9.7. The data in Table 9E.3 are temperature readings from a...

9.7. The data in Table 9E.3 are temperature readings from a chemical process in °C, taken every two minutes. (Read the observations down, from left.) The target value for the mean is $mu_0 = 950$. (a) Estimate the process standard deviation. (b) Set up and apply a tabular CUSUM for this process, using standardized values $h = 5$ and $k = frac{1}{2}$. Interpret this chart. TABLE 9E.3 Chemical Process Temperature Data 953 985 949 937 959 948 958 952 945 973 941 946 939 937 955 931 972 955 966 954 948 955 947 928 945 950 966 935 958 927 941 937 975 948 934 941 963 940 938 950 970 957 937 933 973 962 945 970 959 940 946 960 949 963 963 933 973 933 952 968 942 943 967 960 940 965 935 959 965 950 969 934 936 973 941 956 962 938 981 927

Transcript

00:01 All right, so we have some data here that we're going to look at in a second where, so you get the temperature readings from a chemical process in degrees celsius.

00:10 It's taken every two minutes.

00:12 And the target value for the mean is 950.

00:17 And we're going to estimate the process standard deviation.

00:20 That's the first thing we're going to do.

00:22 S .d.

00:23 And for this, we are going to really just take the standard deviation of all the values.

00:29 And for that, we're going to use a spreadsheet function, st -d -e -v -s in excel.

00:35 Google sheets does the same thing.

00:37 And input today.

00:37 We'll show that in a second.

00:38 You get the standardization.

00:40 And then we're going to set up and apply a tabular q -sum for this process using standardized values where h is 5 and k is one -half.

00:52 And we're going to interpret this chart.

00:53 So let's talk about what this whole thing means.

00:55 So the q -sum formula is as follows.

01:00 So q sum, q sum.

01:06 We have ci plus equals the max of zero and c .i minus one plus plus zi plus k, minus k, excuse me, minus k.

01:22 And we know k, we're told this a half, we'll do this in a second.

01:26 And then we have the minus, c, i minus, which is equal to the max of zero, so, i minus 1 minus zi minus k.

01:39 And we already know k, we said it's a half.

01:41 So i'm just going to plug a half in there.

01:45 All right.

01:46 So what this means is we're going to take the max of zero and whatever this value is.

01:51 And then what we're going to look at is whether or not this value here, whatever this value is, if that is greater than five, that means our process is out of control.

02:01 And z, z, i, should define that as well.

02:04 Well, that's equal to xi the value minus the mean, which is 950, 950 divided by the standard deviation of the sample s or sd.

02:18 All right.

02:21 And let's just let me show you in a spreadsheet and that's just easier to see.

02:25 But one thing to note is that the ci minus 1 plus and ci minus 2, ci minus 1 minus.

02:31 This is telling us to look at the previous value.

02:37 Let me just show you the whole thing.

02:38 That's easier to see.

02:41 Okay, so here's the mean.

02:42 So x is the values.

02:44 I've taken all the data and just made it in one big column.

02:48 And so you just take the average of those values.

02:56 And we see the mean is that.

02:59 Standard deviation is this.

03:06 And you just use std -ev -s.

03:09 You take the values and there's standard deviation.

03:11 13 .97.

03:15 Z is going to be, and i should change that, it's each of these x values minus that 950 mean.

03:31 So that should be 950.

03:34 Let me change that.

03:35 Well, the cool thing about this is once you have it set up, it goes, it goes all the way down...

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