The Linear Failure Rate Distribution (LFRD) is considered. The graphs of its probability density function are examined for selected parameter combinations. Some of them are similar to the well-known exponential distribution. Incidentally exponential distribution is one of the two component models of the LFRD model. In view of the simpler form of exponential model as applicable in inference, looking at the frequency curves of LFRD, a test statistic is proposed based on ratio of likelihood functions containing the standard forms of the density functions of both LFRD and Exponential to discriminate between LFRD and exponential models. The critical values and the powers of the test statistic are developed.

A variable quality characteristic is assumed to follow the well known Laplace Distribution. Control chart constants for the process mean, process dispersion based on a number of sub group statistics including sub group mean and range are evaluated from the first principles. Limits obtained through kurtosis correction method are borrowed from Tadikamalla and Popescu (2003). The performance of these sets of control limits is compared through a simulation study and the relative preferences are arrived at. The methods are illustrated by an example.