Question

In order to establish a control chart for the mean of a process, 20 samples each of size 4
are collected. We note that
P20
i=1 xi = 4000 and
P20
i=1 si = 500. The value of the lower
control limit of the chart for the mean is approximately equal to 195.5.
True False

In order to establish a control chart for the mean of a process, 20 samples each of size 4 are collected. We note that 222, Ti 4000 and 2-1 si 500. The value of the lower control limit of the chart for the mean is approximately equal to 195.5. True False

Answer 1

Solution:

Given

m = 20 sample

n = 4 sample size

$\sum_{i=1}^{20}\bar xi=4000$

20 Σsi = 500 1=1

$\bar{\bar X}= \frac{\sum_{i=1}^{20}\bar xi}{m}=\frac{4000}{20}=200$

5 = 20 i=1 S1 500 20 25 Πη

The lower control limits of X bar chart is

$LCL = \bar {\bar X}- A3 *\bar S$

Where A3 = 1.628 from statistical table at n = 4

LCL = 159.3

The lower control limits of mean chart is not 195.5

The given statement is False.