Question

3. Six electronic controllers were tested under accelerated conditions and the following times to failure were observed: 46, 64, 83, 105, 123 and 150 hours. Do the following: a Determine how you would classify this data, that is individual, grouped, suspended, censored uncensored, and so on. Select rank regression (least squares) method on X as the parameter estimation miethod and determine the parameters for this data using the following distributions and plot the data for each distribution. From the plot, note how well you think each distribution tracks the data, that is how well does the fitted line track the plotted points? b i 2-Parameter Weibull. ii 3-Parameter Weibull. iii Normal. iv Log-normal. v Exponential. vi Extreme Value (Gumbel). vii Gamma. roblems owing to sudden and

Answer 1

a. The given data is is of individual type

b. to find parameters by rank regression method that is by least square method

X is considered from different distribution and following random samples are taken

y weibull normal lognormal exponential gamma extreme
46 0.28101 0.72053 5.49715 2.18920 0.47069 0.52240
64 0.91160 1.48850 1.55441 0.45226 1.33067 0.04686
83 0.93759 -1.29638 3.26693 1.56018 7.02524 0.56067
105 0.64961 -0.32414 0.65800 0.17356 3.20563 -0.75814
123 0.50455 -0.64524 0.23813 1.42705 2.92275 -0.03883
150 1.79579 -0.68728 1.87687 0.56735 4.47738 -3.70976

Scatter plots of X with Y

regession model and least square estimates of model

1)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 55.4 27.2 2.03 0.112

weibull 47.0 28.0 1.68 0.168 1.00

Regression Equation

2)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 92.3 13.8 6.69 0.003

normal -23.5 14.5 -1.62 0.181 1.00

Regression Equation

y = 92.3 - 23.5 normal

3)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 123.4 21.2 5.82 0.004

lognormal -12.93 7.55 -1.71 0.162 1.00

Regression Equation

y = 123.4 - 12.93 lognormal

4)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 118.8 28.1 4.23 0.013

exponential -22.3 22.0 -1.02 0.367 1.00

Regression Equation

y = 118.8 - 22.3 exponential

5)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 70.4 28.3 2.49 0.068

gamma 7.64 7.31 1.05 0.355 1.00

Regression Equation

y = 70.4 + 7.64 gamma

6)

Coefficients

Term Coef SE Coef T-Value P-Value VIF

Constant 84.5 11.5 7.35 0.002

extreme -18.88 7.29 -2.59 0.061 1.00

Regression Equation

y = 84.5 - 18.88 extreme

conclusion : as per the scatter we can conclude that data is good fitted with extreme value distribution