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Likelihood inference for the lifetime performance index C L is discussed in the presence of progressive censoring. We illustrate that many results available in the literature can be traced back to the exponential case using appropriate transformations of the data. Further, we present procedures to compute the MLE of C L under the assumption of gamma distributed lifetimes. The results are illustrated by a simulation study and applied to a data set.

L-moments are expectations of linear combinations of order statistics, their use in reliability analysis has been established. In the present paper we study L-moments in relation to income inequality measures. Models characterized by functional relationships between L-moments and income inequality measures are studied. Finally, we define the ordering based on L-moments and study its implications on other existing orderings.

A generalization of the Marshall–Olkin family of distributions is developed using negative binomial compounding instead of geometric compounding where addition is replaced by minimum of a random number of observations X 1 , X 2 ,..., X N . Here, we consider the Rayleigh distribution and extend it to obtain a Negative Binomial Marshall–Olkin Rayleigh Distribution. Various properties of the new family are investigated. Maximum likelihood estimates are obtained. The use of the model in lifetime modeling is established by fitting it to a real data set on remission times of bladder cancer patients. Also we try to develop a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes governed by this distribution.

Joint schemes for the process mean and the variance are essential to determine if unusual variation in the location and spread of a quality characteristic occurred. This paper comprises a systematic study on the phenomena of misleading , unambiguous and simultaneous signals while dealing with Shewhart and EWMA joint schemes for the process mean and the variance of a normally distributed quality characteristic. Examples have been added to illustrate how the R statistical software can be used to assess the performance of joint schemes in practice, namely when it comes to the occurrence of those valid signals.

In this note I use MIL-STD-414 for contrast and comparison with an alternate way to estimate the distribution of lot percent defective. A slight deviation from traditional distribution assumption parameters affects results associated with an enduring example of double specification limits.