Tolerancing conducted by design engineers to meet customers’ needs is a prerequisite for producing highquality products. Engineers use handbooks to conduct tolerancing. While use of statistical methods for tolerancing is not something new, engineers often use known DISTRIBUTIONs, including the normal DISTRIBUTION. Yet, if the statistical DISTRIBUTION of the given variable is unknown, a new statistical method will be employed to design tolerance. In this paper, we use GENERALIZED LAMBDA DISTRIBUTION for design and analyses component tolerance. We use percentile method (PM) to estimate the DISTRIBUTION parameters. The findings indicated that, when the DISTRIBUTION of the component data is unknown, the proposed method can be used to expedite the design of component tolerance. Moreover, in the case of assembled sets, more extensive tolerance for each component with the same target performance can be utilized.

In this paper, we introduce a three-parameter generalization of the Lindley DISTRIBUTION. This includes as special cases the exponential and gamma DISTRIBUTIONs. The DISTRIBUTION exhibits decreasing, increasing and bathtub hazard rate depending on its parameters. We study various properties of the new DISTRIBUTION and provide numerical examples to show the flexibility of the model. We also derive a bivariate version of the proposed DISTRIBUTION.

In this paper, the GENERALIZED gamma (GG) DISTRIBUTION that is a flexible DISTRIBUTION in statistical literature, and has exponential, gamma, and Weibull as subfamilies, and lognormal as a limiting DISTRIBUTION is introduced. The power and logarithmic moments of this family is defined. A new moment estimation method of parameters of GG family using it’s characterization is presented, this method is compared with MLE method in gamma subfamily for small and large sample size. Here we study GG entropy representation and its estimation. In addition Kullback-Leibler discrimination , Akaike and Bayesian information criterion is discussed. In brief, this paper consist of presentation of general review of important properties in GG family.

In this study, we introduce a new model called the Extended Exponentiated PowerLindley DISTRIBUTION which extends the Lindley DISTRIBUTION and has increasing, bathtub andupside down shapes for the hazard rate function. It also includes the power Lindley DISTRIBUTIONas a special case. Several statistical properties of the DISTRIBUTION are explored, such as thedensity, hazard rate, survival, quantile functions, and moments. Estimation using the maximumlikelihood method and inference on a random sample from this DISTRIBUTION are investigated. Asimulation study is performed to compare the performance of the di® erent parameter estimatesin terms of bias and mean square error. We apply a real data set to illustrate the applicabilityof the new model. Empirical ¯ ndings show that proposed model provides better ¯ ts than otherwell-known extensions of Lindley DISTRIBUTIONs.