Global System for Mobile communication (GSM) is standard set developed by the European Telecommunication Standards Institute to describe technologies for second generation digital cellular network. GSM was created with created with a moderate level of service security. Communications between the subscriber and the base station can be encrypted. GSM uses several cryptographic algorithm for information security. The A5/1 and A5/2 stream ciphers are used for ensuring over the air privacy. However, in the research it will focus only on A5/1 stream cipher algorithm. A5/1 was developed earlier than A5/2 and it is a stronger algorithm used within Europe and United States. However, serious weaknesses have been found in A5 algorithms. A5/1 is based around a combination of three linear feedback shift registers. There is a set of statistical tests to determine the security level that can be provided by various algorithms. The perfect system is the one that gives the best statistical results. Simulation on six purposed models performed on PC using Java language. The generated key of the algorithms are analyzed to see whether the generated key is random or not. Verification of algorithms are analyzed using five statistical tests which are frequency test, run test, serial test, longest runs of one test and linear complexity test. Data analysis of the simulation was done using NIST statistical test suite. After all the test and analysis, the algorithms designed had fulfilled the characteristics for a good stream cipher algorithm.