An Inferential Aptness of a Weibull Generated Distribution and Application

In this article an attempt has been made to develop a flexible single parameter continuous distribution using Weibull distribution. The Weibull distribution is most widely used lifetime distributions in both medical and engineering sectors. The exponential and Rayleigh distribution is particular case of Weibull distribution. Here in this study we use these two distributions for developing a new distribution. Important statistical properties of the proposed distribution is discussed such as moments, moment generating and characteristic function. Various entropy measures like Rényi, Shannon and cumulative entropy are also derived. The kthkt⁢h order statistics of pdf and cdf also obtained. The properties of hazard function and their limiting behavior is discussed. The maximum likelihood estimate of the parameter is obtained that is not in closed form, thus iteration procedure is used to obtain the estimate. Simulation study has been done for different sample size and MLE, MSE, Bias for the parameter λλ has been observed. Some real data sets are used to check the suitability of model over some other competent distributions for some data sets from medical and engineering science. In the tail area, the proposed model works better. Various model selection criterion such as -2LL, AIC, AICc, BIC, K-S and A-D test suggests that the proposed distribution perform better than other competent distributions and thus considered this as an alternative distribution. The proposed single parameter distribution is found more flexible as compare to some other two parameter complicated distributions for the data sets considered in the present study.

Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

Design of Improved EWMA Control Chart for Monitoring the Process Mean Using New Median Quartile Double Ranked Set Sampling

It is essential to monitor the mean of a process regarding quality characteristics for the ongoing production. For enhancement of mean monitoring power of the exponentially weighted moving average (EWMA) chart, a new median quartile double ranked set sampling (MQDRSS) based EWMA control chart is proposed and named as EWMA-MQDRSS chart. In order to study the performance of the developed EWMA-MQDRSS chart, performance measures; average run length, and the standard deviation of run length are used. The shift detection ability of the proposed chart has been compared with counterparts, under the simple random sampling and ranking based sampling techniques. The extensive simulation-based results indicate that the EWMA-MQDRSS chart performs better to trace all kinds of shifts than the existing charts. An illustrative application concerning monitoring the diameter of the piston ring of a machine is also provided to demonstrate the practical utilization of the suggested chart.

Statistical Inference Under Step Stress Partially Accelerated Life Testing for Adaptive Type-II Progressive Hybrid Censored Data

Accelerated life tests (ALTs) are designed to investigate the lifetime of extraordinarily reliable things by exposing them to increased stress levels of stressors such as temperature, voltage, pressure, and so on, in order to cause early breakdowns. The Nadarajah-Haghighi (NH) distribution is of tremendous importance and practical relevance in many real-life scenarios due to its attractive qualities such as its density function always has a zero mode and its hazard rate function can be increasing, decreasing, or constant. In this article, the NH distribution is considered as a lifetime distribution under the step stress partially accelerated life testing (SSPALT) model with adaptive type II progressively hybrid censored samples. The unknown model parameters and acceleration factors are estimated using maximum likelihood estimation (MLE) method assuming that the impact of stress change in SSPALT is explained by a tampered random variable (TRV) model. The Fisher information matrix, which is based on large sample theory, is also constructed and used to produce the approximate confidence intervals (ACIs). Furthermore, two potential optimum test strategies based on the A and D optimality criteria are evaluated. To investigate the performance of the proposed methodologies and statistical assumptions established in this article, extensive simulations using R software have been conducted. Finally, to further illustrate the suggested approach, a real-world example based on the times between breakdowns for a repairable system has been provided.

Reliability Test Plan Based on Logistic-Exponential Distribution and Its Application

In this article, a reliability test plan is developed for Logistic-exponential distribution (LoED) under time truncated life test scheme. The distribution has been chosen because it can used to model lifetime of several reliability phenomenon and it performs better than many well known existing distributions. With the discussions of statistical properties of the aforesaid model, the reliability test plan has been established under the assumption of median quality characteristics when minimum confidence level P* is given. To quench the objective of the paper i.e; to serve as a guiding aid to the emerging practitioners, minimum sample sizes have been obtained by using binomial approximation and Poisson approximation for the proposed plan. Further, operating characteristic (OC) values for the various choices of quality level are placed. Also, minimum ratio of true median life to specified life has been presented for specified producer’s risk. Important findings of the proposed reliability test plan are given for considered value of k=0.75,1,2. To demonstrate the appropriateness of suggested reliability test plan is achieved using four real life situation.

