Optimal Replacement Rate of Devices with Lognormal Failure Distributions

The time dependence of the replacement rate of devices with lognormal failure distributions is studied. The relationship between the peak replacement rate and a, the standard deviation in the corresponding s-normal distribution, is obtained. The study assumes that each device represents a renewal process and the system of devices represents a superimposed renewal process. The peak replacement rate becomes very large for both extreme values of a. The corresponding replacement rate eventually approaches the conventional asymptotic rate only after many MTTFs (Mean Time To Failure), possibly long after the system becomes obsolete. Ways to cope with this situation are suggested. However, the replacement rate curve becomes almost critically damped with a minimum-peak-factor ¿1.03 at ¿ ¿0.63. The study also reveals that asymptotically the lognormal devices with ¿ << 1 would require fewer replacements than the exponential devices with the same MTTF. The difference is equal to one-half of the population in service. For large a, more replacements are required. The results of this paper apply to a variety of reliability studies and maintenance and inventory strategies for communication systems that employ lognormal devices such as a semiconductor laser, LED, avalanche photo diode, or IMPATT diode. In particular, the present approach is especially helpful when such a device is the least reliable component in the system.