NJIT HONOR CODE

All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly.  This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams.  Under the Honor Code, students are obligated to report any such activities to the Instructor.

 

Mathematics 761-101:

Statistical Reliability Theory and Applications

Fall 2007

Course Schedule Link

 

 

*   Instructor:  Prof. Bhattacharjee

*   Website:  http://web.njit.edu/~bhattach

*   Textbook:  Life Time Data: Statistical Models and Methods by Jayant Deshpande & Sudha Purohit. ISBN: 981-256-607-4, World Scientific  (2005).

*   Supplementary Materials: 

*      Chapter 9 in Introduction to Probability Models, by Sheldon Ross. 9th edition; ISBN: 0125980620, Academic Press (2006).

*      Chapters 2-5, 9, 11 in System Reliability Theory: Models, Statistical Methods and Applications, by Marvin Rausand, Arnljot Hoyland.  2nd edition; ISBN: 047147133X, Wiley-Interscience  (2003).

 

*   Grading Policy:  The final grade in this course will be determined as follows:

      Homework:

 

30%

 

      Midterm Exam:

 

35%

(10/18/07tentative)

      Final Exam:

 

35%

 

Please note that the University Drop Date November 5, 2007 deadline will be strictly enforced.

 

*   Exam Policy:  All examinations will be closed book exams.

 

 

 

 

 

 

MATH DEPARTMENT CLASS POLICIES LINK

All DMS students must familiarize themselves with and adhere to the Department of Mathematical Sciences Course Policies, in addition to official university-wide policies. DMS takes these policies very seriously and enforces them strictly. For DMS Course Policies, please click here.

 

 

September 3

M

Labor Day ~ No Classes Scheduled

November 5

M

Last Day to Withdraw from Classes

November 20

T

Classes Follow a Thursday Schedule

November 21

W

Classes Follow a Friday Schedule

November 22-23

R-F

Thanksgiving Recess ~ No Classes Scheduled

 

 

 

Course Outline:

 

Week 1              9/6

Basic concepts in Statistical Reliability and Survival Analysis

*      Modeling and analysis of time to event data. Engineering and biomedical contexts of applications (components, complex systems of components, survival time of patients).

*      Distribution of lifelength (time to failure) and related functionals : failure (hazard) rate, hazard function, mean residual life.

Week 2              9/13

Parametric families of Life Distributions and their Aging characteristics

*      The concept of  (positive and negative) aging. Increasing, decreasing and bathtub failure rates. The central role of exponential distributions in reliability.

*   Gamma, Weibull, log-normal, Pareto, Makeham families. Lehmann family, life distributions with proportional hazards.

Week 3-4           9/20 & 9/272

Nonparametric Aging notions and  Life Distributions

*   M IFR, DMRL, IFRA, NBU, NBUE  aging properties, corresponding life distribution classes and their duals.  

Week 5-6           10/4 – 10/11

Structure theory (systems of components)

*      Monotone and coherent structures, Series, parallel (hot standby) and cold standby systems.  Preservation of some aging properties by certain structures .systems.

*      Component importance, Fault tree analysis.

Week 7              10/18

midterm exam

Week 8              10/25

Age replacement and limiting availability

*      Age replacement policy for deteriorating systems

*      Availability Analysis.

Week 9-10         11/1 – 11/8

Parametric Analysis of Survival data

*      Likelihood based statistical analysis of failure /survival data for some specific parametric families of life distributions, with and without censoring.

Week 11            11/15

Nonparametric estimation of the Survival function

*      Continuous Uncensored (complete sample) case.

*      Censored data : Kaplan-Meier and other estimators.

Week 12-13       11/20 – 11/29

Testing for Aging

*      TTT (Total Time on Test) transform and TTT-statistic.

*      Nonparametric hypothesis testing for Exponentiality vs. some aging alternatives

Week 14            12/6

Proportional Hazards model and Competing Risk

*      Introduction to analysis of proportional hazards model and competing risk

Finals Week

FINAL EXAM:  Thursday December 20, 2007

Prepared By: Dr. M.C. Bhattacharjee

Last revised:  August 29, 2007