A novel Muth generalized family of distributions: Properties and applications to quality control

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Abstract
In this paper, we propose a novel family of distributions called the odd Muth-G distributions by using Transformed-Transformer methodology and study their essential properties. The distinctive feature of the proposed family is that it can provide numerous special models with significant applications in reliability analysis. The density of the new model is expressible in terms of linear combinations of generalized exponentials, a useful feature to extract most properties of the proposed family. Some of the structural properties are derived in the form of explicit expressions such as quantile function, moments, probability weighted moments and entropy. The model parameters are estimated following the method of maximum likelihood principle. Weibull is selected as a baseline to propose an odd Muth-Weibull distribution with some useful properties. In order to confirm that our results converge with minimized mean squared error and biases, a simulation study has been performed. Additionally, a plan acceptance sampling design is proposed in which the lifetime of an item follows an odd Muth-Weibull model by taking median lifetime as a quality parameter. Two real-life data applications are presented to establish practical usefulness of the proposed model with conclusive evidence that the model has enough flexibility to fit a wide panel of lifetime data sets.

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