00:01
Hello students, here from the question they given that the sample size n is equal to 4.
00:08
After 30 samples that is the sum of i is equal to 1 to 30, the xi bar is equal to 12, 8, 7, 0 and the sum of i is equal to 1 to 30, the si which is equal to 4, 1, 0.
00:33
Now here we need to find the 3 sigma limits for the x bar and s charts.
00:39
This is the subpart a, the formula for calculating the 3 limits for x bar chart which is u cl is equal to x double bar plus a3 into s bar and lcl which is equal to x double bar minus a3 s bar where the cl which is equal to x double bar.
01:14
Now here the a3 value which is equal to 1 .628.
01:27
Now here we substitute the known values in the formula of u cl the x double bar which is equal to 429 plus 1 .628 into s bar which is sum of si divided by n that is equal to 13 .6667.
01:46
By simplifying this we get 451 .2494 and also the lcl which is 429 minus 1 .628 into 13 .6667 is equal to 406 .7506 and also the control central limit that is x double bar which is equal to 429.
02:18
Now the formula for calculating the s bar chart the 3 limits are u cl which is equal to b4 into s bar and the lcl which is equal to b3 into s bar cl which is equal to s bar...