Checkout time at a supermarket is monitored using a mean (x-bar) and a range chart. Six samples ofn = 20 observations have been obtained and the sample means and ranges (in minutes) were computed as follows:

Sample Mean Range

1 3.06 0.42

2 3.15 0.50

3 3.11 0.41

4 3.13 0.46

5 3.06 0.46

6 3.09 0.45

Determine the 3-sigma upper and lower limits for mean (x-bar) and range charts. Is the process in control? Explain.

Problem #2

Given the following data for the number of defects per spool of cable, using 3-sigma limits, is the process in control?

Observations

1 2 3 4 5 6 7 8 9 10 11 12 13 14

Number of defects 2 3 1 0 1 3 2 0 2 1 3 1 2 0

Problem #3

Given the following list of machines, the standard deviation for each, and specifications for a job that may be processed on that machine, determine which machine(s) arecapable of performing the given jobs.

Machine Standard Deviation (in.) Job Specification (+/- in.)

001 0.02 0.05

002 0.04 0.07

003 0.10 0.18

004 0.05 0.15

005 0.01 0.04

Problem #4

A car radio supplier is going to open a new plant., and is trying to decide on whether to locate in Dallas or Detroit. Given the following costs:

Dallas Detroit

Fixed costs $600,000 $800,000

Variable costs $28/radio $22/radio

a) Perform an analysis of the volume over which each location is preferable.

b) How does your answer change if Dallas’s fixed costs increase by 10%?