| Summary: | 碩士 === 淡江大學 === 統計學系碩士班 === 98 === In recent years, many process capability indices (PCIs) have been widely used in quality monitoring by many manufacturing industries. Most PCIs assume that the quality characteristic has a normal distribution. However, the lifetime of products frequently possesses an exponential distribution, a Pareto or Weibull distribution etc. In practice, the lifetime performance index is utilized to measure lifetime performance for products with some lifetime distributions, where is the lower specification limit. In lifetime testing experiments, we may not be able to obtain a complete sample due to time limitation or other restrictions. Therefore, censored samples arise in practice.
In this thesis, we construct a maximum likelihood estimator (MLE) of based on the Progressively type Ⅱ right censored sample from the Rayleigh distribution and the Gompertz distribution. The MLE of is then utilized to develop a new hypothesis testing procedure and the confidence interval under the condition of known . The purchasers can then employ the new hypothesis and the confidence interval to determine whether the lifetime performance of products adhere to the required level.
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