One Factor Reliability Designs: Analysis Results

The following information is provided in the analysis results for one factor reliability designs.

Analysis Results

The following table provides general information about the factor's effects on the times-to-failure.

This table includes the following columns:

- Model displays the model for which the results apply.
- - Reduced assumes that the product life is the same at different levels of the factor.
  - Full assumes that the product life is different at different levels of the factor.
- Degrees of Freedom is the degrees of freedom of this source of variation. This is also the number of parameters in the model for this source.
- Ln(Likelihood Value) is the logarithm transformation of the likelihood value for this source of variation.
- Likelihood Ratio is the likelihood ratio value for this source of variation.
- P Value is the probability that LR is from a chi-squared distribution, which would indicate that the factor has no effect on product life. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, then the factor is considered to have a significant effect on product life. In this case, the effect and its p value will be displayed in red.

The following table provides specific information on the contribution of the factor levels to the variation in the response and an analysis of the significance of this contribution.

This table includes the following columns:

- Term is the factor, factorial interaction, etc. under consideration. Terms displayed in red are considered to be significant.
- Effect is a measure of how much the response value (Y) changes when the value of the corresponding term in the model (using coded values) changes from -1 to 1.
- Coefficient is the regression coefficient of the term, which represents the contribution of the term to the variation in the response.
- Standard Error is the standard deviation of the regression coefficient.
- Low Confidence and High Confidence are the confidence bounds on the regression coefficient, using Fisher bounds.
- Z Value is the normalized regression coefficient, which is equal to Coefficient/Standard Error.
- P Value is the probability that an equal amount of variation in the output would be observed in the case that this source does not affect the output. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, this source of variation is considered to have a significant effect on the output. In this case, the term and its p value will be displayed in red.

The following table gives the characteristic life and standard deviation for the product at each factor level, along with lower and upper confidence bounds.

This table includes the following columns:

- Factor Level is the name of the level.
- Number in Level gives the number of failures (F) and suspensions (S) in the level.
- The next column is the characteristic life at that level.
- - Eta is shown for the Weibull distribution, and it is equal to the time at which unreliability = 63.2%.
  - Ln-Mean is shown for the lognormal distribution, and it is equal to the time at which unreliability = 50%.
  - MTTF (i.e., the mean time to failure) is shown for the exponential distribution.
- The Standard Deviation is also shown for the characteristic life.
- Low Confidence and High Confidence give the two-sided confidence bounds on the characteristic life, based on the risk level entered on the Analysis Settings page of the control panel (e.g., if the risk level is 0.1, then 90% two-sided bounds will be shown).

The following table provides information on comparisons between levels of the factor, allowing you to determine whether one particular level is significantly different from another.

This table includes the following columns:

- Contrast gives the paired comparison of any two levels. Level 1 - Level 2 means the difference between Level 1 and Level 2. Contrasts displayed in red are considered to be significant.
- Mean Difference is the mean value of the difference in output between the two levels.
- Pooled Standard Error is the standard error of the mean difference in output between the two levels.
- Low Confidence is the lower confidence bound of the mean difference.
- High Confidence is the upper confidence bound of the mean difference.
- T Value is the normalized difference, which is equal to Mean Difference/Pooled Standard Error.
- P Value is the probability that an equal amount of variation in the output would be observed in the case that there is no significant difference between the levels. This value is compared to the risk level (alpha) that you specify on the Analysis Settings page of the control panel. If the p value is less than alpha, there is considered to be a significant difference between the levels. In this case, the contrast and its p value will be displayed in red.

This information is presented using multiple tables.

The Response table displays the response that the regression equation applies to and the units of measurement that were entered for the response (if any).
The Additional Settings table shows the transformation and risk level you entered for the response.

Additional Results

All of the following tables provide information that was generated from the main calculations. The available tables will vary depending on design type you are working with. The results that could be available include:

This shows the variance/covariance matrix. The matrix is available for one factor R-DOE designs and all other designs with two or more factors.

This table displays various analysis results for each run and highlights significant values. It is available for one factor R-DOE designs and all other designs with two or more factors.

- Run Order is the randomized order, generated by DOE++, in which it is recommended to perform the runs to avoid biased results. Note that any changes made to the Run Order column on the Data tab will be reflected here.
- Standard Order is the basic order of runs, as specified in the design type, without randomization. Note that any changes made to the Standard Order column on the Data tab will be reflected here.
- Actual Value (Y) is the observed response value for the run, as entered in the response column on the Data tab.
- Predicted Value (YF) is the response value predicted by the model given the factor settings used in the run.
- Residual (or "regular residual") is the difference between the actual value (Y) and the predicted value (YF) for the run.
- Standardized Residual is the regular residual for the run divided by the constant standard deviation across all runs.
- Studentized Residual is the regular residual for the run divided by an estimate of its standard deviation.
- External Studentized Residual is the regular residual for the run divided by an estimate of its standard deviation, where the run in question is omitted from the estimation.
- Leverage is a measure of how much the run influences the predicted values of the model, stated as a value between 0 and 1, where 1 indicates that the actual response value of the run is exactly equal to the predicted value (i.e. the predicted value is completely dependent upon the observed value).
- Cook’s Distance is a measure of how much the output is predicted to change if the run is deleted from the analysis.

Values that are considered to be significant, or outliers, are displayed in red. For the residual columns, significant or critical values are those that fall outside the residual’s upper or lower bounds, calculated based on the specified alpha (risk) value.

The ReliaWiki resource portal has more information on how significant values are determined for the Leverage and Cook's Distance columns at: http://ReliaWiki.org/index.php/Multiple_Linear_Regression_Analysis.

This table shows the least squares means for each effect. The least square means is the average of observations associated with a given factor level. It is available for one factor R-DOE designs and all other designs with two or more factors. [Needs Theory check]

What's Changed? In DOE++ 1, diagnostic information (e.g., the residual for each run) was accessed by clicking an icon on the control panel to open the Diagnostics window. In the current version, this information is placed together with other analysis results in the Analysis Summary window.

	Related Topics:
	Analysis Summary Window