Kanichukattu Korakutty Jose

In this article, a generalization of the Weibull distribution called Harris extended Weibull distribution is studied, and its properties are discussed. We fit the distribution to a real-life data set to show the applicability of this distribution in reliability modeling. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution. The operating characteristic functions of the sampling plans are obtained. The producer’s risk, minimum sample sizes and associated characteristics are computed and presented in tables. The results are illustrated using two data sets on ordered failure times of products as well as failure times of ball bearings.

In this paper, a generalization of the Harris family of distributions, namely, the Harris generalized linear exponential distribution is discussed. The use of the model is established by fitting it to a real data set. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution.

Reliability sampling plans are used for determining the acceptability of any product. In this paper, reliability sampling plans for acceptance or rejection of a lot of products submitted for inspection are developed when the lifetimes follow the Gumbel-uniform distribution. The sampling plan proposed here can save the test time in practical situations. Some tables are also provided for the new sampling plans so that this method can be used conveniently by practitioners. Operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producers risk with respect to the newly developed sampling plans are also presented. The new test plan is applied to ordered failure times of software release to illustrate its use in industrial contexts.

In this paper we consider type II bivariate generalized power series Poisson distribution as a compound Poisson distribution with bivariate generalized power series compounding distribution. We obtain some properties, p.m.f. and conditional distributions. In addition we also give a brief discussion about the multivariate extension of this case. Then we introduce type II bivariate generalized power series Poisson process and consider a bivariate risk model with type II bivariate generalized power series Poisson model as the counting process. For this model we derive distribution of the time to ruin and bounds for the probability of ruin. We obtain partial integro-di fferential equation for the ruin probabilities and express its bivariate transform through two univariate boundary transforms,where one of the initial capitals is fi xed at zero.

Here, we introduce a new class of Lindley generated distributions which results in more flexible model with increasing failure rate (IFR), decreasing failure rate(DFR) and up-side down hazard functions for different choices of parametric values. We explore, various distributional properties including limiting distribution of extreme order statistics explored. Maximum likelihood estimators and the confidence intervals of the parameters are obtained. The applicability of the proposed distribution is shown through modelling two sets of real data on bladder cancer patients and waiting time in a queue. Further, we carry out stress-strength analysis for applying the model in system reliability studies.

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.

In this article, we investigated the bootstrap calibrated generalized confidence limits for process capability indices C _pk for the one-way random effect model. Also, we derived Bissell's approximation formula for the lower confidence limit using Satterthwaite's method and calculated its coverage probabilities and expected values. Then we compared it with standard bootstrap (SB) method and generalized confidence interval method. The simulation results indicate that the confidence limit obtained offers satisfactory coverage probabilities. The proposed method is illustrated with the help of simulation studies and data sets.

Generalized Laplacian distribution is considered. A new distribution called geometric generalized Laplacian distribution is introduced and its properties are studied. First- and higher-order autoregressive processes with these stationary marginal distributions are developed and studied. Simulation studies are conducted and trajectories of the process are obtained for selected values of the parameters. Various areas of application of these models are discussed.