Statistics for Maintenance Modelling: Repairable Systems

# Example of MCNF and MCCF for Motor Vehicles¤

The following data concern repairs to 954 motor vehicles in a warranty period. The values have been averaged over the 954 vehicles and are months in service (MIS), cumulative number of failures per unit and cumulative cost per unit.

MIS | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8
MCNF | 0.397 | 0.547 | 0.688 | 0.807 | 0.95 | 1.064 | 1.173 | 1.305
MCCF | 11.84 | 16.44 | 20.84 | 24.68 | 29.73 | 32.76 | 36.82 | 41.14
ln MIS | 0 | 0.30103 | 0.477121 | 0.60206 | 0.69897 | 0.778151 | 0.845098 | 0.90309
ln MCNF | -0.40121 | -0.26201 | -0.16241 | -0.09313 | -0.02228 | 0.026942 | 0.069298 | 0.115611
ln MCCF | 1.073352 | 1.215902 | 1.318898 | 1.392345 | 1.473195 | 1.515344 | 1.566084 | 1.614264

The chart shows ln MCNF and ln MCCF plotted against ln MIS. Both plots approximate to a straight line with coincidentally similar slopes. The power estimated by the slope is approximately 0.6, so both number of failures and costs are showing a decreasing rate of occurrence over the period.