coefci

Confidence intervals for accelerated life model coefficients

Since R2026a

Syntax

ci = coefci(mdl)

ci = coefci(mdl,alpha)

Description

ci = coefci(mdl) returns 95% confidence intervals for the coefficients in the AcceleratedLifeModel object mdl.

ci = coefci(mdl,alpha) returns the confidence intervals using the confidence level 100(1 – alpha)%.

Examples

Fit Accelerated Life Model

Load the partFailure data set, which contains simulated observations of failure times for an assembly line part at specific humidity and temperature levels.

load partFailure.mat

Fit an accelerated life model to the data in the partFailure table using the fitacclife function. Use the FailureTime table variable as the failure times, and the other table variables as the stressors.

mdl = fitacclife(partFailure,"FailureTime")

mdl = 
AcceleratedLifeModel

Life distribution: weibull
Stress model: arrhenius

    Humidity    Temperature    WeibullA    MeanFailureTime
    ________    ___________    ________    _______________

       90           35          1.4502         1.3928     
       90           30          1.5114         1.4516     
       90           25          1.6015         1.5382     
       90           20          1.7468         1.6777     
       90           15          2.0189          1.939     
       90           12          2.3333          2.241     
       90            8          3.3507         3.2181     
       90            5          6.4271         6.1729     
       80           35          1.4458         1.3886     
       80           30          1.5069         1.4473     
       80           25          1.5967         1.5335     
       80           20          1.7415         1.6727     
       80           15          2.0128         1.9332     
       80           12          2.3263         2.2343     
       80            8          3.3406         3.2084     
       80            5          6.4077         6.1543     
       70           35          1.4402         1.3832     
       70           30           1.501         1.4417     
       70           25          1.5905         1.5276     
       70           20          1.7348         1.6662     
       70           15           2.005         1.9257     
       70           12          2.3173         2.2256     
       70            8          3.3276          3.196     
       70            5          6.3829         6.1304     
       60           35          1.4328         1.3761     
       60           30          1.4933         1.4342     
       60           25          1.5823         1.5197     
       60           20          1.7259         1.6576     
       60           15          1.9946         1.9158     
       60           12          2.3053         2.2141     
       60            8          3.3104         3.1795     
       60            5          6.3499         6.0988     
       50           35          1.4224         1.3662     
       50           30          1.4825         1.4239     
       50           25          1.5709         1.5087     
       50           20          1.7134         1.6456     
       50           15          1.9803         1.9019     
       50           12          2.2887         2.1981     
       50            8          3.2866         3.1566     
       50            5          6.3041         6.0548     


Log-likelihood: 47.0683

mdl is an AcceleratedLifeModel object, which contains information about the fitted model coefficient estimates. By default, the fitacclife function fits an Arrhenius life stress model to the data, and uses a Weibull life distribution. The first and second columns of the displayed output list the unique stressor levels in partFailure. The third and fourth columns list the fitted life distribution parameter values and mean failure times, respectively.

Display information about the fitted model coefficients.

mdl.Coefficients

ans=4×3 table
                    Source        Estimate       SE   
                ______________    ________    ________

    b0          "StressModel"      1.1592     0.039112
    b1          "StressModel"     -2.1731       2.0553
    b2          "StressModel"      8.6848      0.11616
    WeibullB    "Distribution"     12.764      0.72011

The table lists the estimated value and the standard error of each coefficient in the life stress model (b0, b1, and b2), and lists the estimated value and the standard error of the life distribution parameter (WeibullB).

List the 95% confidence intervals for each fitted model coefficient and parameter.

ci = coefci(mdl)

ci = 4×2

    1.0819    1.2364
   -6.2330    1.8868
    8.4554    8.9143
   11.3419   14.1867

All the coefficients are well constrained except the b1 coefficient of the Arrhenius life stress model.

Input Arguments

mdl — Accelerated life model

AcceleratedLifeModel object

Accelerated life model, specified as an AcceleratedLifeModel object created using fitacclife.

alpha — Significance level

0.05 (default) | numeric value in the range [0,1]

Significance level for the confidence intervals, specified as a numeric value in the range [0,1]. The confidence level of ci is equal to 100(1 – alpha)%. alpha is the probability that the confidence intervals do not contain the true value.

Example: 0.01

Data Types: single | double

Output Arguments

ci — Confidence intervals

numeric matrix

Confidence intervals, returned as a k-by-2 numeric matrix, where k is the number of coefficients. The jth row of ci is the confidence interval of the jth coefficient of mdl. The name of coefficient j is stored in the CoefficientNames property of mdl.

More About

Confidence Intervals

The coefficient confidence intervals provide a measure of precision for the accelerated life model coefficient estimates.

A 100(1 – α)% confidence interval gives the range for the corresponding model coefficient with 100(1 – α)% confidence, meaning that 100(1 – α)% of the intervals resulting from repeated experimentation will contain the true value of the coefficient.

The software finds confidence intervals using the Wald method. The 100(1 – α)% confidence intervals for model coefficients are

$$b_i\pm t_{\left(1-\alpha /2,n-p\right)}SE\left(b_i\right),$$

where b_i is the coefficient estimate, SE(b_i) is the standard error of the coefficient estimate, and t_{(1 – α/2,n – p)} is the 100(1 – α/2) percentile of the t-distribution with n – p degrees of freedom. n is the number of observations and p is the number of model coefficients.

Version History

Introduced in R2026a