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Kilgore Manufacturing, Inc. (KMI) is a small manufacturing company in the St. Louis area that produces components used in the aerospace industry. James Kilgore, the president and owner of KMI, started the company five years ago. Although business has been reasonably steady for the last two years, KMI has yet to establish any long-term relationships with major aerospace contractors. This is important, because small companies like KMI only get business as subcontractors to the large aerospace manufacturing companies that win major contracts, many of which are with the federal government.

In the aerospace business, after the federal government awards a new defense project to the major aerospace contractors, these companies, in turn, send out a request for subcontractor bids to smaller companies like KMI for specific work related to the project. Often, the subcontract goes to the company with the lowest bid for the required work. Cost overruns in federal government contracts are commonplace, but are becoming increasingly less accepted. In their desire to win subcontracts from the major aerospace companies, some subcontractors submit unreasonably low bids to perform the work on specific aspects of a major project. Recently, the federal government has been cracking down severely on the major contractors, who in turn have demanded more accountability from their subcontractors. More and more contracts between the major contractor and its subcontractors are including harsher penalties for low production levels, late deliveries, cost overruns, and other failures by the subcontractors to meet the promises. Jim Kilgore has just learned that a new defense contract has been awarded to one of the major aerospace contractors. A certain system in the project requires one of the components produced by KMI, a relay switch manufactured by only three other companies in the U.S. After finding out about the new contract, Jim Kilgore held a strategy meeting with Tim Reynolds, vice-president of manufacturing, and Bill Shelton, plant manager.

So, the goal of KMI is to provide a low bid, but also be accurate in terms of predictions, so that they don't get charged penalties.

Jim: "I don't know if you have heard yet, but a new contract has been awarded to Avionics, Inc. The good news for us is that our R-7 relay switch plays a big role in the project. I think this is the opportunity we have been waiting for. One of my contacts in Washington has given me enough information to estimate that the project will require at least 600 R-7 relay switches per day. But, my guess is that the subcontract will be awarded to the company that can provide the largest number of relay switches per day at the lowest cost to the government. Fortunately, our current contracts for the R-7 are about to run out so that we could devote the entire line of production to this new contract with Avionics. What do you think of this possibility, Bill?"

Bill: "We can easily meet the 6O0-per-day quota. Our production data over the past two years show an average daily production run of around 635 relay switches per day when we're running at full capacity."

Jim: "That's well and good, Bill, but we also need to know something about the amount of variability in daily production levels. In this new subcontract, we have to specify a guaranteed minimum level of daily production in addition to an average or typical daily production level. The government is really serious about contractors and subcontractors meeting their obligations. On those days we fall short of the guaranteed minimum, a $5,000 penalty is assessed!. I know it is steep. However, we do want to play the game. I want this contract; it's the break we've been looking for to get in solid with one of the key aerospace manufacturers. We can't afford, however, to lose money on this contract."

Bill: "Well, let's see what we know. Over the past two years, our lowest daily production run was 494 units and the highest was 768 units. In fact, if I remember right, the actual distribution of daily production levels is described fairly well by a normal distribution with a mean of about 635 units and a standard deviation of about 40 units."

KMI wants to show that they can make at least 600 relay switches per day. For each day they make less than 600, they get charged $5000. Currently, they make an average of 635 per day (range = 494 to 768), with a standard deviation of 40. These numbers are from a 2 year sample.

Tim: "So there are definitely days when ...