Quality and Reliability Methods - SAS

Chapter 5 Shewhart Control Charts 83
Moving Average Charts
Figure 5.10 UWMA Charts for the Clips1 data
Control Limits for UWMA Charts
Control limits for UWMA charts are computed as follows. For each subgroup i,
σˆ
LCL i = X w – k----------------------
min( i,
w)
σˆ
UCL i = X w + k----------------------
min( i,
w)
---
1 1
n i
n ----------- … 1
+ + + ----------------------------------------
i – 1
n 1 + max( i – w,
0)
---
1
n ----------- 1
i
n … 1
+ + + ----------------------------------------
i – 1
n 1 + max( i – w,
0)
where
w is the span parameter (number of terms in moving average)
n i is the sample size of the i th subgroup
k is the number of standard deviations
X w
is the weighted average of subgroup means
σ
is the process standard deviation
Exponentially Weighted Moving Average (EWMA) Charts
Each point on an Exponentially Weighted Moving Average (EWMA) chart, also referred to as a Geometric
Moving Average (GMA) chart, is the weighted average of all the previous subgroup means, including the
mean of the present subgroup sample. The weights decrease exponentially going backward in time. The
weight ( 0 < weight ≤ 1) assigned to the present subgroup sample mean is a parameter of the EWMA chart.
Small values of weight are used to guard against small shifts.
Example: EWMA Charts
Using the Clips1.jmp data table, submit the JSL or follow the steps below.
Control Chart(Sample Size(5), KSigma(3), Weight(0.5), Chart Col( :Gap, EWMA));