# Maths

Topics: Normal distribution, Statistics, Normal probability plot Pages: 3 (317 words) Published: March 27, 2013

|QMDS310 |Assignment 3 |Chan Cheok Hang |B-B0-0199-7 |

5.24
(a)-(2)
(b)-(4)
(c)-(5)
(d)-(1)
(f)-(3)

5.32
When m=5

When m=10
[pic]

When m=20
[pic]

When m=30
[pic]
When m=50
[pic]

When m increase, the probability that at least one of the average will plot outside the control limit increase.

6.8
(a)Based on the chart the process is in statistical control with no out-of-control signals, runs, trends or cycles. [pic]

(b) [pic]. Actual specs are 350 ( 5 V.
With xi = (observed voltage on unit i – 350) ( 10: USLT = +50, LSLT = –50 [pic], so the process is capable.
[pic]

(c) The Normality Test shows the distribution is close to normal. [pic]
6.12
(a) The process is in statistical control with no out-of-control signals, runs, trends, or cycles. [pic]
(b) [pic]
(c) The Normality Test shows the distribution is close to normal. [pic]

(d) [pic], so the process is not capable of meeting specifications. [pic]

(e)
[pic]

6.60
(a)
[pic]

(b)
[pic]

(c)
[pic]

(d)
[pic]

(e)
[pic]

6.66
(a)
[pic]
(b) As you can see the sample 18 and sample 30 is plotted out of the control limit, we can conclude that the process is out of control. (c)
[pic]
The process seems to not in the statistic control, since these data tend to skew to the right and they don’t fit to the line of the probability plot. Therefore, it is not reasonable to assume normality for these data. Since the waiting time refer to people, as we know that people are not accurate than those machine. It is true that the fraud caused by people is more than machine. Assignable causes of variation always occurred in people. Such variability is generally large when compared to out of control process that caused by machine