טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentAlmog Nadav
SubjectA Non-Simulative Approach in Development of Sequential Test
for Parameter Ratio of Two Exponential
Distributions
DepartmentDepartment of Quality Assurance and Reliability
Supervisor Dr. Yefim Haim Michlin


Abstract

When a proposed new system (technology/product) has to be evaluated against the existing (basic) version, it should be checked whether the reliability of the latter has not been impaired. As a comparative decision tool, sequential hypothesis tests are arranged for system lifetime by examining the Time Between Failures parameter (TBF). For cases of lack of information about a proposed system's MTBF, a new parameter has to be introduced, namely the scale parameters ratio of the two system distributions.


A literature survey brought out sequential tests for MTBF estimates, but not for those of MTBF ratios of a pair of products. Two papers dealing with comparative sequential testing were published at the Technion. The first paper dealt with a particular case of the problem. In the second paper, the solution range was enlarged but still remained limited, and further enlargement will necessitate additional research with the risk of inadequate results for the required (a,b) pairs (error probabilities of the first and second kind). Both papers adopted the lately common simulative approach in sequential testing (Monte Carlo method).


The present work is based on direct determination of the α's and β's, replacing the time-consuming conventional simulative approach. The required probabilities are calculated by a specially-developed Matlab-based program which yields null hypothesis acceptance/rejection point positions, according to the sequential test regions in the α-β plane. Summing of the probabilities of the points yields the user's sought α & β.


A second Matlab-based program, operating an appropriate optimization function, searches out automatically the α* and β* parameters determining the decision boundaries and ensuring the required α, β.


The present work provided an answer to a hitherto unresolved aspect diagnosed during previous work at the Technion, namely the discontinuity problem, which concerns regions in which a solution is moot. The answer was based on the observed influence of the decision point pairs (for acceptance/rejection of the null hypothesis) on the above layout. This direction, in conjunction with the developed optimization method, provided a complete solution for the discontinuity problem, enabling the user to choose any required (a,b) pair, with the maximum deviation reduced to several tenths of a percent per pair.


The proposed method makes for automatic and fast design of the sequential test for the user. The research contributes to the comparative sequential testing discipline.