Chapter 7 Apply Your Understanding

Sammys Jumbo Franks (Textbook Page 260)

Late last month, Jim Runnels, a sales representative for Sammys Jumbo Franks (SJF), was called to the office of the Greenville Coliseum and Sport Complex, his largest account. The manager for food and beverages for the Greenville Coliseum was complaining that the jumbo hot dogs it had received over the last couple of weeks were not within the specified range of 4.95.1 oz.

The off-weight hot dogs had not been detected by the coliseums receiving staff. The problem arose when the coliseum began serving the hot dogs to people attending sporting and other events. In particular, the off-size hot dogs created two problems for the coliseum: the hot dogs were either too big or too small for the hot dog buns, and the variation in the weights meant that standard cooking times resulted in either over- or undercooking the hot dogs.

In consequence, the coliseum had to issue special cooking instructions to all of its food servers that required them to weigh each hot dog and sort them by weight so that batches of similar weight hot dogs could be cooked together. The manager of food services at the coliseum made it clear that a new supplier for jumbo hot dogs would be sought if this problem continued. SJFs quality control department was immediately summoned to assist in determining the cause of the problem.

SJFs quality manager, Ronald Wilson, speculated that the cause of the problem was with the second shift. To analyze the problem, he entered into a spreadsheet the data from all the previous samples taken over the last two months. As it turned out, 15 random samples had been taken over the two-month period for both the first and the second shifts. Samples always consisted of 10 randomly selected hot dogs. Also, separate sampling schedules were used for the first and second shifts so that the second shift would not automatically assume that it would be subject to a random sample just because the first shift had been earlier in the day.

After entering the sample weight data of the hot dogs into the following spreadsheet and calculating the sample means, Ronald was quite puzzled. There did not seem to be any noticeable difference in the average weights across the two shifts. Furthermore, although the lines were running at less than full capacity during the first six samples, there still did not seem to be any change in either line after reaching full production with the start of the basketball season.

1. Show the X-bar control chart for the two shifts. (hint: you can get UCL and LCL for sample means from page 253) (10 points) Can you identify any difference between the first and second shifts that explains the weight problem? If so, when is this difference first detectable? (10 points)
2. Show the range charts for the two shifts. (hint: you can get UCL and LCL for sample range from page 253) (10 points). What can you learn from the range charts? (10 points)