OPS MGMT Assignment 3 Two Problems

1. Some citizens complained to Victoria city council members that there should be equal protection

under the law against the occurrence of crimes. The citizens argued that this equal protection should

be interpreted as indicating that high-crime areas should have more police protection than low crime

areas. Therefore, police patrols and other methods for preventing crime (such as street lighting or

cleaning up abandoned areas and building) should be used proportionately to crime occurrence.

The city is divided into 20 geographical areas, each containing 5000 residences. The 1000 sampled

from each area showed the following incidences of crime during the past month:

Area Crimes

Sample

Size

1 14 1000

2 3 1000

3 19 1000

4 18 1000

5 14 1000

6 28 1000

7 10 1000

8 18 1000

9 12 1000

10 3 1000

11 20 1000

12 15 1000

13 12 1000

14 14 1000

15 10 1000

16 30 1000

17 4 1000

18 20 1000

19 6 1000

20 30 1000

Suggest a reallocation of crime protection effort based on a p-chart analysis. Use a 95% confidence level

( i.e. z = 1.96)2. The following table containsthe measurement of the key length dimension from a fuel injector. These

sample of size five were taken at one hour interval.

Sample number 1 2 3 4 5

1 .486 .499 .493 .511 .481

2 .499 .506 .516 .494 .529

3 .496 .500 .515 .488 .521

4 .495 .506 .483 .487 .489

5 .472 .502 .526 .469 .481

6 .473 .495 .507 .493 .506

7 .495 .512 .490 .471 .504

8 .525 .501 .498 .474 .485

9 .497 .501 .517 .506 .516

10 .495 .505 .516 .511 .497

11 .495 .482 .468 .492 .492

12 .483 .459 .526 .506 .522

13 .521 .512 .493 .525 .510

14 .487 .521 .507 .501 .500

15 .493 .516 .499 .511 .513

16 .473 .506 .479 .480 .523

17 .477 .485 .513 .484 .496

18 .515 .493 .493 .485 .475

19 .511 .536 .486 .497 .491

20 .509 .490 .470 .504 .512

Construct a three sigma X-bar chart and R chart for the length of the fuel. What can you say about this

process?