if l = 2/(w 1) for the EWMA control chart, then this chart is equivalent to a w-period moving average control chart in the sense that the control limits are identical in the steady state. Use this hint: for the EWMA chart, the steady-state control limits are usually, l = 3. UCL = ( )

Answer 1

To show equivalence between MA and EWMA control charts, the smoothing constant (λ) in EWMA must be set to 2/(w + 1), where w is the width of the moving period in MA. This aligns the control limits in a steady state for both charts, using a typical standard deviation factor of 3 for calculation.

Step-by-step explanation:

The equivalence between moving average (MA) and exponentially weighted moving average (EWMA) control charts can be demonstrated when the smoothing constant λ (lambda) in the EWMA chart is set to 2/(w + 1), where w is the width of the moving period in the MA chart. This establishes identical control limits for both types of charts in a steady-state scenario. For the EWMA chart, we typically use a value of 3 standard deviations for the control limits calculation, which represents a 99.73% confidence interval if the underlying process distribution is normal.

The formula for the upper control limit (UCL) for an EWMA chart is based on the sum of weighted previous and current measurements, with the weights determined by the smoothing constant λ. In a steady state, these weights sum to 1, leading to comparable control limits between the EWMA and the simple moving average control charts for the same dataset when λ is set as indicated.