Section A
Q1.
(a) What are the situations that depict the lack of control in \overlineX and R charts?
(b) What are Military Standard Tables ? Explain its uses in Statistical Quality Control theory?
(c) Explain the concepts of Type I censoring and Type II censoring. Describe the situation of them arising either by design or due to experimental circumstances.
(d)
State the duality theorem in linear programming problem. Write the dual of the following primal problem :
Minimize z = 2x1 + 3x2 + 4x3
subject to 2x1 + 3x2 + 5x3 ≥ 2
3x1 + x2 + 7x3 = 3
x1 + 4x2 + 6x3 ≤ 5
x1, x2 ≥ 0, x3 unrestricted in sign.
(e)
Describe different features of a transition probability matrix in reference to a Markov chain. Given the following transition matrix of a Markov chain with three states 1, 2 and 3 and with initial probability distribution π_0 = [0.7, 0.2, 0.1], find the value of
$P[X3 = 2, X2 = 3, X1 = 3] : \beginbmatrix
0.10 & 0.50 & 0.40 \\
0.60 & 0.20 & 0.20 \\
0.30 & 0.40 & 0.30
\endbmatrix$
