b) Explain about charts for attributes and explain their uses. 4) a) Distinguish the difference between CUSUM charts and Shewartz control charts.

Transcription

1 ASSIGNMENT - 1, DEC PAPER- I : STATISTICAL QUALITY CONTROL (DMSTT 21) 1) a) Explain about Midrange control chart and median control chart. b) Explain about average run length for X chart. 2) a) List out uses of p, np chart explain about R-Chart. b) Explain about charts for attributes and explain their uses. 3) a) Explain control charts of p. b) Explain construction of C-chart with varying sample sizes. 4) a) Distinguish the difference between CUSUM charts and Shewartz control charts. b) Explain about construction and uses of p-chart. 5) Explain about a) Cusum design. b) χ 2 Control chart. c) Multivariate Control Chart.

2 ASSIGNMENT - 2, DEC PAPER- I : STATISTICAL QUALITY CONTROL (DMSTT 21) 1) a) Explain about EWMA chart. b) Explain about Hotelling T 2 control chart. 2) a) Explain the terms: i) AQL. ii) LTPD plan. iii) AOQL plan. b) Explain and Distinguish Producer s risk and Consumer s risk. 3) a) Explain about Double Sampling and derive O.C. and A.T.I. b) Explain sequential sampling plans for attribute. 4) a) Explain MIL STD plan with suitable example. b) Explain about Skiplot sampling plans and TQM. 5) a) Describe the role of multilevel sampling plan and CSP-2. b) Explain about MIL STD 414.

3 ASSIGNMENT - 1, DEC PAPER- II : OPERATIONS RESEARCH (DMSTT 22) 1) a) Define O.R. What are the characteristics of O.R? b) What do you mean by a LPP and what are its limitations. 2) a) Solve the linear programming problem. b) Solve the following LPP by simplex method Max z 3xx 2 Subject to 2x 3x 90 x 2x 36 3x 4x 120 x, x 0 3) a) Explain the steps involved in dual simplex method. b) Solve the following LPP using the dual simplex method Min z x1 x2 subject to 2x x 16 x 2x 24 3x 5x 300 x, x 0 4) a) Describe the different types of inventory systems. b) What are the Economic order quantity problems. 5) a) Write short notes on: i) Pure and mixed strategies. ii) Maximum and minimax principle.

4 iii) iv) Gamas without Saddle point. Arithmatic Calculus. b) Solve the game whose pay-off motion is

5 ASSIGNMENT - 2, DEC PAPER- II : OPERATIONS RESEARCH (DMSTT 22) 1) a) Explain the method of solving a two person zero-sum game by using simplex method. b) Show how a game can be formulated as an LPP. 2) a) Explain the terminologies of queuing system. b) Explain the following: i) Service discipline. ii) Service distribution. iii) Service channel. iv) Asrivd pattern. 3) a) Define: i) m m 1 ii) iii) iv) m m s m k 1and M G 1 queries with infinite capacities. b) Explain about various assumptions made in single-channel queuing theory. 4) a) What do you mean by slack? Define critical paths in the light of the definition of slack. b) Consider the following project network using the PERT three time estimate approach. Suppose that the time required (in months) for each of the activities are

6 Activity Optimistic Mostlikely Pessimistic estimate estimate estimate Designing the start of the project at time 0, the scheduled time by contract to complete the project in 25 months. 5) a) Explain the terms: i) Optimistic time. ii) Critical path. iii) PERT. b) Consider the following data of a project Activity Immediate Duration Weeks Predecessor (s) a m b A - 3 B C A D B 3 E A F C,D G C,D E 3 H F 9 Construct the project network find the critical path and the expected project completion time.

7 (DMSTT 23) ASSIGNMENT - 1, DEC PAPER- III : ECONOMETRICS 1) a) Specify the general linear model and obtain the OLS estimator of the parameters. Show that the OLS estimators are BLVE s. b) Write about three variable linear model and its tests of significance. 2) a) Write about log linear regression model. b) List out the properties of linear model. 3) a) State and prove Gauss-Markoff Theorem. b) Explain about general linear model, give its assumptions and consequences of assumptions when we are violating assumptions of general linear model. 4) a) Define 2 R and 2 R and explain these two concepts are useful in model selection. b) Deduce relationships between t and f ratios in regression analysis. 5) a) Distinguish between linear and log linear regression model. b) Write about MWD test.

8 (DMSTT 23) ASSIGNMENT - 2, DEC PAPER- III : ECONOMETRICS 1) a) Discuss the technique of using dummy variables for testing structural differences. b) What are dummy variables? Explain their usage in testing for structural change. 2) a) Explain briefly the concept of multicollinearity. State different solutions for multicollinearity explain any two of these solutions. b) Describe the sources of non-spherical disturbances. 3) a) What are the consequences of OLS estimation in the presence of heteroscedastic disturbances. b) Describe Goldfeld-Quandt test for testing heteroscedasticity. 4) a) What is meant by Auto Correlation? Describe the use of Durbin-Watson test in detecting auto - correlation. Explain the search procedure for estimating auto correlation. b) Explain LPM and How do you estimate the model. 5) a) Explain about PROBIT model. How do you estimate the model. b) Write about Quantitative Regression models and list out its merits and demerits.

9 (DMSTT 24) ASSIGNMENT - 1, DEC PAPER- IV : MULTIVARIATE ANALYSIS 1) a) Let (X, Y) be jointly distributed with density f (x, y) = y (1 + x) -4 exp (-y(1+x) -1 ), x, y > 0. Find E(X n Y m ) and E(Y/X). b) Let X be a p-variate normal vector find the first and second moments of X. 2) a) Let X be a p-variate normal vector. Derive the conditional distributions. b) Obtain the maximum likelihood estimators of the mean vector and the covariance matrix in a p-variate normal. 3) a) Define Hotelling s T 2 statistic. Derive its distribution. b) Explain the test for testing the hypothesis that the mean vector is a given vector. 4) a) Show that T 2 -Test is most powerful. b) Explain MANOVA for one-way classification. Develop the likelihood ratio test for the same. 5) a) Let X be a random vector of p-components with the covariance matrix. Obtain the principal components when i) is positive semidefinite and ii) has multiple roots b) Explain the factor analysis model. Discuss different methods of rotation.

10 (DMSTT 24) ASSIGNMENT - 2, DEC PAPER- IV : MULTIVARIATE ANALYSIS 1) a) Prove that the generalised variance of the vector of principal components is the generalized variance of the original vector, and the sum of the variances of principal components is the sum of the variances of the original variates. b) Obtain the m.l. estimators of the parameters in the factor model. 2) a) Explain the problem of classification. Explain the procedure of classification into one of two known multivariate populations. b) Discuss Fisher s method for classification into one of several populations. 3) a) Discuss the problem of classification into one of several multivariate normal populations. b) Deduce Fisher s discriminant function. Describe the Fisher s computational procedure. 4) a) Describe the basic concept and scope of cluster analysis and its importance. Explain the similarity measures. b) Discuss the agglomerative methods of clustering. 5) a) What are the guidelines to decide on the number of clusters? How is cluster analysis used to group variables? b) Explain K-means method. What are the disadvantages of non-hierarchical methods?