Occurrence Sampling n Problem how do you know

Occurrence Sampling n 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? ¨ n One solution – continuous time study expensive ¨ not well suited for nonstandard work ¨ n Alternatively – discrete sampling select random sample of population ¨ record activities at discrete intervals ¨ ISE 311 1

Determining Sample Size n 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 ¨ n Sample size depends on … desired absolute accuracy, A n note difference between absolute and relative accuracy, s ¨ (estimated) proportion of occurrence, p ¨ desired confidence level, c ¨ ISE 311 2

Sample size example n n 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 -. 0675 +. 0675 c = 90% z = ± 1. 64 table 10. 1, pg. 137 ISE 311 0. 3825 0. 45 0. 5175 3

Sampling – design and data collection n Overcoming the 3 problems in obtaining a representative sample: Define reasonable strata (categories) for data collection n time of day (morning, afternoon, evening, etc. ) n day of week (or weekend/weekday, week in the month, etc. ) n gender n region n socio-economic status n level of education / training n etc. Base sample size on smallest estimated proportion ¨ Randomness table 10. 3, pg. n defining random sampling times/locations 142 (ERGO, Excel) n randomness with restrictions ¨ ISE 311 4

Data Gathering n ISE 311 Who & how? ¨ person or machine? ¨ additional duty for employee or hire temp? ¨ automated data collection? n level of detail n the problem of influence ¨ does the presence of the observer affect the actions or performance of the entity being observed? ¨ techniques to minimize influence n unobtrusive observation n random sample n distance, video, etc. n communication with the observed 5

Data Analysis & Use n Comparing frequency data ¨ n procedure on pg. 145 Example: is there a difference in number of times there are students waiting for printouts between morning and afternoon? Strata Times Waiting Times not Waiting morning 36 64 afternoon 25 75 na = nb = 100 ISE 311 6

Frequency example n 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. ISE 311 7

Data Analysis & Use n n ISE 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 8