The NBRULC Reliability Class: Mathematical Theory and Goodness-of-Fit Testing with Applications to Asymmetric Censored and Uncensored Data (original) (raw)
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Quality and Reliability Engineering has acquired its overwhelming application in industries as producer and consumer are aware of its vital importance in producing quality products. Reliability sampling is an algorithm driven tool of Statistical Quality Control which enables the Quality Control engineers to select appropriate sampling plans for testing the products and hence the decision of acceptance or rejection is made on the batches or lots. A new type of sampling plans called Mixed Censoring Reliability Sampling Plans are developed involving type I and type II censoring. In general, either type I censoring or type II censoring schemes are adopted in designing sampling plans. But in this study an attempt has been made to design sampling plans by blending the two censoring schemes. This pressurizes the producer to maintain the quality of the batches or lots. R-Language is used to determine the parameters of the reliability sampling plans. Necessary tables are constructed using the designing procedure and illustration is given for easy implementation in industries.
A revisit to early failure analysis in life testing
Exponential distribution has been widely used as a model in areas ranging from studies on the lifetimes of manufactured items to research involving survival or remission times in chronic diseases. Early failures (or inliers) are natural occurrences of a life test, where some of the items fail immediately or within a short time of life test due to inferior quality or faulty construction. We intend to review some of the early failure models in this paper. Keeping the underlying distribution as exponential distribution, we study various estimators and characteristics of parameters the models. The study is supported by simulation and numerical illustrations.
Analysis of Hybrid Life-tests in Presence of Competing Risks
Metrika, 2007
The mixture of Type-I and Type-II censoring schemes, called the hybrid censoring scheme is quite common in life-testing or reliability experiments. In this paper, we consider the competing risks model in presence of hybrid censored data. Under this set up, it is assumed that the item may fail due to various causes and the corresponding lifetime distributions are independent and exponentially distributed with different scale parameters. We obtain the maximum likelihood estimators of the mean life of the different causes and derive their exact distributions. Using the exact distributions, all the moments can be obtained. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumptions of independent inverted gamma priors of the mean life of the different causes. Different methods have been compared using Monte Carlo simulations. One real data set has been analyzed for illustrative purposes.
Interval Estimation for Censored Accelerated Life Tests Based on the Lognormal Model
Journal of Quality Technology, 1989
Simulation studies in this paper indicate that the standard large sample confidence intervals applied to censored samples from accelerated life tests tend to be too short for the required confidence level. Alternative confidence limits are derived which are asymptotically equivalent to the standard large sample confidence limits. These new confidence limits are asymmetric for finite-sized samples and produce a more accurate upper confidence limit. If the main point of an investigation is to determine whether the median or percentile lifetime is below a certain value, a one-sided confidence bound can be used and the proposed technique will yield more accurate results. Assumptions Let the log times to failure Y I , •• " Y n be independent and normally distributed with standard deviation (1 and mean JL = fJo + fJI x, where x is a known function of stress. The standard deviation is assumed to be independent of the stress level and all units are started on test simultaneously. Let the subsamples at each of k stress conditions be of size nilj = 1, •. " k with the units on test subject to failure or time censoring. The parameters fJo, s., and (1 are assumed to be unknown characteristics of the products with maximum like
Quality and Reliability Engineering International, 2019
The accelerated life testing (ALT) is an efficient approach and has been used in several fields to obtain failure time data of test units in a much shorter time than testing at normal operating conditions. In this article, a progressivestress ALT under progressive type-II censoring is considered when the lifetime of test units follows logistic exponential distribution. We assume that the scale parameter of the distribution satisfying the inverse power law. First, the maximum likelihood estimates of the model parameters and their approximate confidence intervals are obtained. Next, we obtain Bayes estimators under squared error loss function with the help of Metropolis-Hasting (MH) algorithm. We also derive highest posterior density (HPD) credible intervals of the model parameters. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation. Finally, one data set has been analyzed for illustrative purposes. KEYWORDS accelerated life testing, cumulative exposure model, highest posterior density, Markov chain Monte Carlo, maximum likelihood estimation 1 | INTRODUCTION Life testing experiments are significant in assessing the reliability of various devices used in electrical, mechanical, and medical testing. Such experiments play an important role in deciding the over all per unit cost of products. In this era of highly advanced technologies, traditional life testing experiments are no more appreciable because of high cost of testing in terms of time and costs. The reason behind this situation is increased market competition and demand for highly reliable products. To handle such problem of cost and time effectiveness, researchers have come up with some other life testing experiments where products are tested in some severe stress conditions to obtain early failures and then analyze and extrapolate to study the failure patterns and life characteristics in normal operating conditions. This kind of experiments where testing is done under higher than normal stress levels are, in literature, known as accelerated life testing (ALT). The stress loading in ALT are applied in various ways and some of the widely used methods are constant stress, step stress, and progressive stress. Nelson 1 discussed the advantages and disadvantages of each of such methods. Constant-stress ALT is a kind of testing where products are tested under some constant high stress levels to obtain early failures of the products (see, Figure 1 [left]). In such tests, the test is terminated when the failure times of all the Abbreviations: ALT, accelerated life testing; MH, Metropolis-Hastings; HPD, highest posterior density.
