The OC curve and the information above is what you encounter. The chances of getting a shift
Question:
The OC curve and the information above is what you encounter. The chances of getting a shift in the parameter in a random day are given in the below frequency distribution;
Shift: | ±0.005 | ±0.010 | ±0.015 | ±0.020 | ±0.025 |
P(Shift): | 0.011 | 0.008 | 0.005 | 0.003 | 0.001 |
Whenever there’s a shift, it takes 1hour to reconfigure the production line as a separate setup cost. You stop the production, reset everything and start again. You lose all profit during that time.
You produce 200 items per hour. You sell each item for $5. The number of defective items produced depend on your sample size and ARL.
When you sample, you do destructive testing. So a revenue worth your sample size becomes void. Also you have a testing cost of $0.2 per item tested.
REGULAR:
- Simulate this problem. Generate a sample arithmetic mean based on the frequency table above to generate shifts (a MonteCarlo Simulation could help).
- Make a daily table (stretch it for a couple of years). Let sample size be a variable. Play around with the model to decide on the optimal sample size.
- Your model should,
- Calculate net profit
- Calculate testing costs
- Calculate defective production costs
- Calculate setup costs
KING SIZE:
- Copy your model to another sheet and try to incorporate;
- False alarms (use probabilities based on Z, and make Excel decide if an out of bounds point is a false alarm)
- Type II errors (use type II error probabilities combined with the frequency table above to decide whether an in control point is actually an unlucky out of control point)
Business Statistics a decision making approach
ISBN: 978-0133021844
9th edition
Authors: David F. Groebner, Patrick W. Shannon, Phillip C. Fry