Fatigue Life Analysis
Part 1: Calculation of Mean and Standard Deviation
Given the dataset of fatigue life measurements:
{570, 706, 716, 746, 785, 797, 844, 880, 886, 930, 980, 990, 990, 990, 1000, 1010, 1016, 1018, 1020, 1055, 1085, 110
The mean (µ) and standard deviation (σ) are calculated as follows:
570 + 706 + . . . + 2440
µ=
101
r
(570 − µ)2 + (706 − µ)2 + . . . + (2440 − µ)2
σ=
101
After computation, the mean is found to be µ = [1386.23] and the standard
deviation is σ = [473.78].
Part 2: Rank the Lifetime Data and Calculate Probability
of Failure
Sort the given data in ascending order: 570, 706, 716, 746, 785, 797, 844, 880,
886, 930, 980, 990, 990, 990, 1000, 1010, 1016, 1018, 1020, 1055, 1085, 1102,
1102, 1115, 1120, 1134, 1140, 1150, 1199, 1200, 1200, 1200, 1200, 1200, 1200,
1203, 1235, 1238, 1252, 1258, 1260, 1262, 1270, 1293, 1300, 1310, 1313, 1315,
1330, 1355, 1390, 1416, 1419, 1420, 1420, 1420, 1450, 1452, 1475, 1478, 1481,
1485, 1502, 1505, 1522, 1522, 1530, 1540, 1560, 1567, 1578, 1594, 1600, 1602,
1604, 1630, 1642, 1674, 1730, 1750, 1750, 1763, 1768, 1781, 1782, 1792, 1820,
1868, 1881, 1890, 1893, 1895, 1910, 1923, 1940, 1945, 2023, 2100, 2130, 2215,
2268, 2440
The data is sorted in ascending order and ranks are assigned from 1 to
101. The probability of failure for each data point (Pi ) is calculated using the
formula:
i − 0.3
Pi =
101 + 0.4
where i is the rank of the data point.
Part 3: Apply the Weibull Model in MATLAB
The following MATLAB code performs the analysis:
% Given data
data = [570, 1016, 1235, 1419, 1567, 1820, 706, 1018, 1238, 1420, 1578, 1868, 716, 1020,
% Part 1: mean and standard deviation
mean_value = mean(data);
1
Part 1: Calculation of Mean and Standard Deviation
Given the dataset of fatigue life measurements:
{570, 706, 716, 746, 785, 797, 844, 880, 886, 930, 980, 990, 990, 990, 1000, 1010, 1016, 1018, 1020, 1055, 1085, 110
The mean (µ) and standard deviation (σ) are calculated as follows:
570 + 706 + . . . + 2440
µ=
101
r
(570 − µ)2 + (706 − µ)2 + . . . + (2440 − µ)2
σ=
101
After computation, the mean is found to be µ = [1386.23] and the standard
deviation is σ = [473.78].
Part 2: Rank the Lifetime Data and Calculate Probability
of Failure
Sort the given data in ascending order: 570, 706, 716, 746, 785, 797, 844, 880,
886, 930, 980, 990, 990, 990, 1000, 1010, 1016, 1018, 1020, 1055, 1085, 1102,
1102, 1115, 1120, 1134, 1140, 1150, 1199, 1200, 1200, 1200, 1200, 1200, 1200,
1203, 1235, 1238, 1252, 1258, 1260, 1262, 1270, 1293, 1300, 1310, 1313, 1315,
1330, 1355, 1390, 1416, 1419, 1420, 1420, 1420, 1450, 1452, 1475, 1478, 1481,
1485, 1502, 1505, 1522, 1522, 1530, 1540, 1560, 1567, 1578, 1594, 1600, 1602,
1604, 1630, 1642, 1674, 1730, 1750, 1750, 1763, 1768, 1781, 1782, 1792, 1820,
1868, 1881, 1890, 1893, 1895, 1910, 1923, 1940, 1945, 2023, 2100, 2130, 2215,
2268, 2440
The data is sorted in ascending order and ranks are assigned from 1 to
101. The probability of failure for each data point (Pi ) is calculated using the
formula:
i − 0.3
Pi =
101 + 0.4
where i is the rank of the data point.
Part 3: Apply the Weibull Model in MATLAB
The following MATLAB code performs the analysis:
% Given data
data = [570, 1016, 1235, 1419, 1567, 1820, 706, 1018, 1238, 1420, 1578, 1868, 716, 1020,
% Part 1: mean and standard deviation
mean_value = mean(data);
1
