Nelson: Dialectric breakdown data

In NISTnls: Nonlinear least squares examples from NIST

Description

The Nelson data frame has 128 rows and 3 columns of data from an accelerated test of dialectric breakdown.

Format

This data frame contains the following columns:

y

A numeric vector of dialectric breakdown strength values.

x1

A numeric vector of time values.

x2

A numeric vector of temperature values.

Details

These data are the result of a study involving the analysis of performance degradation data from accelerated tests, published in IEEE Transactions on Reliability. The response variable is dialectric breakdown strength in kilo-volts, and the predictor variables are time in weeks and temperature in degrees Celsius.

Source

Nelson, W. (1981). Analysis of Performance-Degradation Data. IEEE Transactions on Reliability. Vol. 2, R-30, No. 2, pp. 149-155.

Examples

Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x1, data = Nelson, log = "y")
plot(y ~ x2, data = Nelson, log = "y")
coplot(y ~ x1 | x2, data = Nelson)
coplot(y ~ x2 | x1, data = Nelson)

Try(fm1 <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson,
           start = c(b1 = 2, b2 = 0.0001, b3 = -0.01), trace = TRUE))
Try(fm1a <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson,
            trace = TRUE, alg = "port",
            start = c(b1 = 2, b2 = 0.0001, b3 = -0.01)))

Try(fm2 <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson,
           start = c(b1 = 2.5, b2 = 0.000000005, b3 = -0.05), trace = TRUE))
Try(fm2 <- nls(log(y) ~ b1 - b2*x1 * exp(-b3*x2), data = Nelson,
           trace = TRUE, alg = "port", 
           start = c(b1 = 2.5, b2 = 0.000000005, b3 = -0.05)))

Try(fm3 <- nls(log(y) ~ cbind(1, -x1 * exp(-b3*x2)), data = Nelson,
           start = c(b3 = -0.01), trace = TRUE, algorithm = "plinear"))

Try(fm4 <- nls(log(y) ~ cbind(1, -x1 * exp(-b3*x2)), data = Nelson,
           start = c(b3 = -0.05), trace = TRUE, algorithm = "plinear"))

Example output

63.08354 :   2e+00  1e-04 -1e-02
Error in nls(log(y) ~ b1 - b2 * x1 * exp(-b3 * x2), data = Nelson, start = c(b1 = 2,  : 
  singular gradient
  0:     31.541770:  2.00000 0.000100000 -0.0100000
  1:     28.065153:  2.08616 0.000123557 -0.0110165
  2:     21.356185:  2.23755 0.000194410 -0.0133408
  3:     21.185499:  2.31323 0.000177884 -0.0130475
  4:     20.391589:  2.34848 0.000187398 -0.0132589
  5:     15.499022:  2.40098 0.000248759 -0.0146253
  6:     15.499022:  2.40098 0.000248759 -0.0146253
Error in nls(log(y) ~ b1 - b2 * x1 * exp(-b3 * x2), data = Nelson, trace = TRUE,  : 
  Convergence failure: false convergence (8)
48.48993 :   2.5e+00  5.0e-09 -5.0e-02
45.65385 :   2.505640e+00  2.160872e-09 -5.395902e-02
31.19039 :   2.516271e+00  1.975837e-09 -5.712236e-02
17.92663 :   2.534881e+00  2.874542e-09 -5.758987e-02
7.114617 :   2.562785e+00  4.246998e-09 -5.769909e-02
3.797685 :   2.590684e+00  5.617844e-09 -5.770157e-02
3.797683 :   2.590684e+00  5.617759e-09 -5.770102e-02
Nonlinear regression model
  model: log(y) ~ b1 - b2 * x1 * exp(-b3 * x2)
   data: Nelson
        b1         b2         b3 
 2.591e+00  5.618e-09 -5.770e-02 
 residual sum-of-squares: 3.798

Number of iterations to convergence: 6 
Achieved convergence tolerance: 9.84e-08
  0:     24.244964:  2.50000 5.00000e-09 -0.0500000
  1:     21.011692:  2.45039 5.91682e-09 -0.0506647
  2:     13.839060:  2.40064 8.24092e-09 -0.0520920
  3:     13.839060:  2.40064 8.24092e-09 -0.0520920
Error in nls(log(y) ~ b1 - b2 * x1 * exp(-b3 * x2), data = Nelson, trace = TRUE,  : 
  Convergence failure: false convergence (8)
24.46736 :  -0.01000000  2.71451219  0.00182973
10.23184 :  -2.369586e-02  2.699570e+00  5.768998e-05
4.631308 :  -0.041291592  2.634389402  0.000000504
3.826826 :  -5.398329e-02  2.599042e+00  1.560159e-08
3.797812 :  -5.744161e-02  2.591240e+00  6.032954e-09
3.797683 :  -5.769413e-02  2.590698e+00  5.628412e-09
3.797683 :  -5.770085e-02  2.590684e+00  5.618020e-09
3.797683 :  -5.770101e-02  2.590684e+00  5.617777e-09
Nonlinear regression model
  model: log(y) ~ cbind(1, -x1 * exp(-b3 * x2))
   data: Nelson
        b3      .lin1      .lin2 
-5.770e-02  2.591e+00  5.618e-09 
 residual sum-of-squares: 3.798

Number of iterations to convergence: 7 
Achieved convergence tolerance: 4.869e-07
3.938286 :  -5.000000e-02  2.608949e+00  4.654491e-08
3.799312 :  -5.678605e-02  2.592665e+00  7.224035e-09
3.797685 :  -5.766917e-02  2.590752e+00  5.667156e-09
3.797683 :  -5.770026e-02  2.590685e+00  5.618935e-09
3.797683 :  -5.770100e-02  2.590684e+00  5.617799e-09
Nonlinear regression model
  model: log(y) ~ cbind(1, -x1 * exp(-b3 * x2))
   data: Nelson
        b3      .lin1      .lin2 
-5.770e-02  2.591e+00  5.618e-09 
 residual sum-of-squares: 3.798

Number of iterations to convergence: 4 
Achieved convergence tolerance: 2.524e-06

NISTnls documentation built on May 2, 2019, 2:37 a.m.