Optimal Tests for No Contamination in Reliability Models
2000
Inferences on mixtures of probability distributions, in general, and of life distributions, in particular, are receiving considerable importance in recent years. The likelihood ratio procedure of testing for the null hypothesis of no contamination is often very cumbersome and lacks its usual asymptotic properties. Recently, SenGupta (1991) has introduced the notion of an 'L-optimal' test for such testing problems. The idea is to recast the original several parametric hypotheses representation of the null hypothesis in terms of only a single hypothesis involving an appropriately chosen parametric function. This approach is shown to be both mathematically elegant and operationally simple for a quite general class of mixture distributions which contains, in particular, all mixtures of the one-parameter exponential family and also a very rich subclass of mixtures useful in life-testing and reliability analysis. It is also illustrated through two examples-one based on real-life data and the other on a simulated sample.
LIFE TESTING USING PROBABILITY DISTRIBUTIONS
This paper is concerned with the type of accelerated life testing using exponential and Weibull distributions for the accelerated life testing involving acceleration of failures with single purpose of the quantification of the life characteristics of product at normal conditions. The parameters involved in the distributions were estimated by method of moments and maximum likelihood to determine general equation for failure rate function and failure time distribution including the mean life of the system through these distributions. At the end, some hypothetical examples were given to highlight the results.
Testing NBU(2) class of life distribution based on goodness of fit approach
Journal of King Saud University - Science, 2010
In this paper, new testing procedures for exponentiality against the NBU(2) class is addressed based on the goodness of fit approach. It is shown that the proposed test has high relative efficiency for some commonly used alternative and enjoys a good power. The critical values of the proposed statistic are calculated and some applications are given to elucidate the use of the proposed test in reliability analysis.
Quality and Reliability Engineering International, 2017
In this paper, a Cox proportional hazard model with error effect applied on the study of an accelerated life test is investigated. Statistical inference under Bayesian methods by using the Markov chain Monte Carlo techniques is performed in order to estimate the parameters involved in the model and predict reliability in an accelerated life testing. The proposed model is applied to the analysis of the knock sensor failure time data in which some observations in the data are censored. The failure times at a constant stress level are assumed to be from a Weibull distribution. The analysis of the failure time data from an accelerated life test is used for the posterior estimation of parameters and prediction of the reliability function as well as the comparisons with the classical results from the maximum likelihood estimation.
International Journal of Analysis and Applications
A device has a better failure rate at specific age t0 property, denoted by BFR-t0 if its failure rate r(t) increases for t≤t0 and for t>t0, r(t) is not less than its value at t0. A test statistic is proposed to test exponentiality versus BFR-t0 based on a randomly right censored sample of size n. Kaplan-Meier estimator is used to estimate the empirical life distribution. Properties of the test are measured by power estimates, estimated risks, and test of normality. The efficiency loss due to censoring is investigated by using tests for censored sample data.