Question

Instructions:  Read the information below.  Provide a print screen of your work when using a software tool.

Adbul is the new maintenance supervisor at a local manufacturing plant. He is responsible for the maintenance of machinery for production line processes.  Abdul is interested in the level of machine failures. He would like to simulate the number of machine failures each month.  Using historical date, Abdul established the probability of failures during a month as follows:

Number of Machine failures	Probability
1	0.10
2	0.17
4	0.21
5	0.28
6	0.16
7	0.07
8	0.01

Simulate Abdul’s monthly machine failures for a period of 3 years.  Replicate the failures 300 times.  Provide the following information:

A copy of the completed Excel spreadsheet                                       

The average number of failures per month for one replication         (1 mark)

The average number of failures per month for 300 replications       (1 mark)

Explain any difference(s) between the simulated average failures and the expected value of failures (long run value).                 

Answer 1

(a)
First, we determine the ranges of the random numbers for the probablity distribution of the number of breakdowns as follows:
Number of machine failures (x)	Probability of failure [p(x)]	Cumulative Probability	Random Number Range	x * p(x)
1	0.1	0.1	01 - 10	0.1
2	0.17	0.27	11 - 30	0.34
4	0.21	0.48	31 - 48	0.84
5	0.28	0.76	49 - 76	1.4
6	0.16	0.92	77 - 92	0.96
7	0.07	0.99	93 - 99	0.49
8	0.01	1	99 - 00	0.08
Next, we simulate the machine breakdowns for 3 years (36 months) by generating 36 random numbers in the range 00-99:
Month	Random Number	Number of failures
1	20	2
2	51	5
3	82	6
4	67	5
5	1	1
6	38	4
7	31	4
8	23	2
9	97	7
10	81	6
11	53	5
12	38	4
13	36	4
14	10	1
15	39	4
16	30	2
17	45	4
18	44	4
19	96	7
20	85	6
21	14	2
22	84	6
23	24	2
24	30	2
25	46	4
26	21	2
27	77	6
28	30	2
29	93	7
30	98	7
31	24	2
32	20	2
33	24	2
34	16	2
35	91	6
36	50	5
(b)	Mean number of failures per month =	3.9
	Statistically expected number of breakdowns per week = S [x * p(x)] =		4.21
(c)	Mean number of failures per month for 300 replications =		4.1
(d) It is assumed that the expected value result represents the real behavior of the machine.
The simulation result represents the behavior of the same machine based on its theoretical model.