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Operations Management Student Name _______________________.

Skill Builder Exercise #3

Problem 1.

Resistor for electronic circuits are manufactured on a high-speed automated machine. The machine

is set up to produce a large run of resistors of 1,000 ohms each.

To set up the machine and to create a control chart to be used throughout the run, 15 samples weretaken with four resistors in each sample. The complete list of samples and their measured alues are

as follows!Sample # Readings (in ohms)

1 1010 991 985 986

2 995 996 1009 994

3 990 1003 1015 10084 1015 1020 1009 998

5 1013 1019 1005 993

6 994 1001 994 1005

7 989 992 982 1020

8 1001 986 996 996

9 1006 989 1005 1007

10 992 1007 1006 979

11 996 1006 997 989

12 1019 996 991 1011

13 981 991 989 1003

14 999 993 988 984

15 1013 1002 1005 992

a" #10 points" $alculate control limits for R-chart.

b" #10 points" $alculate control limits for x -chart.

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c" #%0 points" &rom the charts, what comments can 'ou make about the process(

Problem2:

)eeral complaints recentl' hae been sent to the *otham $it' police department regarding theincreasing incidence of congestion on the cit'+s streets. The complaints attribute the cause of

these traffic tie-ups to a lack of s'nchroniation of the traffic lights. The lights are controlled b'

a main computer s'stem, and adusting this program is costl'. Therefore, the controllers are

reluctant to change the situation unless a clear need is shown.uring the past 'ear, the police department has collected data at 1,000 intersections. The data

were compiled on a monthl' basis as shown below!

Month Congestion IncidenceJanuary 14

February 18

March 14

April 12

May 16

June 8

July 19

August 12

September 14

ct!ber 7

"!#ember 10

$ecember 18

a) #%0 points" $ompute the following parameters

Mean proportion! ///////////////////

)tandard deiation! ///////////////////

b) #10 points" $alculate control limits and draw the control chart #use a multiple of times

sigma for the control limits".

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$2! ////////////////////

2$2! /////////////////////

d" #10 points" 3 new sample is collected at the ne4t anuar'. Out of 1000 intersections there are 15congestion incidences. 6s the process in control( 3nd wh'(

Problem 3:#%0 points" $-)pec, 6nc. is attempting to determine whether an e4isting machine is

capable of milling an engine part that has a ke' specification of 780.00 inches. 3fter a trial run on

this machine, $-)pec has determined that the machine has a sample mean of 7.001 inches with astandard deiation of 0.0015 inch.

)hould $-)pec use this machine to produce this part( 9h'(