# r_squared_profiling: R²-Profile Function for Log-Location-Scale Distributions with... In weibulltools: Statistical Methods for Life Data Analysis

## Description

This function evaluates the coefficient of determination with respect to a given threshold parameter of a three-parametric lifetime distribution. In terms of Median Rank Regression this function can be optimized (`optim`) to estimate the threshold parameter.

## Usage

 ```1 2``` ```r_squared_profiling(x, y, thres, distribution = c("weibull3", "lognormal3", "loglogistic3")) ```

## Arguments

 `x` a numeric vector which consists of lifetime data. Lifetime data could be every characteristic influencing the reliability of a product, e.g. operating time (days/months in service), mileage (km, miles), load cycles. `y` a numeric vector which consists of estimated failure probabilities regarding the lifetime data in `x`. `thres` a numeric value of the threshold parameter. `distribution` supposed distribution of the random variable. The value can be `"weibull3"`, `"lognormal3"` or `"loglogistic3"`.

## Value

Returns the coefficient of determination for a specified threshold value.

## References

Meeker, William Q; Escobar, Luis A., Statistical methods for reliability data, New York: Wiley series in probability and statistics, 1998

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```# Alloy T7987 dataset taken from Meeker and Escobar(1998, p. 131) cycles <- c(300, 300, 300, 300, 300, 291, 274, 271, 269, 257, 256, 227, 226, 224, 213, 211, 205, 203, 197, 196, 190, 189, 188, 187, 184, 180, 180, 177, 176, 173, 172, 171, 170, 170, 169, 168, 168, 162, 159, 159, 159, 159, 152, 152, 149, 149, 144, 143, 141, 141, 140, 139, 139, 136, 135, 133, 131, 129, 123, 121, 121, 118, 117, 117, 114, 112, 108, 104, 99, 99, 96, 94) state <- c(rep(0, 5), rep(1, 67)) df_john <- johnson_method(x = cycles, event = state) # Determining threshold parameter for which the coefficient of determination is # maximized subject to the condition that the threshold parameter must be smaller # as the first failure cycle, i.e 94: threshold <- seq(0, min(cycles[state == 1]) - 0.1, length.out = 100) profile_r2 <- sapply(threshold, r_squared_profiling, x = df_john\$characteristic[df_john\$status == 1], y = df_john\$prob[df_john\$status == 1], distribution = "weibull3") threshold[which.max(profile_r2)] # plot: # plot(threshold, profile_r2, type = "l") # abline(v = threshold[which.max(profile_r2)], h = max(profile_r2), col = "red") ```

weibulltools documentation built on May 2, 2019, 11:01 a.m.