Question

2 2. A bakery is interested in understanding more about the temperature of their ovens. The process calls for an average temperature of 375 degrees Fahrenheit. History has shown the process to have a standard deviation of 9 degrees Fahrenheit. They take 7 measurements during each oven run. They recorded the average of the temperature measurements for each oven run in the table below. i. Construct a 3-Sigma control chart for this process. Sample Average Temperature 1 382 379 3 385 4 372 5 382 6 385 7 372 8 376 9 367 10 388 11 375 12 385 13 384 14 369 15 384 3. The bakery from question 2 wants is exploring their data a little deeper. i. The bakery wants to know the probability of inferring that the baking process is out of control when it is in fact in control. Calculate the risk of Type I error. ii. The bakery wants to know if they could use this chart to detect if the mean oven temperature shifts to 380 degrees Fahrenheit when the first sample is plotted. Calculate the risk of Type II error of the first sample. iii. What is the probability of detecting the shift by the second sample, if the samples are chosen independently?

Answer 1

Que.2

First we find control limits

$\small LCL = \bar{\bar{X}} - 3\frac{\sigma }{\sqrt{n}} = 375 - 3 \frac{9}{\sqrt{7}} = 364.79$

$\small CL = \bar{\bar{X}} = 375$

$\small UCL = \bar{\bar{X}} + 3\frac{\sigma }{\sqrt{n}} = 375 + 3 \frac{9}{\sqrt{7}} = 385.21$

Control Chart :

y 360 365 370 375 380 385 390 0 תם ס ס ס 10 15 ס