166 4. RELIABILITY OF A COMPONENT UNDER STATIC LOAD
Solution:
In this example, the maximum static loading, according to the survey, is a discrete random vari-
able. e total number of sample data will be 10 C 20 C 40 C 32 C 5 D 107. en the probabil-
ity of the loading equal to 1100 will be 40=107. So, we can use the following PMF to describe
the loading:
p
.
l
/
D
8
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
<
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
:
10=107 D 0:0935 l D 1000 (lb)
20=107 D 0:1869 l D 1050 (lb)
40=107 D 0:3738 l D 1100 (lb)
32=107 D 0:2991 l D 1150 (lb)
5=107 D 0:0467 l D 1200 (lb):
Example 4.5
A company collected maximum static loading for a component. One hundred components at
different services were selected for collecting loading data. For each component, the maximum
loading on the component was collected during one-month regular service. e collected data
are listed in Table 4.3. Create the histogram and then determine the type of distribution and
corresponding distribution parameters.
Table 4.3: One hundred sample data of the maximum static loading on the component
e Maximum Static Loading X on Components (lb)
2532, 1987, 2877, 2588, 2511, 2682, 2568, 2026, 2377, 2384, 2211, 3207, 2056, 2232, 2130, 1922, 2363, 2327,
3139, 2338, 1971, 3172, 3006, 2347, 1772, 2250, 2380, 2574, 2332, 2650, 2626, 1887, 2023, 2117, 2221, 2306,
2456, 1087, 2244 ,3009, 1970, 2870, 2608, 2437, 2532, 1746, 2412, 3172, 2494, 2469, 2120, 2436, 2555, 2642,
2282, 2344, 3361, 1434, 3453, 2602, 2900, 1701, 2184, 2325, 2640, 1698, 2662, 1904, 2480, 2744, 2597, 2937,
2903, 2157, 2566, 2025, 1855, 2866, 2450, 2425, 2860, 2718, 2608, 3013, 2868, 2558, 2139, 2157, 2986, 1725,
2439, 1573, 2909, 2838, 2451, 2418, 1331, 2712, 1463, 1406,
Solution:
1. Use MATLAB to create a histogram.
We can follow Section 2.8 and use the MATLAB program to create the histogram. We
need to input the data of from the Table 4.3 in an Excel file, where the data will be inputted
in the first column. e file name will be “Example 4.5.” en we can use the following
MATLAB program to import the data and create the histogram. e histogram is dis-
played in Figure 4.2. From the histogram, we could assume that the loading follows a
normal distribution.