A chocolate factory has weighed 4 chocolate truffles coming out of production over 5 working days to obtain the following data, weights are in grams.
Mon Tue Wed Thu Fri
10am 30.50 30.30 30.15 30.60 30.15
11am 29.75 31.00 29.50 32.00 30.25
2pm 29.90 30.20 29.75 30.10 30.50
3pm 30.25 30.50 30.00 30.00 29.70
a) Group the data by day into five samples and find the sample average and range for each sample.
b) Suppose the process has a mean of 30 and a standard deviation of 0.3. Construct the 3 - sigma control limits of the mean chart. Is the process mean under control? [Hint: you can just provide the limits and don’t need to draw a graph].
c) Construct the control limits of the range chart. Is the process range under control? [Hint: you can just provide the limits and don’t need to draw a graph]
d) Suppose the process has a standard deviation of 0.2. The factory quality assurance requires rework for chocolate truffles weighted less than 28.5 grams, or more than 31.5. What is the capability ratio of the current process?
Please give explanations