University of Rajasthan 2007 M.Sc Statistics M.A./ - exam paper

3 hrs. duration 100 Marks

Section-A
Statistical Quality Control: Meaning of Specification limits, item, quality, process and process control, Objectives of S.Q.C., Control Charts for measurable quality characteristic. Chance variation and assignable causes of variation. Mean X and R charts. Determination of control limits and central line in different situations.

Meaning of Statistical Control and its relation with specification limits. replaced control limits, warning limits and tolerances limits. Methods of estimation inherent variability, Rational sub-Grouping, sucessive estimate; control charts for defectives.'P' and 'nP'control charts for number of defects per unit, 'C' chart.

Advantages of S.Q.C. Comparision of Mean X and R chart with P chart when both can be used for identical situation

Acceptance sampling by attributes. Need for sampling inspection methods for acceptance. Lot quality and lot by lot acceptances. A.O.Q.L., producer's risk customer's risk, recification O.C. Function, A.S.N. and avg. to inspection of an acceptance procedure. Single and Double sampling plans and their mathematical analysis.

Knowledge of Standard Sampling inspectiontables. Dodge and Roming table and Mil Std. 105A. Sampling inspectionplans for continuous production process where lots can be formed.

Sampling inspection plans by variables - 1 sided specification standard (known and unknown). 2 sided specifications (known and unknown). Use of design in experiments in SPC. factorial experiments.fractional factorial designs.

Section-B
Definition and Scope of Operational Research; Phases in operations Research; Models and their solutions; decision-making under uncertainity and risk, use of various criteria; sensitivity analysis

Review of L.P.problems: duality theorem; transportation and assignment problems; Non-linear programming - Kuhn Tucker cvonditions. Wolfe's and Beale's algorithms for solving quadratic programming issues. Bellman's principle of optimality general formulation. Computational methods and application of dynamic programming.

Analytical structure of inventory problems; EOQ formula of Harris. its sesitivity analysis and extensions allowing volume discounts and shortages, Multi-item inventory subject to constraints. Models with random demand, the static risk model. P and Q-systems with constsant and random lead times.

Queuing models- specifications and effectiveness measures. steady-state solutions of M/M/1 and M/M/C models with associated distributions of Queue-length and waiting time. M/G/1 queue and Pollazeek Khinchine outcome. Steady-state solutions of M/EK/1 and EK/M/1 queues. Machine interference issue.

Sequencing and scheduling issues. two machine n-job and 3-machine n-job issues with identical machine sequence for all jobs, 2-job n-machine issue with various routings. Branch and bound method for solving travelling salesman issue.

Reference:
Grant,E.L.: Statistical Quality Control.
Bowker and Goode: Sampling Inspection by variables.
Burr.I.W.: Engineering Statistics and Quality Control.
Montegomri: Introduction to S.Q.C.
Toha,H.A.(1982) Operational Research: An Introduction, McMillan.
Hiller,F.S. and Leiberman,G.J. (1962): Introduction to Operation Research; Holden Day.
Kanti Swarup, Gupta,P.K. and Singh,M.M. (1985): Oprerations Research, Sultan Chand & Sons.
Philips D.T., Ravindran A. and Solberg J.: Operations Research, Principles and Practice.

Earning:   Approval pending.