A Novel Transmuted Ailamujia Distribution with Statistical Properties and Applications to Reliability Data - Odat, Naser (International Journal of Industrial Engineering: Theory, Applications and Practice, 2026)
This article proposes the Transmuted Ailamujia Distribution (TAD), a generalization of the Ailamujia distribution with an extra shape parameter (γ) to account for different behaviors of reliability data. The paper provides the essential statistical inferences of TAD, such as moments, generating functions, and entropy. Parameters are estimated using maximum likelihood estimation for both full and right-censored data. A simulation study using Monte Carlo simulation (1000 runs, n = 30-500) is conducted to compare the performance of the estimators. The simulation results show that γ is estimable even when the data is censored. The application of TAD to vinyl chloride concentration data shows that TAD is superior to Weibull, Gamma, and other alternative distributions (CVM = 0.3456, AIC = 119.87). The article also gives the explicit reliability function: mean time to failure (MTTF = 3.907 units), hazard rates to indicate wear-out, stress-strength reliability P(X > 2.0) = 0.734, and process control limits (95th percentile = 5.82 units).