Stat 567:Statistical Reliability
Final Exam
December 12, 1996
2:45 p.m.

---

Useful information about the final exam

• The exam will be comprehensive
  
• The exam is:
  • Closed book
  • Closed notes
    
• You should bring to class a calculator
  
• You can and should bring to class up to five pages of personal notes plus photocopied tables.
  • The notes should have mostly formulas. The rest should be in your head.
  • You will not be able to turn these notes in for credit as you did in the midterm exam
    
• Other recommendations
  • Know how to interpret all JMP input and output that we have seen in class, homework, projects, and in the course homepage.
  • Know how to interpret all graphs and tables in the book
  • Review the study questions at the end of the class summaries of this course homepage
  • Be prepared to discuss the relative merits of the different procedures discussed in class.

Most important topics in the course (This is not a guarantee that only these topics will be included in the exam.)

• Fundamentals
  • Hazard rate and related concepts
  • Exponential distribution
  • Weibull and Gumbel distribution
  • Lognormal and normal distribution
  • Simple analysis techniques based on moments
  • Right-censored data
  • Product-Limit estimator and related standard errors
  • QQ plots
• Maximum likelihood estimation
  • Particular likelihood functions involving right-censored data
  • Maximum likelihood estimates
  • Variance-Covariance matrix
  • Confidence intervals based on standard errors
  • Confidence intervals based on likelihood ratios
  • Delta Method: univariate and multivariate
    • Standard error calculations
    • Confidence intervals for quantiles
    • Confidence intervals for survival probabilities
  • Use of JMP's Nonlinear Fit platform
    • Loss function associated with ML estimation
  • PP plots and their construction
• General regression models
  • Accelerated life model
  • Proportional hazards model
  • Diagnostic plots used with these two models
• Simple parametric regression
  • Weibull regression and its assumptions
  • Lognormal regression and its assumptions
  • Using JMP's Survival platform
  • Using JMP's Nonlinear Fit platform
  • Interpretation of outputs
• More complicated parametric regression
  • Weak-link model and similar models
  • Using likelihood ratios to test hypothesis involving nested models
• JMP's Nonlinear Fit platform
  • Programing the model function
  • Programing the loss function
  • Restricting parameter values to ease likelihood ratio tests
  • Log-likelihood calculations involving separate models at each stress level
  • Interpretation of outputs
• Reliability calculations involving reliability block diagrams
  • Reliability Block Diagrams
  • Series-parallel systems
  • Conditional calculations
  • Cut-set approximation
• Availability
  • Model assumptions
  • Steady state availability
  • Simple Markov diagrams
  • Calculations associated with Markov diagrams
• Expected number of failures
  • Model assumptions
  • Happy and Sad systems
  • Nonhomogeneous Poisson process
  • Difference between minimal and overhaul repairs
    

Take a look at some of my old exams

Do you have something to tell me?