Analysis and Optimum Plan for 3-Step Step-Stress Accelerated Life Tests with Lomax Model Under Progressive Type-I Censor
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Analysis and Optimum Plan for 3-Step Step-Stress Accelerated Life Tests with Lomax Model Under Progressive Type-I Censoring N. Chandra1 · Mashroor Ahmad Khan1
Received: 16 February 2016 / Revised: 18 January 2017 / Accepted: 6 December 2017 © School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract In this paper, the optimum test plan and parameter estimation for 3-step stepstress accelerated life tests in the presence of modified progressive Type-I censoring are discussed. It is assumed that the lifetime of test units follows a Lomax distribution with log of characteristic life being quadratic function of stress level. The maximum likelihood and Bayesian method are used to obtain the point and interval estimators of the model parameters. The Bayes estimates are obtained using Markov chain Monte Carlo simulation based on Gibbs sampling. The optimum plan for 3-step step-stress test under modified progressive Type-I censoring is developed which minimizes the asymptotic variance of the maximum likelihood estimators of log of scale parameter at design stress. Finally, the numerical study with sensitivity analysis is presented to illustrate the proposed study. Keywords Accelerated life test · Lomax distribution · Maximum likelihood estimation · Bayesian estimation · Progressive Type-I censoring Mathematics Subject Classification 62N01 · 62N02 · 62N05 · 62F15 · 68U20
1 Introduction Accelerated life testing (ALT) is generally practiced to obtain failure time data for data analysis and to shorten the period between product design and market release time
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N. Chandra [email protected] Mashroor Ahmad Khan [email protected]
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Department of Statistics, Pondicherry University, Puducherry, India
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N. Chandra, M. A. Khan
and to improve the product performance and reliability. Nowadays, the human-made products such as computers, washing machine, refrigerator, electronic camera, cell mobile are well designed, highly sophisticated and giving good services to customers. But, the researchers are facing problems in getting failure time data of such types of highly reliable products under normal use condition. Thus, ALT is preferable to get failure time data more quickly of highly reliable product at a higher-than-usual level of stress (e.g., temperature, voltage, pressure, vibration, humidity, cycling conditions). Failure time data collected from ALT at higher stress are then extrapolated to the design stress to estimate the lifetime distribution. Moreover, censoring is frequently used in life-testing experiment and most commonly used censoring schemes are Type-I and Type-II. But, these conventional censoring schemes have a disadvantage, i.e., continuous monitoring up to termination of experiment. Recently, progressive censoring (PC) scheme has received considerable attention in the step-stress accelerated life testing (SSALT) planning. The main advantage of PC schemes is that it is possible to remove experimental units during
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