AGENDA Nonterminating analysis End term review LECTURE 17 Non-terminating Analysis TYPES OF NON-TERMINATING SYSTEMS Most manufacturing systems Service systems that do not close Service systems where the customer leaves something to be picked up at another time Examples Automobile plant Repair facilities Hospitals NON-TERMINATING SYSTEM TIME TACTICAL CONSIDERATIONS Starting conditions… Determining steady state… Autocorrelation… Length of replication… Batch method… STARTING CONDITIONS Begin with the system empty Preferred Begin with the system loaded How many to load with? DETERMIING STEADY STATE Must eliminate initial transient Graphical approach… Linear regression approach… GRAPHICAL APPROACH Visually determine when the slope of the initial transient approaches 0 Highly subjective and influenced by individual interpretation Not recommended LINEAR REGRESSION Uses the least squares method to determine where the initial transient ends If the observations’ slope is not zero, advance the range to a later set of observations Eventually the range of data will have an insignificant slope coefficient Steady state behavior has been reached AUTOCORRELATION Correlation between performance measure observations in the system Possible issue with non-terminating systems Problem if not addressed Practitioner may underestimate variance Results in the possibility of concluding that there is a difference when this actual is not Methods to address Can be accounted for by complex calculations Can be avoided by special techniques BATCH METHOD Identify the non-significant correlation lag size Make a batch 10 times the size of the lag Make the steady state replication run length 10 batches long EXAMPLE Run single replication for 10,000 minutes Observe 4000 entities Initial transient requires 2000 minutes Steady state for 8000 minutes EXAMPLE DETERMINE RUN LENGTH Non-significant lag occurs at 200 observations Batch size 200 x 10 = 2000 observations to remove autocorrelation 2000 x 10 batches = 20000 total observations Time for each observation 10000 / 4000 = 2.5 minutes per observation Total simulation length must be 2000 + 20000 x 2.5 = 52000 minutes FINAL ANALYSIS Remove initial transients Split remainder into 10 batches / replications Process just like terminating simulations REVIEW Verification Validation Replication analysis Experimental Design Output analysis of two systems Output analysis of more than two systems VERIFICATION What is it? How do you do it? VALIDATION Face Statistical Data collection issues Modeling issues Process Check for normality with chisquared test F-test Independent-T, equal variance Smith-Satterwaithe unequal variance Non-parametric test REPLICATION ANALYSIS Relative precision approach Procedure EXPERIMENTAL DESIGN Factors Levels 2^k designs TWO SYSTEMS Very simple simulation studies Welch CI approach... WELCH CI APPROACH Assumes worst case with respect to variance Uses CI based on adjusting degrees of freedom MORE THAN TWO SYSTEMS One Way Analysis of Variance... Duncan Multiple Ranges Test ... ANOVA Calculate Sums of squares Mean sums of squares F statistic Interpret results DUNCAN MULTIPLE RANGE TEST Calculate least significant range values Determine ranges with no statistical difference Graphically represent results Be able to provide recommendations