A Combinatorial Approach for Analyzing Start-Up Demonstration Tests

2016 ◽  
Author(s):  
Amos E. Gera
Keyword(s):  
Combinatorial Approach ◽  
Start Up

scholarly journals A Comparison of Start-Up Demonstration Test Procedures Based on a Combinatorial Approach

2018 ◽  
Vol 3 (3) ◽  
pp. 195-219 ◽  
Author(s):  
Amos E. Gera
Keyword(s):  
Markov Chain ◽  
Comparative Study ◽  
Confidence Level ◽  
Optimization Problem ◽  
Combinatorial Approach ◽  
Constrained Optimization Problem ◽  
Scan Statistic ◽  
Expected Number ◽  
Test Procedures ◽  
Start Up

A comparative study is presented of various start-up demonstration procedures based on a combinatorial approach. The expected number of required tests and the probability of accepting the tested unit are derived using a set of auxiliary functions. A constrained optimization problem is solved for minimizing the number of required tests subject to some confidence level requirements. The variables for this optimization include the total number of successes, failures, and the maximal lengths of runs of successes and failures. Various extensions to scan statistic-based and weighted tests are included and also to the testing of several units in parallel. The alternative Markov Chain embedding approach might involve in some cases the inversion of very large matrices. This disadvantage does not exist here.

scholarly journals Run Statistics Defined on the Multicolor URN Model

2008 ◽  
Vol 45 (04) ◽  
pp. 1007-1023 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Type Systems ◽  
Exact Distribution ◽  
Sampling Scheme ◽  
Combinatorial Approach ◽  
Urn Model ◽  
Joint Distributions ◽  
Start Up ◽  
Exact Distributions ◽  
Binary Trials ◽  
Success Run

Recently, Makri, Philippou and Psillakis (2007b) studied the exact distribution of success run statistics defined on an urn model. They derived the exact distributions of various success run statistics for a sequence of binary trials generated by the Pólya-Eggenberger sampling scheme. In our study we derive the joint distributions of run statistics defined on the multicolor urn model using a simple unified combinatorial approach and extend some of the results of Makri, Philippou and Psillakis (2007b). As a consequence of our results, we obtain the joint distributions of success and failure runs defined on the two-color urn model. The results enable us to compute the characteristics of particular consecutive-type systems and start-up demonstration tests.

scholarly journals Run Statistics Defined on the Multicolor URN Model

2008 ◽  
Vol 45 (4) ◽  
pp. 1007-1023 ◽  
Author(s):  
Serkan Eryilmaz
Keyword(s):  
Type Systems ◽  
Exact Distribution ◽  
Sampling Scheme ◽  
Combinatorial Approach ◽  
Urn Model ◽  
Joint Distributions ◽  
Start Up ◽  
Exact Distributions ◽  
Binary Trials ◽  
Success Run

Recently, Makri, Philippou and Psillakis (2007b) studied the exact distribution of success run statistics defined on an urn model. They derived the exact distributions of various success run statistics for a sequence of binary trials generated by the Pólya-Eggenberger sampling scheme. In our study we derive the joint distributions of run statistics defined on the multicolor urn model using a simple unified combinatorial approach and extend some of the results of Makri, Philippou and Psillakis (2007b). As a consequence of our results, we obtain the joint distributions of success and failure runs defined on the two-color urn model. The results enable us to compute the characteristics of particular consecutive-type systems and start-up demonstration tests.

Start-Up Funds Needed

1990 ◽  
Author(s):  
Keyword(s):  
Start Up

Roles of Entrepreneurial Personality and Job Conditions on Business Start-Up Motivation

2010 ◽  
Author(s):  
Bora Lee ◽  
Elke Schroder ◽  
Rainer Silbereisen
Keyword(s):  
Start Up ◽  
Job Conditions

Nicolas Schulwitz: Alles auf eine Karte

2016 ◽  
Vol 21 (06) ◽  
pp. 70-73
Author(s):  
Christian Schünemann
Keyword(s):  
Online Video ◽  
Start Up

Bei einer Hochzeit hörte Nicolas Schulwitz (32) von einer zündenden Idee: Wie wäre es, mit einer Online-Video-Sprechstunde das Verhältnis von Arzt und Patient zu revolutionieren? Gesagt, getan. Schulwitz kündigte einen sicheren Job und gründete das Start-up-Unternehmen Patientus.

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