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Comparing Rates

DATA:

Defective Nondefective

Domestic Clients:
Layog 3 293
Togram 12 307
Jones 131 2368

Overseas clients
Layog 255 1247
Togram 75 359
Jones 81 123

ASSIGNMENT:

Provide an analysis of the situation at your company and a recommendation of what action, if any, should be taken. In particular, you should address the following issues:

a) Is Jones correct? That is, using the more complete data set, is it true that Jones has the lowest defect rate overall? Are Jones's percentages correct overall (i.e. combining domestic and overseas production)?

b) Is Layog correct? That is, what percentage of Layog's production was more demanding? How does it compare to the other two managers? (Note: you may wish to compare conditional probabilities, given the managers, combining defective and nondefective production.)

c) Look carefully at the conditional defect rates given various combinations of manager and production client. What do you find?

d) Should you recommend that Layog start looking for another job? If not, what do you suggest? (Hint: One way to approach this problem would be to employ the following experiment. Based on the available production information, what would be the anticipated outcome of removing one of the production managers and splitting all of their production among the remaining managers.) What other concerns might you need to take into account when considering a possible course of action?

CASE REPORT:

You work for a company that produces air filtration systems for use in commercial buildings. A recent SARS (Severe Acute Respiratory Syndrome) alert sent your sales through the roof as customers looked to exploit a special design aspect of your products that aids in preventing the transmission of airborne diseases. Accompanying the recent sales increase, there has been a rise in the defect rate for a sensitive and crucial component of your filtration systems, namely the primary air pump. The air pump is constructed on a production line under the supervision of a manager controlling important aspects of the production process. The responsibility has fallen on your shoulders to identify the problem so that it can be fixed. Two of the three production line managers (Jones, Layog and Togram) have already been in to see you, and their stories are intriguing. Some accuse Jones of being the problem, using words like "careless" based on anecdotal evidence of performance. Some of this is ordinary office politics to be discounted, of course, but you feel that the possibility should certainly be investigated nonetheless. Jones has countered by saying that defects are actually produced at a high rate when others are in charge, and that Layog has a much higher error rate. To support his position, Jones provides the following data:

Percent defect
Layog 14.35%
Jones 7.84%

Soon after, Layog, not known for his tact, comes into your office, yelling that Jones is not to be believed. After calming down somewhat, there is mumbling - something about being given difficult assignments by the upper-level management. However, even when asked directly, the high error rate is not denied. You are suspicious. It certainly appears that you have found the problem. However, you also know that Layog has a good reputation among technical experts and that he should not be accused without first considering possible explanations and alternatives.

Decide that it would be prudent to look at Togram's error rates, as well as the two primary types of production - one for domestic clients and one for overseas clients.

Overseas clients are much more demanding as to the specifications of the pump primarily due to stricter regulations in Europe that require the system to filter out more particulate matter. Below, you will find more complete data, consisting of counts of items produced recently.

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You work for a company that produces air filtration systems for use in commercial buildings. A recent SARS (Severe Acute Respiratory Syndrome) alert sent your sales through the roof as customers looked to exploit a special design aspect of your products that aids in preventing the transmission of airborne diseases. Accompanying the recent sales increase, there has been a rise in the defect rate for a sensitive and crucial component of your filtration systems, namely the primary air pump. The air pump is constructed on a production line under the supervision of a manager controlling important aspects of the production process. The responsibility has fallen on your shoulders to identify the problem so that it can be fixed. Two of the three production line managers (Jones, Layog and Togram) have already been in to see you, and their stories are intriguing. Some accuse Jones of being the problem, using words like "careless" based on anecdotal evidence of performance. Some of this is ordinary office politics to be discounted, of course, but you feel that the possibility should certainly be investigated nonetheless. Jones has countered by saying that defects are actually produced at a high rate when others are in charge, and that Layog has a much higher error rate. To support his position, Jones provides the following data:

Percent defect
Layog 14.35%
Jones 7.84%

Soon after, Layog, not known for his tact, comes into your office, yelling that Jones is not to be believed. After calming down somewhat, there is mumbling - something about being given difficult assignments by the upper-level management. However, even when asked directly, the high error rate is not denied. You are suspicious. It certainly appears that you have found the problem. However, you also know that Layog has a good reputation among technical experts and that he should not be accused without first considering possible explanations and alternatives.

There is an increased error rate in the production. There are 3 managers. Is Jones the problem because he is "careless"? Is Layog the problem (14.35% defect rate)? What about Togram?

Decide that it would be prudent to look at Togram's error rates, as well as the two primary types of production - one for domestic clients and one for overseas clients.

Overseas clients are much more demanding as to the specifications of the pump primarily due to stricter regulations in Europe that require the system to filter out more particulate matter. Below, you will find more complete data, consisting of counts of items produced recently.

Defective Nondefective
Domestic ...

$2.19