The Estimation of Finite Population Variance Under Stratified Sampling Technique

The efficiency of the study variable can be improved by incorporating the information from the known auxiliary variables. Usually two techniques ratio and regression estimation are used with the help of auxiliary information in different approaches to acquire the high precision of the estimators. Considering the very heterogeneous population to get the size of the sample it may be originating impossible to get a sufficiently accurate and precise estimate by taking the simple random sampling technique from the complete population. Occasionally taking sample issue may differ significantly in different part of the entire population. For example, under study population consists of people living in apartments, own homes, hospitals and prisons or people living in plain regions and hill regions so in such situations the stratified sampling is one of the most commonly used approach to get a representative sample in survey sampling from different cross units of the population. The present study is set out on the recommendation of generalized variance estimators for finite population variance incorporating stratified sampling scheme with the information of single and two transformed auxiliary variables. The expressions of bias and mean square error (MSE) are obtained for the advised exponential type estimators. The conditions are obtained for which the anticipated estimators are better than the usual estimator. An empirical and simulation study is conducted to prove the superiority of the recommended estimator.

Ratio in Ratio Type Exponential Strategy for the Estimation of Population Mean

This paper is an attempt to develop an estimator for finite population mean. Motivated by Kiregyera (1984), a ratio in ratio type exponential strategy is developed for estimation of population mean in double sampling for stratification. To compare with relevant considered estimators, expressions for bias and mean squared error of the developed estimator have been derived. The developed estimator has been compared with usual unbiased estimator, Ige and Tripathi (1987), ratio estimator and ratio type exponential estimator given by Tailor et al (2014) theoretically as well as empirically.

Modeling Age at Menstrual Onset and Developing Menarcheal Life Table

Population scientists are generally developing mathematical models/techniques in demography and to provide brief explanation of extensive data sets. The prime objective of the present paper is to propose a probability model to illustrate the distribution of female’s age at first menstrual onset. Menarcheal age distribution is used to evaluate risk associated to reproductive issues and may be used as a demographic indicator of female fecundity. The suitability of proposed model is tested with the real data sets. Parameters of the proposed distribution have been estimated through least square estimation technique. It is observed that older female’s age at menarche is somewhat higher than the younger female’s age at menarche. Also we have constructed a life table for menarcheal age using a probability model. This life table is enable to provide expected duration of getting menarche for a girl of a particular age.

Regression-in-Ratio Estimators for Population Mean by Using Robust Regression in Two Phase Sampling

The estimation of population mean is not meaningful using ordinary least square method when data contains some outliers. In the current study, we proposed efficient estimators of population mean using robust regression in two phase sampling. An extensive simulation study is conduct to examine the efficiency of proposed estimators in terms of mean square error (MSE). Real life example and extensive simulation study are cited to demonstrate the performance of the proposed estimators. Theoretical example and simulation studies showed that the suggested estimators are more efficient than the considered estimators in the presence of outliers.

A Study On Reliability Using Pendant, Hexant, Octant Fuzzy Numbers

The weaving machine’s reliability is assessed using newly introduced fuzzy numbers. The fuzzy numbers introduced in this study give a better method to improve the reliability than other techniques. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number are all introduced in this present study. Pendant Fuzzy Number, Hexant Fuzzy Number, and Octant Fuzzy Number,α-cuts are defined, as well as their mathematical operations. The numerical examples are utilised to conduct a comparative research of reliability using various Fuzzy Numbers, and their defuzzification is accomplished using various ways such as Signed Distance method, Graded Mean Integration Method and Centroid Method. The purpose of this study is to discover the most reliable value for a weaving machine.