00:01
Hello students, draw the control charts for the x and the r that is the x bar and the r range from the following data relating to the 20 samples.
00:10
Each of the size 5.
00:11
Only the center line we have to draw the center line upper and the lower control limits for the x bar and the r chart.
00:17
First we know that the control limit for x bar chart r and these control limits when the standards are not given.
00:37
Then upper control limit, central line, lower control limit.
00:42
Upper control limit is equals to x double bar plus a2 r bar, central line x double bar, lower control line x bar x double bar minus a2 r bar and where x double bar is equals to summation of xi upon number of samples and r bar is equals to summation of here is a x bar i summation of ri upon number of samples and the value a2 is the statistical constant.
01:25
Then we know the values of x bar.
01:28
Look at here this is the all x bar values related with the all 20 samples.
01:33
Then take the sum of 8 and we get this summation 587 divided by number of samples.
01:42
The number of samples are 20 and after simplification we get value of x double bar is equals to 29 .35.
01:53
Next r bar, r bar is equals to summation of ri.
01:57
This is the all ranges related with the samples 20 samples and then take summation of it we get 420 divided by number of samples which is a 20 and after simplification we get value of r bar is equals to 21.
02:10
Now a2, a2 is the statistical constant for the sample size n equals to 5.
02:19
Then the value of a2 by using the statistical tables we get the value as 0 .577.
02:29
Now look at here the value of x double bar also known a2 also known r bar also known.
02:34
Then just put and simplify we get the value of upper confidence interval after simplification is 41 .467.
02:42
The value of x double bar is 29 .35 and value of lower confidence interval equals to 17 .233.
02:51
In this way we get the control limits for the x bar chart.
02:55
Now the control limits for r chart are and again these are the same when the standards are not given.
03:13
Then upper control limits upper control limit formula is d4 r bar center line equals to just r bar and the lower control limit equals to d3 r bar.
03:27
Again d3 and the d4 are the statistical constant for the sample size n equals to 5.
03:33
By using a statistical table the value of d3 we get is 0 and d4 is equal to 2 .115.
03:42
The value of r bar is already known which is equals to 21.
03:46
Just put here after simplification we get the upper control limit for the r bar chart is 44 .415.
03:57
R bar is equals to 21 and the d3 is 0.
04:00
So this quantity will be 0.
04:02
Now we have to plot the chart...