Using the data below, calculate the overall average of the means and the average

Question

Using the data below, calculate the overall average of the means and the average range. What are the upper and lower control limits for a 99.7% control chart for the mean? Does this process appear to be in control? Calculate upper and lower control limits for the range. Do these samples indicate that the process is in control? 8 points each

Note: your Z=3 chart is on p. 544, and gives you A2, D4 and D3.

SAMPLE Mean Range 1 979 50 2 1087 94 3 1080 57 4 934 65 5 1072 135 6 1007 134 7 952 101 8 986 98 9 1063 145 10 958 84

Explanation / Answer

Solution :-

Calculation for, the overall average of the means :-

Data - 934, 952, 958, 979, 986, 1007, 1063, 1072, 1080, 1087

Sum of data = 10118

Population size = 10

Average = Sum of data / Count

= 10118 / 10 = 1011.8

Now, Calculating, average range :-

Data - 50, 94, 57, 65, 135, 134, 101, 98, 145, 84

Count = 10

Sum = 963

Average = 963 / 10 = 96.3

The upper and lower control limits for a 99.7% control chart for the mean?

At 99.7% the rule is,

= (Mean - 3 × std) and (Mean + 3 × std)

Here, mean = 1011.8

Standard deviation = 58.5

Therefore, Lower and Upper control limits

= (1011.8 - 3 * 58.5) and (1011.8 + 3 * 58.5)

= 836.3 and 1187.3

Thus we say, 99.7% of the values fall between 836.3 and 1187.3.

Does this process appear to be in control?

In-control, process are those, whose measure under evaluation is in a state of statistical control.

Yes, the process does appear to be in control.

Calculate upper and lower control limits for the range.

Using the same formula above, we get

99.7% of the values fall between -4.5 and 197.1.

Do these samples indicate that the process is in control?

No, these samples indicate that the process is not in control.

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