A new industrial oven has just been installed at the Piatt Bakery. To develop ex
ID: 3316923 • Letter: A
Question
A new industrial oven has just been installed at the Piatt Bakery. To develop experience regarding the oven temperature, an inspector reads the temperature at four different places inside the oven each half hour. The first reading, taken at 8:00 A.M, was 340 degrees Fahrenheit. (Only the last two digits are given in the following table to make the computations easier).
Reading
Time 1 2 3 4
8:00
40
50
55
39
8:30
44
42
38
38
9:00
41
45
47
43
9:30
39
39
41
41
10:00
37
42
46
41
10:30
39
40
39
40
Construct an R-chart for this process and comment on whether the process is “in control”. Hint: you must compute the range for each time period. R-bar is calculated by summing all of the ranges and dividing by the total number of ranges. To determine D3 and D4, the number of items in the sample would be the number of temperatures read each time period.
8:00
40
50
55
39
8:30
44
42
38
38
9:00
41
45
47
43
9:30
39
39
41
41
10:00
37
42
46
41
10:30
39
40
39
40
Explanation / Answer
First you need to find the mean of each row, xbar1, xbar2, ... , xbar6, and then the mean of the means, xbarbar. The next step is to find the range of each row and the mean range.
xbar1 = 346
xbar2 = 340.5
xbar3 = 344
xbar4 = 340
xbar5 = 341.5
xbar6 = 337
xbarbar = 341.5
R1 = 16
R2 = 6
R3 = 6
R4 = 2
R5 = 9
R6 = 10
Rbar = 49/6
The Control limits for the X-chart when Rbar is used as an estimate of xBar then the center line and the 3 upper and lower control limits are given by:
3 upper limit = xbarbar + A * Rbar
center line = xbarbar
3 lower limit = xbarbar - A * Rbar
A is found in tables and depends on the sample size. I find the sample size to be 6 and A = 0.483
3 upper limit = 345.4445
center line = 341.5
3 lower limit = 337.5555
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