Arriving at the office a bit early, Ted finds Luke Thorndike in a fit of rage. Mr. Thorndike is sipping coffee and looking over Ted’s notes on the defective racquets that were constructed with aluminum purchased from each of the company’s three suppliers.
In rummaging through the basement crate, Ted has found a total of 30 defective racquets. Of these, 5 were made of aluminum supplied by the Snowmet Corporation and 5 were made of aluminum purchased from Barstow Aluminum, Inc. These were the two suppliers from whom Thorndike Sports Equipment had been buying aluminum for many years, and with good results.
The cause of Mr. Thorndike’s anger is the total of 20 defective racquets made from aluminum purchased from the company’s newest and lowest-priced supplier, Darwood Discount Metals, Inc. Luke recently placed a big order with Darwood, and he is counting the minutes until 10 a.m. so that he can call the West Coast firm, cancel the order, and give Mr. Darwood a big piece of his mind. The arrival of the morning mail only serves to heighten Luke’s anger, as three more complaints are received from disgruntled customers demanding immediate replacements for their broken racquets.
Ten o’clock finally rolls around, and Luke places a person-to-person collect call to Mr. Darwood. After berating Mr. Darwood and his products, Luke demands that the order be canceled immediately. Mr. Darwood does not appreciate the elder Thorndike’s tirade, but he is quite cognizant of the fact that 10% of his company’s profits come from Thorndike Sports Equipment. Though irritated, hepatiently tries to reason with Mr. Thorndike.
According to Mr. Darwood, independent metallurgists have conducted a lot of tests in which they found Darwood aluminum to be every bit as good as the product supplied by Snowmet and Barstow. He suggests that the unusually high number of defective racquets found by Luke is merely a fluke. Already operating on a short fuse, Mr. Thorndike responds that he doesn’t much care for silly rhymes in the middle of the morning, and he warns Darwood not to load any more aluminum onto Thorndike-bound trucks until he and Ted have a chance to further examine the information Ted collected over the weekend. He promises to call Mr. Darwood with a final decision by 3 p.m., Pacific Time.
Ted spends a very busy morning and skips lunch, but by 2 p.m. he comes up with some data that might prove useful. Most important, he has uncovered a research study in which it was found that 0.8% of all aluminum racquets end up being returned as defective. The number of Snowmet and Barstow racquets in the “defectives” crate is about 1% of those produced. However, of the 1200 racquets made from Darwood aluminum, 20 (about 1.7%) are defective. Ted decides to consider the situation as a binomial probability distribution in which the probability of a defect on a given trial is 0.008, corresponding to the research finding that 0.8% of all the aluminum racquets produced are defective. Using the estimate for the entire industry, the expected number of defectives among the 1200 racquets made of Darwood aluminum would be nπ = 1200(0.008), or 9.6, but 20 defectives were observed.
To determine how unusual this result really is, Ted uses Excel and n = 1200, π 5 0.008 to find the cumulative probabilities for the number of defects. The results are shown in Table 6.7.
Receiving a telephone call from home and finding out that the water pipes have just burst and his house is flooding, Ted has to flee the office. On his way out, he asks you to use the information he has found, along with Table 6.7, in giving advice to Mr. Thorndike before he makes his call to Darwood.