Candidates who are preparing for the Civil Services Main Exam in the forthcoming year, can find out what kind of questions were asked in this exam in the year 2013. Some questions from Statistics Paper I of UPSC Civil Services Main Exam 2013 are as follows:

(a) What is meant by Statistical Quality Control (SQC)? What is its main purpose? Give its uses. Also mention different tools for SQC.
(b) What are the different methods for determining Reliability? Explain any two of them and also give their merits and demerits.
(c) Explain different steps in the preparation of Control Charts.
(d) Give any three definitions of Operations Research. What are the advantages and disadvantages of operations research models?
(e) What is Linear Programming? Give its advantages and limitations.

(a) Explain Double sampling Plan and develop expression required for drawing OC curve in Double sampling Plan.
(b) Explain the procedure for drawing the 5-points A S N curve for the sequential sampling plan.
(c) In welding of seams, number of defects that were identified in one seam each hour are given below :
2-1-2013

 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 AM 11:00 AM 12 noon 1:00 PM 2:00 PM 3:00 PM 4:00 PM 5:00 PM 6:00 PM 2 4 7 3 1 4 8 9 5 3 7 11 6

3-1-2013

 6:00 AM 7:00 AM 8:00 AM 9:00 AM 10:00 AM 11:00 AM 12 noon 1:00 PM 3:00 PM 4:00 PM 5:00 PM 4 9 9 6 4 3 9 7 4 7 12

Q.3.(a) Four counters are being opened on the frontier of a country to check the passports and necessary papers of the tourists. The tourists choose the counter at random. If the arrivals at the frontier are Poisson at the rate λ and the service time is exponential with parameters λ/2, what is the steady state average queue at each counter?

Q.3.(b) Solve the following game problem graphically :

 Player B → I II III IV Player A ↓ I 8 5 -7 9 II -6 6 4 -2

Q.3.(c) A cement factory manager is considering the least way to transport cement from his three factories A, B and C to depots P, Q, R and S. The weekly production and demands along with transportation costs are given below. What should be the distribution programme?

 Factory Depot P Depot Q Depot R Depot S Production A 10 8 7 12 500 B 12 15 6 10 500 C 8 10 12 14 900 demand 700 550 450 300