Reliability Analysis

Paper Code: 
24STT324(C)
Credits: 
6
Contact Hours: 
90.00
Max. Marks: 
100.00
Objective: 

This paper aims at teaching the students to deal with reliability and replacement policies of statistical data.

Course Outcomes: 

Course

Course Outcomes

Learning and teaching strategies

Assessment Strategies

Course Code

Course Title

24STT324(C)

Reliability Analysis

(Theory)

CO 97: Classify different components and systems based on their reliability characteristics, distinguishing between coherent and non-coherent systems.

CO 98: Analyze the data of various life tables and estimate the parameters.

CO 99: Identify different classes of life distributions along with their duals, and recognize their properties.

CO 100: Evaluate the reliability estimation methods for univariate and bivariate shock models, comparing the effectiveness of various techniques and life testing with censoring.

CO 101: Outline the policies to be framed on the given data and identify the reliability of that policy.

CO 102: Contribute effectively in course-specific interaction.

Approach in teaching: 

Interactive Lectures, 

Group Discussion, 

Classroom Assignment,

Problem Solving Sessions.

 

Learning activities for the students:

Assignments,

Seminar,

Presentation,

Subject based  Activities.

Classroom Quiz,

Assignments,

Class Test,

Individual Presentation.

 

18.00
Unit I: 
Concepts and Measures of Reliability

Reliability: Concepts and measures, components and systems, coherent systems, reliability of coherent systems; cuts and paths, modular decomposition, bounds on system reliability, structural and reliability importance of components.

 

18.00
Unit II: 
Life Distributions and Parameter Estimation

Life distributions, reliability function; hazard rate; common life distributions-exponential, Weibull, Gamma etc. Estimation of parameters and tests in these models.

 

18.00
Unit III: 
Ageing Notations and Convolution

Notations of ageing, IFR, IFRA, NBU, DMRL and NBUE classes and their duals, loss of memory property of the exponential distribution; closures or these classes under formation of coherent systems, convolutions and mixtures.

 

18.00
Unit IV: 
Shock Models and Reliability Estimation

Univariate shock models and life distributions arising out of them; bivariate shock models; common bivariate exponential distributions and their properties. Reliability estimation based on failure times in variously censored life tests and in tests with replacement of failed items stress-strength reliability and its estimation.

 

18.00
Unit V: 
Maintenance and Replacement Policies

Maintenance and replacement policies, availability of repairable systems, modeling of a repairable system by a non-homogeneous Poisson process. Reliability growth models, probability plotting techniques, Hollander-Proschan and Deshpande tests for exponentiality; tests for HPP vs. NHPP with repairable systems. Basic ideas of accelerated life testing.

 

Essential Readings: 
  • Barlow, R.E. and Proschan, F.(1985): Statistical Theory of Reliability and Life Testing, Holt,Rinehart and Winston.
  • Lawless, J.F. (1982): Statistical Models and Methods of Life Time Data, John Wiley.
  • Bain, L.J. and Engelhardt, (1991): Statistical Analysis of Reliability and Life Testing Models, Marcel Dekker, sixth edition.

 

SUGGESTED READINGS:

  • Nelson, W (2003): Applied Life Data Analysis, John Wiley.
  • Zacks, S.(2004): Reliability Theory, Springer.
  • Sinha, S.K.(1986): Reliability & Life Testing,Wiley
  • Cox, D.R. and Oakes, D (1984): Analysis of Survival Data, Chapman and hall , New York.
  • Kalbfleisch , J.D. & Prentice, R.L. (2002): The Statistical Analysis of Failure Time Data, John Wiley.

 

e-RESOURCES:

 

JOURNALS:

  • Sankhya The Indian Journal of Statistics, Indian Statistical Institute
  • Aligarh Journal of Statistics, Department of Statistics and Operations Research, Aligarh Muslim University
  • Afrika Statistika, Saint-Louis Senega University
  • International Journal of Statistics and Reliability Engineering, Indian Association for Reliability and Statistic
  • Journal of the Indian Society for Probability and Statistics, Indian Society for Probability and Statistics
  • Journal of the Indian Statistical Association, Indian Statistical Association
  • Statistica, Department of Statistical Sciences Paolo Fortunato, University of Bologna
  • Statistics and Applications, Society of Statistics, Computer and Applications
  • Stochastic Modeling and Applications, MUK Publications and Distributions

 

Academic Year: 
2024-2025
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