Section A
Q1. Define hazard function. Obtain the survival function of the following hazard function:
(a) h(t) = (1)/((α_0 + α_1 t)(β_0 + β_1 t)) ; t > 0, α_0, β, α_1, β_1 > 0.
(b)
The diameter of one end of a drive-shaft is required within 1140 ± 10. The control charts for \overlineX and R-charts are initiated. After 30 sub-groups of 5 shafts each have been examined, \Sigma \overlineX = 34,290 and \Sigma R = 330
(i) Establish the mean μ' and standard deviation σ' of the process assuming that it is in statistical control.
(ii) Determine the 3-sigma limits of \overlineX and R-charts.
(iii) Determine the natural specification limits of the process.
(Given that d2 = 2.326, A2 = 0.58, D3 = 0 and D4 = 2.11)
(c)
Four teachers A, B, C and D are capable of teaching any of the four different courses a, b, c and d. The course preparation time (in hours) taken by four teachers are given in the table below. Each teacher is assigned only one course. How are the courses assigned to teachers so as to minimize the total course preparation hours?
Courses
Teachers
a
b
c
d
A
7
15
14
12
B
20
9
19
13
C
18
19
21
16
D
9
20
18
14
