A normally distributed quality characteristic is monitored with a moving average (MA) control chart. The monitored moving average at time t is defined as M
t
​
=
2
x
ˉ

t
​
+
x
ˉ

t−1
​

​
(sample size n=1.) Suppose the process mean is μ when t≤2 and then has a 1σ shift (i.e.: process mean is μ+1σ ) at t≥3. (a) Write out the 3-sigma upper control limits for this MA chart at t=1 and t≥2. (0.5 point) (b) Write out the distribution type, mean, and variation of M
t
​
when t≥3. (1 point) (c) Calculate the detection power of the control charts designed in (a) at t≥3. (1 point)