article · Symmetry
A new statistical model called the two-parameter Chris-Jerry distribution extends the existing Chris-Jerry distribution to better model lifetime data. Statistical evaluations demonstrate that the distribution falls within the Gumbel domain of attraction and offers reliable stress-strength properties. Furthermore, tail analysis reveals a substantial tail, indicating versatility across varied analytical contexts. The model was evaluated for single acceptance sampling plans using both simulated data and real-world scenarios. Parameters were estimated through both classical techniques and Bayesian methods, utilising Markov chain Monte Carlo simulations alongside mean squared error, linear-exponential, and generalised entropy loss functions. When applied to real lifetime datasets across two distinct events, the two-parameter distribution proved competitive and outperformed several standard lifetime models, confirming its practical utility in capturing increasing hazard rates and reliability dynamics.
Reliable assessment of equipment lifespan and product durability requires accurate statistical distributions that handle increasing failure rates over time. By offering improved tail behaviour and dependable stress-strength metrics, this model enhances the accuracy of quality inspection plans. This enables engineers and quality controllers to make more dependable decisions when testing components, reducing premature failures and improving operational safety.
The model is applicable to industrial quality assurance, specifically within single acceptance sampling plans used by manufacturing quality-control teams and reliability engineers to accept or reject product batches. Tested on real lifetime datasets and simulations, the methodology sits at an applied research stage. To reach commercial deployment, the mathematical framework would need integration into industrial quality-assurance software packages or statistical reliability toolkits used in manufacturing environments.
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This article is an extension of the Chris-Jerry distribution (C-JD) in that a two-parameter Chris-Jerry distribution (TPCJD) is suggested and its characteristics are studied. Based on the determined domain of attraction and other major statistical properties, the proposed TPCJD seems to fit into the Gumbel domain. Additionally, it has been confirmed that the stress strength is reliable. The tail study suggests that the TPCJD’s substantial tail makes it suited for a range of applications. The study took into account the single acceptance sampling approach using both simulation and real-life situations. The parameters of the TPCJD were estimated by some classical and Bayesian approaches. The mean squared errors (MSE), linear-exponential, and generalized entropy loss functions were deployed to obtain the Bayesian estimators aided by the Markov chain Monte Carlo (MCMC) simulation. An analysis of lifetime data on two events justified the use of the proposed distribution after comparing the results with some standard lifetime models.
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DOI: 10.3390/sym15101881
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