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In this article we propose and study a new family of distributions which is defined by using the genesis of the truncated Poisson distribution and the exponentiated generalized-G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability and Shannon entropy are derived. Estimation of the parameters using the method of maximum likelihood is discussed. Although this generalization technique can be used to generalize many other distributions, in this study we present only two special models. The importance and flexibility of the new family is exemplified using real world data.

In this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary moments, generating function, incomplete moments, order statistics, moment of residual life and reversed residual life. The model parameter is estimated by using the maximum likelihood method. A real data application is given to illustrate the flexibility of the model. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study.

A double acceptance sampling plan (DASP) based on truncated life tests is suggested in this paper when the lifetime of a product follows the exponentiated generalized inverse Rayleigh distribution (EGIR). For a fixed value of the consumer’s confidence level, the minimum sample sizes of the first and second samples needed to ensure the specified mean life are obtained. The operating characteristic values according to the different quality levels are obtained and the minimum ratios of the mean life to the specified life are calculated. The important tables based on the suggested DASP are calculated and illustrated.

Control charts have been established as major tools for quality control and improvement in industry. Therefore, it is always required to consider an appropriate design of a control chart from an economical point of view before using the chart. The economic design of a control chart refers to the determination of three optimal control chart parameters: sample size, the sampling interval, and the control limits coefficient. In this article, the double sampling (DS) X¯{\bar{X}} control chart is considered for the economic design using nonlinear mixed integer programming approach. The triple sampling (TS) X¯{\bar{X}} control charts are developed for economic design based on the results of solving the DS X¯{\bar{X}} chart design problems. In this model, we assume that the process must be shut down during the search for the assignable cause. Multiple sampling X¯{\bar{X}} charts can be designed for quick detection of a small shift in process. The results of the comparison between the economic-statistical design of DS and TS X¯{\bar{X}} control charts show that TS X¯{\bar{X}} control charts are more efficient in terms of minimizing the average sample size, but its expected average cost takes larger values.