M.Sc Student | Leshchenko Elena |
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Subject | Time to Decision in Sequential Test for Parameter Ratio of Two Exponential Distributions |

Department | Department of Quality Assurance and Reliability |

Supervisor | Dr. Yefim Haim Michlin |

Full Thesis text - in Hebrew |

The present work deals with comparison testing of two systems: one
“basic” (subscript *b*) and the other “new” (subscript *n*) with
exponentially distributed times between failures. In there tests, the
hypothesis is checked that the ratio of the means of these times (MTBF_{n}/MTBF_{b}) equals a
specified value, versus the alternative that it is smaller than the latter.

In the present work, the considered test procedure was converted into binomial form, where we were able to make use of the well-known SPRT theory. This in turn made for drastic saving in computer time for determination of the test characteristics, and considerably simplified that of the test boundaries, which are parallel straight lines.

In these tests the duration is an indefinite random value, i.e. it can far exceed the average, with the attendant practical inconvenience. The remedy is provided by truncating the test. Since this makes for an increased average test time, the truncation type should be chosen on the basis of analysis of the average sample number (ASN) and operating characteristic (OC) of the test.

The various commonly used types of truncation, and their influence on the test features, were examined and compared, with the non-truncated version as reference. In binomial tests the most widely used type is truncation by straight lines - a single line parallel to one of the coordinate axes, or a pair parallel to both. The last-named version, with the lines intersecting at a point called the truncation apex (TA), was found to be optimal, permitting the heaviest truncation and involving the least increase in the ASN.

The problem of determination of the optimal TA was studied for the
particular case *α = β *. The relevant criterion
was developed, and an evaluation index R * _{ASN}* proposed for
increase of the ASN versus the non-truncated test. It was found that for this
particular case the optimal points lie closest to the centerline through the
origin, parallel to the test boundaries.

An algorithm was developed for finding the TA at the maximal possible truncation, as well as at the heaviest truncation with given percentage increase in the ASN versus the non-truncated test. An approximative formula was obtained for the TA coordinates.

On the basis of the above findings, a planner’s algorithm was developed for the test type in question, and a program for recursive calculation of the decision probabilities at given points of the test, which serve as basis for exact calculation of the truncated test characteristics.