Template:Mixed data camsaa-cd

Mixed Data
In the RGA Software, the Discrete Data > Mixed Data option gives a data sheet that can have input data that is either configuration in groups or individual trial by trial, or a mixed combination of individual trials and configurations of more than one trial. The calculations use the same mathematical methods described in section 5.3 for the Crow-AMSAA grouped data. Example 9 Table 5.7 shows the number of fai $$\widehat{\beta }=0.7950$$ lures of each interval of trials and the cumulative number of trials in each interval for a reliability growth test. For example, the first row of Table 5.7 indicates that for an interval of 14 trials, 5 failures occurred.

Using RGA 7, the parameters of the Crow-AMSAA model are estimated as follows:


 * and:


 * $$\widehat{\lambda }=0.5588$$

As we have seen, the Crow-AMSAA instantaneous failure intensity, $${{\lambda }_{i}}(T)$$, is defined as:


 * $${{\lambda }_{i}}(T)=\lambda \beta {{T}^{\beta -1}},\text{with }T>0,\text{ }\lambda >0\text{ and }\beta >0$$

Using the above parameter estimates, we can calculate the or instantaneous unreliability at the end of the test, or $$T=68.$$


 * $${{R}_{i}}(68)=0.5588\cdot 0.7950\cdot {{68}^{0.7950-1}}=0.1871$$

This result that can be obtained from the Quick Calculation Pad (QCP), for $$T=68,$$  as seen in Figure Mixednst.FI. The instantaneous reliability can then be calculated as:


 * $${{R}_{inst}}=1-0.1871=0.8129$$

The average unreliability is calculated as:


 * $$\text{Average Unreliability }({{t}_{1,}}{{t}_{2}})=\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}$$

and the average reliability is calculated as:


 * $$\text{Average Reliability }({{t}_{1,}}{{t}_{2}})=1-\frac{\lambda t_{2}^{\beta }-\lambda t_{1}^{\beta }}{{{t}_{2}}-{{t}_{1}}}$$

Bounds on Average Failure Probability for Mixed Data
The process to calculate the average unreliability confidence bounds for mixed data is as follows:
 * 1)	Calculate the average failure probability.
 * 2)	There will exist a $${{t}^{*}}$$  between  $${{t}_{1}}$$  and  $${{t}_{2}}$$  such that the instantaneous unreliability at  $${{t}^{*}}$$  equals the average unreliability    . The confidence intervals for the instantaneous unreliability at  $${{t}^{*}}$$  are the confidence intervals for the average unreliability.

Bounds on Average Reliability for Mixed Data
The process to calculate the average reliability confidence bounds for mixed data is as follows:
 * 1)	Calculate confidence bounds for average unreliability    as described above.
 * 2)	The confidence bounds for reliability are 1 minus these confidence bounds for average unreliability.