1 ISE 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

2 ISE 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

3 ISE 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) = c = 90%  z = ± 1.64 table 10.1, pg

4 ISE 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)

5 ISE 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

6 ISE 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? n a = n b = 100 StrataTimes WaitingTimes not Waiting morning3664 afternoon2575

7 ISE 311 Frequency example Solution, 1. Smallest of 4 numbers = Other number in the column = “Observed contrast” = from Table 10.4, minimum contrast = ______ 5. Compare observed contrast Answer: Morning is / is not different from afternoon.

8 ISE 311 Other comparison methods  χ 2 (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