Question

Several complaints recently have been sent to the LA city office regarding the increasing incidence of congestion on the city’s streets. The complaints attribute the cause of these traffic tie-ups to a lack of synchronization of the traffic lights. The lights are controlled by a main computer system, and adjusting this program is costly. Therefore, the city is reluctant to change the situation unless a clear need is shown. During the past three months, the office initiated a study and collected 150 data each month at major intersections and identify the # of congestion incidents. The congestion data is shown below.

Month	Congestion Incidents
1	12
2	18
3	15

• Keep 3-decimal if not exact, do not round up. For example, 0.24364....will be kept as 0.243
• Both formats, 0.243 or .243, are acceptable

1. What is the sample size of the study?  
2. What is the p-value of sample 1 (month 1)?  
3. What is the p-bar value of the study?  
4. What is the upper control limit, for a 3-sigma quality standard, based on the above data?  
5. Assume the p-chart for an acceptable traffic congestion rate is [0.02, 0.09], and last month's # of congestions is 203 from a 2300 traffic-observation, what is last month's sample p-value?  Does last month's congestion situation acceptable or not, comparing to the assumed p-chart? (answer Y or N here)

Answer 1

Sample Size = 150 each month

np = 150*3 = 450

Total Congestion = 12+18+15 = 45

p value of Month 1 = 12/150 = 0.08

p-bar = Total Congestion / np

p-bar = 45/450

p-bar = 0.10

UCLp = p-bar + 3*(p-bar*(1-p-bar)/n)^(1/2)

UCLp = 0.10 + 3*(0.10*(1-0.10)/150)^(1/2)

UCLp = 0.173

LCLp = p-bar - 3*(p-bar*(1-p-bar)/n)^(1/2)

LCLp = 0.10 - 3*(0.10*(1-0.10)/150)^(1/2)

LCLp = 0.026

__________________________________________________________________________

Last Month p -value = 230/2300 = 0.088

Since p-value is within the control limit of [0.02, 0.09], hence we can conclude that congestion situation is acceptable.