1ISE 311

Occurrence Sampling Problem: how do you know how much time a particular

person, group, or function is spending on any given activity? e.g., How much of a student’s time is spent waiting for a report

to print in the computer lab during ‘peak’ times? How much of the maintenance technicians’ time is spent

waiting for repair calls?

One solution – continuous time study expensive not well suited for nonstandard work

Alternatively – discrete sampling select random sample of population record activities at discrete intervals

2ISE 311

Determining Sample Size Law of diminishing returns

amount of information grows proportionately with the square root of sample size, n

cost of information grows directly with n therefore, there will be a sample size beyond which additional

information is not worth the cost of additional study

Sample size depends on … desired absolute accuracy, A

note difference between absolute and relative accuracy, s (estimated) proportion of occurrence, p desired confidence level, c

3ISE 311

Sample size example It is estimated that students in the computer lab must

wait in line for their document to print about 45% of the time. To justify an additional printer, you wish to verify that estimate within 15% (relative accuracy) and with a confidence level of 90%.

Solution,

p = 0.4

A = (0.45)(0.15) = 0.0675

c = 90% z = ± 1.64

)1()1(

2

2

2

2

A

ppz

ps

pzn

table 10.1, pg. 137

0.45 0.51750.3825

+.0675-.0675

4ISE 311

Sampling – design and data collection Overcoming the 3 problems in obtaining a

representative sample: Define reasonable strata (categories) for data collection

time of day (morning, afternoon, evening, etc.) day of week (or weekend/weekday, week in the month, etc.) gender region socio-economic status level of education / training etc. Base sample size on smallest estimated proportion

Randomness defining random sampling times/locations randomness with restrictions

table 10.3, pg. 142 (ERGO, Excel)

5ISE 311

Data Gathering Who & how?

person or machine? additional duty for employee or hire temp? automated data collection?

level of detail the problem of influence

does the presence of the observer affect the actions or performance of the entity being observed?

techniques to minimize influence unobtrusive observation

random sample distance, video, etc. communication with the observed

6ISE 311

Data Analysis & Use Comparing frequency data

procedure on pg. 145

Example: is there a difference in number of times there are students waiting for printouts between morning and afternoon?

na = nb = 100

Strata Times Waiting Times not Waiting

morning 36 64

afternoon 25 75

7ISE 311

Frequency example Solution,

1. Smallest of 4 numbers = 25

2. Other number in the column = 36

3. “Observed contrast” = 11

4. from Table 10.4, minimum contrast = ______

5. Compare observed contrast

Answer: Morning is / is not different from afternoon.

8ISE 311

Other comparison methods χ2 (independence) or t-test to test for significant difference in

means control charts to test for time (or sequence) effects

Purpose of the analysis – determine if data should remain stratified or can be combined if no difference, combine data and refer to overall proportions if there is a difference, keep data, analysis, and conclusions

separate

Data Analysis & Use