טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentShai Yair
SubjectSequential Testing of Hypotheses about Ratio of Two
Exponential Scale Parameters
DepartmentDepartment of Quality Assurance and Reliability
Supervisor Dr. Yefim Haim Michlin


Abstract

In evaluation of competing systems with the MTBF as the comparison parameter, the competitors often have to be tested simultaneously. Thus, on the one hand, uncontrolled factors are neutralized, but on the other, one has to deal with random MTBF values. A survey indicates that sequential testing for exponential distribution of the TBF is important and common, but there is no reference to comparative experimentation. An approach to construction of sequential tests based on the Monte-Carlo method was developed at the Technion (Michlin 2002) and applied in comparative experimentation (Michlin and Migdali 2002). This solution, however, concerned a particular case and entailed a lengthy iterative process towards the decision parameters for acceptance/rejection of the null hypothesis and prediction of the test duration. In this work a method was developed, enabling the user to find the required parameters for designing the comparative sequential test and predict its duration directly, dispensing with the Monte-Carlo method. The development process involved study of the interdependences of the parameters which in turn yielded the requisite formulas. Unlike an earlier work (Michlin and Migdali 2004), a method was found for successive expression, stage by stage, of the test results and of the plottable accept/reject bounds. Moreover, it was also found that the accept/reject bounds meet, and this point limits the maximum test duration. Formulas for calculating the comparative sequential test parameters and predicting its duration immediately upon receipt of the test specifications make for lower cost, more efficient design, simplicity and better practicability.