IFS Statistics Paper II 2020 (Main) – Page 1 & 2

Q1.

(a) SECTION-A 1. Develop survival function, when the hazard rate of the system is described by the function μ(t) = a + 2bt; a > 0, b > 0 and t > 0. Also write the name of the distribution, which a life pattern of a system follows.

(b) The average fraction defective of a large sample of a product is 0.1537. Calculate the control limits using subgroup size as 2000. What modification do you need, if the subgroup size is not constant?

(c) Define the term reliability function and compute hazard rate [h(t]], when the life pattern of a system is described by the log-normal distribution f
(x) = (1)/(√(2π) α x) e^{-1/2 ((log x - μ)/(σ))2}; μ > 0, σ > 0 and x > 0 Also compute h(e^μ).

(d) Why is simulation used? Explain how simulation can be applied in the case of inventory control, where the demand is probabilistic and lead time is fixed.

(e) Solve the game whose payoff matrix is given below : Player B Player A \beginbmatrix 3 & 2 & 4 & 0 \\ 3 & 4 & 2 & 4 \\ 4 & 2 & 4 & 0 \\ 0 & 4 & 0 & 8 \endbmatrix (a) Explain the purpose of \barx-chart, R-chart, p-chart and the parameters that

Q1.

(a) SECTION-A 1. Develop survival function, when the hazard rate of the system is described by the function μ(t) = a + 2bt; a > 0, b > 0 and t > 0. Also write the name of the distribution, which a life pattern of a system follows.

(b) The average fraction defective of a large sample of a product is 0.1537. Calculate the control limits using subgroup size as 2000. What modification do you need, if the subgroup size is not constant?

(c) Define the term reliability function and compute hazard rate [h(t]], when the life pattern of a system is described by the log-normal distribution f
(x) = (1)/(√(2π) α x) e^{-1/2 ((log x - μ)/(σ))2}; μ > 0, σ > 0 and x > 0 Also compute h(e^μ).

(d) Why is simulation used? Explain how simulation can be applied in the case of inventory control, where the demand is probabilistic and lead time is fixed.

(e) Solve the game whose payoff matrix is given below : Player B Player A \beginbmatrix 3 & 2 & 4 & 0 \\ 3 & 4 & 2 & 4 \\ 4 & 2 & 4 & 0 \\ 0 & 4 & 0 & 8 \endbmatrix (a) Explain the purpose of \barx-chart, R-chart, p-chart and the parameters that

Q2. must be known or estimated to establish their control limits and also give 15 interpretation of the above charts. Consider the following transition probability matrix : (b) P = \beginbmatrix 1 - α & α \\ β & 1 - β \endbmatrix; \quad 0 < α, \quad β < 1 Show that the process is ergodic. 10 Explain Box-Jenkins methodology for ARIMA (p, d, q) model. 15
(c) JKLO-B-STSC/63 \overline{\mathbf2}

Q2. must be known or estimated to establish their control limits and also give 15 interpretation of the above charts. Consider the following transition probability matrix : (b) P = \beginbmatrix 1 - α & α \\ β & 1 - β \endbmatrix; \quad 0 < α, \quad β < 1 Show that the process is ergodic. 10 Explain Box-Jenkins methodology for ARIMA (p, d, q) model. 15
(c) JKLO-B-STSC/63 \overline{\mathbf2}

Q3. 10

Q4. 15