Adding two more parameters for shaping provides a flexible way to make any basic bivariate distribution function (df) more adaptable. The extended bivariate dfs can better handle different kinds of bivariate data by including these parameters. They can handle a wide range of skewness and kurtosis indices well. The innovation lies in introducing a novel multiplicative bivariate stable-symmetric normal (MBSSN) distribution with two parameters, extending the conventional bivariate standard normal distribution. We conducted a detailed examination of the statistical properties of the MBSSN family and compared it to other significant competitors, such as generalized families of bivariate dfs, using real-world data like air pollution. The findings underscore the advantages and effectiveness of the MBSSN family in capturing the nuances of diverse datasets. We also applied the same methodology to develop a new two-parameter extension for two variations of bivariate extreme value distributions, which we then useed to analyze Lossalae datasets. This extension showcases the versatility and practicality of the proposed approach across different scenarios and distribution types.

It is often desired for practical reasons to cease a life test at a predetermined period ${𝓽}_0$. In this study, we provide sequential inspection sampling plan (SISP) for amputated life tests underlying the Burr Ⅻ (BTXII) distribution. We considered the ${\rho }^{\mathrm{t}\mathrm{h}}$ percentile lifetime of a product as the quality parameter. The sequential sampling plan is a dynamic and efficient technique to quality control and statistical decision-making. Unlike fixed sample plans, which require a predetermined number of samples before deciding, sequential plan enables ongoing analysis as a batch is examined. This flexible plan enables decisions- such as rejecting, accepting or continuing the sampling process - to be made after each sample, which is cumulative data for the number of nonconforming items. Acceptance, rejection limit lines, and optimal sample size at levels of manufacturer and customer errors were analyzed. A technique is provided for calculating the operation characteristic (OC) function and average sample number (ASN) in the suggested SISP. The effectiveness of the SISP was compared to the single, double, and repeating sampling strategies. In comparison to the single, double, and repetitive acceptance sampling plans (RASPs) the proposed sequential sampling acceptance strategy requires fewer sample resources on average for amputated life testing. The suggested method's uses are demonstrated with illustrated instances. In industrial applications, two actual sets of data are employed to demonstrate the SISP's flexibility.