Template:Management strategy ratio crow extended

Management Strategy Ratio & Initial Failure Intensity

When a system is tested and failure modes are observed, management can make one of two possible decisions, either to fix or not fix the failure mode. Therefore, the management strategy places failure modes into two categories: A modes and B modes. A modes are all failure modes such that, when seen during the test, no corrective action will be taken. This accounts for all modes for which management determines that it is not economically or otherwise justified to take a corrective action. B modes are either corrected during the test or the corrective action is delayed to a later time. The management strategy is defined by what portion of the failures will be fixed.
Let [math]\displaystyle{ {{\lambda }_{I}} }[/math] be the initial failure intensity of the system in test. [math]\displaystyle{ {{\lambda }_{A}} }[/math] is defined as the A mode initial failure intensity and [math]\displaystyle{ {{\lambda }_{B}} }[/math] is defined as the B mode initial failure intensity. [math]\displaystyle{ {{\lambda }_{A}} }[/math] is the failure intensity of the system that will not be addressed by corrective actions even if a failure mode is seen during test. [math]\displaystyle{ {{\lambda }_{B}} }[/math] is the failure intensity of the system that will be addressed by corrective actions if a failure mode is seen during testing.
Then, the initial failure intensity of the system is:

[math]\displaystyle{ {{\lambda }_{I}}={{\lambda }_{A}}+{{\lambda }_{B}} }[/math]

The initial system MTBF is:

[math]\displaystyle{ {{M}_{I}}=\frac{1}{{{\lambda }_{I}}} }[/math]

Based on the initial failure intensity definitions, the management strategy ratio is defined as:

[math]\displaystyle{ msr=\frac{{{\lambda }_{B}}}{{{\lambda }_{A}}+{{\lambda }_{B}}} }[/math]

The [math]\displaystyle{ msr }[/math] is the portion of the initial system failure intensity that will be addressed by corrective actions, if seen during the test. The Type A and B failure mode initial failure mode intensity is:

[math]\displaystyle{ \begin{align} & {{\lambda }_{A}}= & \left( 1-msr \right)\cdot {{\lambda }_{I}} \\ & {{\lambda }_{B}}= & msr\cdot {{\lambda }_{I}} \end{align} }[/math]