Bayesian prediction for type-II progressive-censored data from the Rayleigh distribution under progressive-stress model

Inference for a geometric‐poisson‐Rayleigh distribution under progressive‐stress accelerated life tests based on type‐I progressive hybrid censoring with binomial removals

“…Prediction has many applications in the field of quality control, reliability, medical sciences, business, and engineering. It has been studied by many authors, including AL‐Hussaini, Basak et al, Raqab et al, and Abdel‐Hamid and AL‐Hussaini …”

“…Commonly used methods are constant-stress, step-stress, and progressive-stress, see, for example, Nelson,12 AL-Hussaini and Abdel-Hamid, 13,14 and Abdel-Hamid and AL-Hussaini. 15 The stress applied to a test product increases in time during a progressive-stress ALT, see, for example, Yin and Sheng, 16 Abdel-Hamid and AL-Hussaini, 17 Abdel-Hamid and Abushal, 18 and AL-Hussaini et al 19 Censoring is very common in life tests. It may be applied when the experimenter is unable to get total information on lifetimes for each unit or to reduce the total test time and the associated cost.…”

“…It has been studied by many authors, including AL-Hussaini, 33 Basak et al, 34 Raqab et al, 35 and Abdel-Hamid and AL-Hussaini. 17 A two-sample prediction scheme is performed as follows: Assume that, for l = 1, … , ℏ, (t l1 , … , t lB l ) is an informative type-I progressively hybrid censored sample of size B l obtained from GPRD under progressive-stress ALT. Assume also that ( l1 , … , ln * l ) is a future (unobserved) independent sample of size n * l obtained from the same population.…”

“…Commonly used methods are constant ‐stress, step ‐stress, and progressive ‐stress, see, for example, Nelson, AL‐Hussaini and Abdel‐Hamid,() and Abdel‐Hamid and AL‐Hussaini . The stress applied to a test product increases in time during a progressive‐stress ALT, see, for example, Yin and Sheng, Abdel‐Hamid and AL‐Hussaini, Abdel‐Hamid and Abushal, and AL‐Hussaini et al…”

Prediction Intervals for Future Observations Based on Samples of Random Sizes

“…Barakat et al (2014) obtained prediction intervals of future observations for a sample of random size from a continuous distribution. For similar prediction problems, one also may refer to Balakrishnan et al (2005;Sultan and Ellah, 2006;Asgharzadeh and Valiollahi, 2010;Abdel-Hamid and AL-Hussaini, 2014;El-Adll and Aly, 2016). Prediction intervals based on two-sample prediction problems is discussed, for example, in Fligner and Wolfe (1976;1979) for order statistics.…”