I'm in my last semester of school, and I'm trying my damndest to complete this course. The problem is, i'm supposed to write a paper as a response to the question below, only every time I work it out, I'm wrong. Can someone tell me how to solve this? Thanks.
Your company produces and sells widgets with annual sales of $100 million. A recent quality audit revealed that 15% of the widgets manufactured were defective. The following are estimates of the costs associated with passing defective widgets:
Replacements
$1,500,000
Lost Business
2,000,000
Productivity
500,000
Liability Claims
6,000,000
Total Costs
$10,000,000
The executive team feels that the costs of passing defective widgets are much too high and that costs associated with defects should not exceed 1% of total sales. To attain this goal, the team wants to implement a quality assurance program using inspections. They have determined that inspections of raw materials, manufacturing processes, and finished products are necessary. The cost of inspecting each production lot at all three of these stages is $500 per lot.
Two million widgets are to be produced in lots of 100 widgets each. Given the cost of inspection the executive team feels that it is not practical to inspect every lot during each phase.
The executive team has asked you to complete the following task.
Task:
Determine the predicted number of inspections that would be necessary to reach the cost of passing defective widgets not exceeding 1% of total sales. Explain the approach you used to arrive at your answer.
You think they could give you more info... Profit margin of each widget sold, advertising budget, overhead, unionized labor force?, but I guess it's suppose to be a perfect world scenario....
Well, It doesn't seem like there is a clear cut numeric answer that is right. You can't arbitrarily test 10, 20, 50, 60, et...% of outgoing widgets in the hope of catching 15% of the defects. Essentially you will end up spending as much in testing as you would in compensation, then what's the point? Maybe customer satisfaction...I've formed an answer on what "I" personally would say in my paper, however I'm not going to give you an answer to a problem solving exercise whos point is in how you solve it. However, here's some things you should look at:
- What's 1% of the total sales? * This is your ceiling.
- Widgets cost $50 each
- There's 100 widgets in a lot and lot inspections are $500 each
- How many lots go out.
I'd also be curious as to how the inspections breakdown by raw materials, manufacturing, and final inspection, as well as what the costs would be between just running final inspection and recycling defects back into manufacturing/materials, but I guess for this problem it doesn't matter.
You need to attain resonable assurance that you are actually testing a representative sample of the population. There is some Stat work involved in this, I would assume.
Heh. I just noticed that it gave you a nice little problem. 15% of production is defective - or 300,000 units, the cost to test a random 15% of production would be $1,500,000 or 50% over budget.
You can test a maximum of 200,000 units at a cost of $1,000,000.
What an acceptable level of defects? Does it tell you how much of an increase in efficiency is expected as a result of the new testing system?
Answer: Call McKinsey. Offer then $1,000,000 to solve this problem. Try not to cry when they laugh and hang up. Gather yourself, and call Accenture. Do not admit this to your friends. Allow them to waste a year of your time, distract any efficient managers in the organization, waste 12% of budget on expenses and then leave you in a situation that will take you another year to analyze.
I just noticed the liability claims part. Couldn't you spend $500,000 on a warning label and then the remaining $500k whittling down the number of defective units?
That first $500,000 has a huge bang-for-the-buck quotient.
I just noticed the liability claims part. Couldn't you spend $500,000 on a warning label and then the remaining $500k whittling down the number of defective units?
That first $500,000 has a huge bang-for-the-buck quotient.
I don't think, for the purposes of this problem, that you can break out individual defect costs. I think it's just a flat $10MM for the whole 15% defect thing. Reduce defect costs + add inspection costs = $1MM.
I don't think, for the purposes of this problem, that you can break out individual defect costs. I think it's just a flat $10MM for the whole 15% defect thing. Reduce defect costs + add inspection costs = $1MM.
This is part of the problem and why I believe there is no clear answer, you spend 1Million, yet there is no guaranty that you catch even .01% of defective units without testing them all. If you test 10% of the units and catch even 5% of defects you should buy a lotto ticket, however the other 10% of defects that pass through still hit you in the back end in returns/recalls. So you've spent your $1M budget, yet you still end up losing more than you might had you just tested all 100% of product to begin with. The devil is in the variables. The only way I could come up with a definitive numeric answer was to assume that the defects would be assorted equally across the entire production number, and I don't think that's a very wise assumption for me to make.
This is part of the problem and why I believe there is no clear answer, you spend 1Million, yet there is no guaranty that you catch even .01% of defective units without testing them all. If you test 10% of the units and catch even 5% of defects you should buy a lotto ticket, however the other 10% of defects that pass through still hit you in the back end in returns/recalls. So you've spent your $1M budget, yet you still end up losing more than you might had you just tested all 100% of product to begin with. The devil is in the variables. The only way I could come up with a definitive numeric answer was to assume that the defects would be assorted equally across the entire production number, and I don't think that's a very wise assumption for me to make.
If you are dealing with a completely automated system, with human involvement limited to turning such a system on, then it would be safe to assume a linear distribution (i.e. every sixth item is defective). If we are dealing with a labor intensive process employing minimum wage workers, then you would be safer assuming products produced at certain times/ days are more likely to be defective (i.e. 7AM monday, 4PM Friday, etc).
The only way I could come up with a definitive numeric answer was to assume that the defects would be assorted equally across the entire production number, and I don't think that's a very wise assumption for me to make.
I think that's a fair assumption in this problem - and in general, that's the rationale for random inspections in SPC.
I don't know what level economics this is and if SPC has been introduced but I'm guessing that application of SPC might be part of the solution.
Well the numerical answer I got was 200 lot inspections. Anyone else?
That then implies that you got 100% of the defects and have no defect costs. I still think there's a balance where you get, say, 90% of the 15% defects and pay for the last 10% of the 15% defects.
You forgot to mention the 34 million dollar unexpected CEO buy out when he send your company into the shitter. Oh you said widgets I thought you were talking airlines or Car manufacturers.
