Tham khảo tài liệu 'engineering statistics handbook episode 10 part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | . Gamma r Í -j PDh w4 or 1 I ÍỈ j CDF i i- f Ị dí I RELIABILITY K I FAILURE RATE h t 4 Kfi Ml-AN nr u J or v J VARIANCE 4- 2 yfl1 The exponential is a special case of the gamma Note When a 1 the gamma reduces to an exponential distribution with b Another well-known statistical distribution the Chi-Square is also a special case of the gamma. A Chi-Square distribution with n degrees of freedom is the same as a gamma with a n 2 and b .5 or y -2 . Ĩ The following plots give examples of gamma PDF CDF and failure rate shapes. Shapes for Gamma data http div898 handbook apr section1 2 of 6 5 1 2006 10 41 46 AM . Gamma Gamma CDF shapes http div898 handbook apr section1 3 of 6 5 1 2006 10 41 46 AM . Gamma Gamma failure rate shapes EXAMPLES OF GAMMA FAIl URE RATE SHAPES The gamma is used in Standby system models and also for Bayesian reliability analysis Uses of the Gamma Distribution Model 1. The gamma is a flexible life distribution model that may offer a good fit to some sets of failure data. It is not however widely used as a life distribution model for common failure mechanisms. 2. The gamma does arise naturally as the time-to-first fail distribution for a system with standby exponentially distributed backups. If there are n- standby backup units and the system and all backups have exponential lifetimes with parameter then the total lifetime has a gamma distribution with a n and b . Note when a is a positive integer the gamma is sometimes called an Erlang distribution. The Erlang distribution is used frequently in queuing theory applications. 3. A common use of the gamma model occurs in Bayesian reliability applications. When a system follows an HPP exponential model with a constant repair rate and it is desired to make use of prior information about possible values of a gamma Bayesian prior for is a convenient and popular choice. http div898 handbook apr section1 .
