Implementing a Lifetime Performance Index of Products with a Two-Parameter Rayleigh Distribution Under a Progressively type II Right Censored Sample

In manufacturing, quality control is a process that ensures customers receive products free from defects and meet their needs. Process capability analysis has been widely applied in the field of quality control to find out how well a given process meets a set of specification limits. The lifetime performance index \begin {math} C_L ,\end {math} a type of process capability index is used to measure the larger-the-better type quality characteristics.  Under the assumption of Two-Parameter Rayleigh Distribution, this study constructs a maximum likelihood estimator of  \begin {math} C_L \end {math} based on the progressively type II right censored sample. The maximum likelihood estimator of  \begin {math} C_L \end {math} is then utilized to develop the new hypothesis testing procedure. The testing procedure can be employed the testing procedure to determine whether the lifetime of a product adheres to the required level

Implementing lifetime performance index of products with two-parameter exponential distribution

[[abstract]]The manufacturing industry has prioritised enhancing the quality, lifetime and conforming rate of products. Process capability indices (PCIs) are used to measure process potential and performance. The process capability is evaluated with product survival time and a longer lifetime implies a better process capability and a higher reliability. In order to save experimental time and cost, a censored sample arises in practice. In the case of product possessing a two-parameter exponential distribution, this study constructs a uniformly minimum variance unbiased estimator (UMVUE) of the lifetime performance index based on the type II right-censored sample. Then the UMVUE of the lifetime performance index is utilised to develop the new hypothesis testing procedure in the condition of known lower specification limit. Finally, two practical examples are illustrated to employ the testing procedure to determine whether the product is reliable.[[journaltype]]國外[[incitationindex]]SCI[[booktype]]紙本[[countrycodes]]GB