Case Study $1($Summer $2024)$ Due Tuesday, June $11,2024$

Instructions

Complete the questions listed below and submit electronically in the drop box.

$1.$ Productivity

Brown$$s$,$ a local bakery, is worried about increased costs$$particularly energy. Last year$$s records can provide a fairly good estimate of the parameters for this year. Wende Brown, the owner, does not believe things have changed much, but she did invest an additional $$3,000$ for modifications to the bakery$$s ovens to make them more energy efficient. The modifications were supposed to make the ovens at least $15\%$ more efficient. Brown has asked you to check the energy savings of the new ovens and also to look over other measures of the bakery$$s productivity to see if the modifications were beneficial. You have the following data to work with:

Last Year

This Year

Production

$1500$

$1500$

Labor

$350$

$325$

Capital Investment $($$$)$

$$15000$

$$18000$

Energy

$3000$

$2750$

$2.$ Location Strategy

A location analysis for Cook Controls, a small manufacturer of parts for high$-$technology cable systems, has been narrowed down to four locations. Cook will need to train assemblers, testers, and robotics maintainers in local training centers. Lori Cook, the president, has asked each potential site to offer training programs, tax breaks, and other industrial incentives. The critical factors, their weights, and the ratings for each location are shown in the following table. High scores represent favorable values.

$3.$ Statistical Process Control

a$.$ Twelve samples, each containing five parts, were taken from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were:

a$)$ Determine the upper and lower control limits and the overall means for x$-$charts and R$-$charts. b$)$ Draw the charts and plot the values of the sample means and ranges. c$)$ Do the data indicate a process that is in control?

b$.$ One of New England Air$$s top competitive priorities is on$-$time arrivals. Quality VP Clair Bond decided to person$-$ ally monitor New England Air$$s performance. Each week for the past $30$ weeks, Bond checked a random sample of $100$ flight arrivals for on$-$time performance. The table that follows contains the number of flights that did not meet New England Air$$s definition of $$on time$$:

a$)$ Using a $95\%$ confidence $($Z$=2)$ level, plot the overall percentage of late flights $($p$)$ and the upper and lower control limits on a control chart. b$)$ Assume that the airline industry$$s upper and lower control limits for flights that are not on time are $\mathrm{.}1000$ and $\mathrm{.}0400,$ respectively. Draw them on your control chart.

c$.$ The manager of an organic yogurt processing plant desires a quality specification with a mean of $16$ ounces, an upper specification limit of $16\mathrm{.}5,$ and a lower specification limit of $15\mathrm{.}5.$ The process has a mean of $16$ ounces and a standard deviation of $1$ ounce. Determine the Cpk of the process.