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The lifetime performance index is commonly used in the manufacturing industry to evaluate the performance of the capabilities of the production process. For products with multiple components, the comprehensive lifetime performance index, which is a monotonically increasing function of the overall process yield, is used to relate to each individual lifetime performance index. For products where the lifetime of the ith component follows an exponentiated Fréchet lifetime distribution, we examine the maximum likelihood estimators for both the comprehensive and individual lifetime performance indices based on the progressive type I interval-censored samples, deriving their asymptotic distributions. By specifying the target level for the comprehensive lifetime performance index, we can set the desired level for individual indices. A testing procedure, using the maximum likelihood estimator as the test statistic, was developed to determine if the comprehensive lifetime performance index meets the target. Given that the lifetime distribution is asymmetric, this study pertains to asymmetrical probability distributions and their applications across diverse fields. We illustrate the power analysis of this testing procedure with figures and summarize key findings. Finally, we demonstrate the application of this testing algorithm with a practical example involving two components to verify if the overall production process achieves the assigned target level. [ABSTRACT FROM AUTHOR]

For the lifetime of products following a Burr XII distribution, the lifetime performance index was measured to assess the performance of the manufacturing process under type I interval censoring. The sampling design is investigated to reach the given level of significance and power level. When the inspection interval length is fixed, the required number of inspection intervals and sample size are determined to reach the minimum total cost. When the termination time of experiment is not fixed, the required number of inspection intervals, sample size and equal interval length are determined to reach the minimum total cost. The optimal sampling design for different situations is tabulated for the practical use of users. At last, one practical example is given for illustrative aim to show the use of the optimal sampling design to collect data and then conduct the testing procedure to see if the process is capable. [ABSTRACT FROM AUTHOR]

Abstract In this article, we present a new one-stage multiple comparison procedure for exponential mean lifetimes with the control under heteroscedasticity including one-sided and two-sided confidence intervals by improving the coverage probability and average confidence length compared with the old one. Users can use these simultaneous confidence intervals to identify better-than-the-control, worse-than-the-control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the mean lifetimes. In the end, one example is used to demonstrate the proposed procedure. [ABSTRACT FROM AUTHOR]

In this paper, we present new two-stage multiple comparison procedures with the average for location parameters of two-parameter exponential distributions under heteroscedasticity by modifying the existing one proposed by Wu and Wu. Not like one-stage procedures, two-stage multiple comparison procedures are design oriented. A simulation comparison study is done for the new two stage procedures, the old two stage procedures in Wu and Wu and the existing one-stage procedures. The results show that the proposed procedures have shorter confidence length with coverage probabilities closer to the nominal ones than the old two-stage one. At last, an example of four drugs for the treatment for leukemia is studied for illustrative aims. [ABSTRACT FROM AUTHOR]

The lifetime performance index was used for the evaluation on the process performance to promote the quality and productivity especially with products following a one-parameter exponential distribution. Based on the hypothesis testing procedure using the maximum likelihood estimator as testing statistic, the sampling design is determined under different situations. For given power of hypothesis testing, the minimum sample size is determined and tabulated to reach the given power. When the termination time is fixed and the number of inspection intervals is not fixed, the required number of inspection intervals and sample size with minimum total cost are determined and tabulated. When the termination time is not fixed, the required number of inspection intervals, sample size and equal interval length to reach the minimum total cost are determined and tabulated. At last, one numerical example is given to illustrate the use of this sampling design to collect data and then implement the testing procedure to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

In this paper, we present a modified one-stage multiple comparison procedure for exponential location parameters with the control under heteroscedasticity including one-sided and two-sided confidence intervals to improve the coverage probability and average confidence length than the old one. These intervals can be used to identify a subset which includes all no-worse-than-the-control treatments in an experimental design and to identify better-than-the-control, worse-than-the- control and not-much-different-from-the-control products in agriculture, stock market, pharmaceutical industries in terms of the minimum guarantee lifetimes. A simulation comparison is done for this modified procedure with the old one in terms of the confidence length and coverage probability. One example is given to demonstrate the proposed modified procedure. [ABSTRACT FROM AUTHOR]

Lifetime performance indices CL is usually used as the measurement for the larger-the-better type quality characteristics to assess the process performance of products. The lifetimes of products are assumed to have Rayleigh distribution in this study. This research presents another approach to the hypothesis testing procedure for the index without the transformation of Rayleigh distribution to the exponential distribution. The maximum likelihood estimator is used to estimate the lifetime performance index based on the progressive type I interval censored sample and its asymptotic distribution of this estimator is also developed to build a new hypothesis testing procedure under a pre-assigned lower specification limit. A simulation study is done and the results show that the power performance of this approach is better than the existing one. Finally, two practical examples are given to illustrate the use of two testing algorithmic procedures to determine whether the process is capable. [ABSTRACT FROM AUTHOR]

In the field of ranking and selection, the quality engineer would like to compare the mean lifetimes of several treatment populations with the control for exponential distribution. In most cases, the scale parameters are unknown and unequal. We proposed a one-stage multiple comparison procedure for comparing k-1 treatment exponential mean lifetimes with the control based on doubly censored samples under heteroscedasticity. The tables of critical values for the multiple comparison procedures are listed for the practical use. At last, one example of duration of remission for 20 patients each taking one of four drugs for the treatment of leukemia is given to demonstrate the application of our proposed method. [ABSTRACT FROM AUTHOR]