97. A product is made up of two subsystems in series. The first subsystem consis
ID: 470657 • Letter: 9
Question
97.
A product is made up of two subsystems in series. The first subsystem consists of 20 components in series. The second subsystem consists of 3 components in parallel. The components in subsystem 1 are all of the same design and each has a 1/10,000 chance of failure. The parallel components each has a 3/10,000 chance for failure. What is the overall reliability of the system?
A machine shop owner wishes to monitor the diameter of an engine boring operation where the piston bore should be 4.25”. He obtains 8 samples of 5 and records the following data. Calculate the lower and upper control limits for an X-bar chart and R chart. Is the process in control?
Sample #
1 2 3 4 5 6 7 8
5.1 4.7 4.3 4.6 4.6 4.8 4.9 4.3
4.4 4.5 4.6 4.4 4.3 4.3 5.1 4.8
4.7 4.9 4.4 5 4.7 4.8 4.5 5
4.9 5.1 4.6 4.9 5 5 4.6 4.7
4.9 5.2 4.9 4.7 4.7 4.3 4.7 5.2
The RC and More Superstore decides to track customer complaints as part of their ongoing customer satisfaction improvement program. After collecting data for two months, their check sheet appears as follows:
Type of Problem
Frequency
(number of times)
Batteries not included
6
Items damaged when received
21
Literature not included in box
9
Parts missing
13
Unit not working
1
Construct a Pareto chart including the cumulative % frequency. What is the cumulative percentage of the two leftmost bars?
4)
A product manager has conducted a customer satisfaction survey of
30 customers on a scale of 1 to 5. The survey data is shown below. Calculate the mean and standard deviation of the survey and plot a histogram of the data. Does the distribution approximate Normal?
Customer
Satisfaction rating
1
4
2
3
3
2
4
5
5
5
6
2
7
1
8
4
9
3
10
4
11
4
12
5
13
3
14
3
15
2
16
1
17
5
18
3
19
4
20
3
21
4
22
2
23
4
24
4
25
3
26
3
27
3
28
2
29
2
30
3
5)
A project manager at System Design Corporation has collected the following data on the size of software programs and the length of programming time. The company is bidding on a new system that is estimated to consist of 250000 lines of code. Please use the data to find the correlation function of coding time to the program size and estimate the number of days it would take to code the system.
Module
Size in 1000 lines of code (KLOC)
Number of days to code
1
160
68
2
158
66
3
148
70
4
135
59
5
178
72
6
170
68
7
158
64
8
138
65
9
200
70
10
195
68
11
189
65
12
173
68
13
159
70
14
163
71
15
150
66
16
140
65
17
206
73
18
144
64
19
157
70
20
183
74
21
195
75
22
190
77
23
182
69
24
152
65
25
174
69
97.
A product is made up of two subsystems in series. The first subsystem consists of 20 components in series. The second subsystem consists of 3 components in parallel. The components in subsystem 1 are all of the same design and each has a 1/10,000 chance of failure. The parallel components each has a 3/10,000 chance for failure. What is the overall reliability of the system?
A machine shop owner wishes to monitor the diameter of an engine boring operation where the piston bore should be 4.25”. He obtains 8 samples of 5 and records the following data. Calculate the lower and upper control limits for an X-bar chart and R chart. Is the process in control?
Sample #
1 2 3 4 5 6 7 8
5.1 4.7 4.3 4.6 4.6 4.8 4.9 4.3
4.4 4.5 4.6 4.4 4.3 4.3 5.1 4.8
4.7 4.9 4.4 5 4.7 4.8 4.5 5
4.9 5.1 4.6 4.9 5 5 4.6 4.7
4.9 5.2 4.9 4.7 4.7 4.3 4.7 5.2
Explanation / Answer
1. Overall reliability of the system
Reliability series system is calculated using following formula;
RS = R1 x R2 x R3 x R4 ...... x Rn
Reliability of paraller system is calculated as;
RP = 1 - (1-R1) (1-R2) (1-R3) .......(1-RN)
where, R1,R2, .... Rn - Reliability of components in series.
Now in the given system, first we will calculate the reliability of the subsystems separrately;
Reliability of subsystem 1,
RS = R1 x R2 x R3 x R4 ... x R20
Where, reliability of components in series is,
R1 = R2 = R3 = ... = RN = (1 - chance of failure) = (1 - 1/10000) = 0.99990
RS = (0.99990)20
RS = 0.998002
Now, reliability of subsystem 2 with paraller system,
RP = 1 - (1 - R1)(1 - R2)(1 - R3)
where R1 = R2 = R3 = (1 - chance of failure) = (1 - 3/10000) = 0.9997
RP = 1 - (1 - 0.9997)3
RP = 1 (approximately)
Now, the overall relaibaility of system with these two subsystems in parallel;
RO = RS x RP
RO = 0.998002 x 1
Overall reliability RO = 0.998002
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