Vol.3 No.04(2014), Article ID:14302,7 pages
DOI:10.12677/AAM.2014.34027

Acceptance Sampling Plans with Type-I Hybrid Censoring Scheme of Weibull Distribution

Jiawei Li

School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou

Email: sysuljw@126.com

Received: Aug. 15th, 2014; revised: Sep. 25th, 2014; accepted: Oct. 4th, 2014

ABSTRACT

Lifetime is an important quality variable of a product. Sampling plans used to determine the acceptability of a product, with respect to its lifetime, are known as acceptance sampling plans. In this paper, we discuss acceptance sampling plans of Weibull distribution with considering the Type-I hybrid censoring schemes. Firstly, we give the exact conditional distribution of the maximum likelihood estimator (MLE) of the scale parameter. Secondly, using the exact distribution of a pivotal quantity, we establish an acceptance sampling procedure satisfying the producer and consumer risks. Finally, some numerical results are tabulated for illustration.

Keywords:MLE, Type-I Hybrid Censoring, Consumer Risk, Producer Risk

Email: sysuljw@126.com

1. 引言

Epstein [1] 首先提出这一删失计划，并且研究了指数分布失效率的置信区间。Fairbanks等[2] 改进了Epstein的相关结论。Chen和Bhattacharya [3] 获得了指数分布参数MLE的精确分布函数以及在混合删失条件下参数的置信区间。在Chen和Bhattacharya的研究基础上，Gupta和Kundu [4] 获得了参数的精确置信区间。在混合-I型和混合-II型情形下，Childs等[5] 得到了参数MLE精确分布更为简洁的表达形式。上述文献的研究结果都是基于指数分布参数MLE的分布函数是单调递增函数得到的，相关证明都只是通过数值模拟加以验证。随后，Balakrishnan和Iliopoulos [6] 对于这一假设给出了严格的证明。

2. 尺度参数的精确分布

(1)

(2)

(3)

(4)

*

3. 可接受抽样计划

3.1. 可接受抽样计划步骤

，这里的是通常的Gammm函数。为了设计可接受抽样计划步骤，假定形状参数

(5)

(6)

(7)

(8)

3.2. 数值试验

1) 当增大的差距时，需要的试验样品数目有递减的趋势。

2) 当增大删失时刻时，需要的试验样品数目有递减的趋势。

3) 一般说来，当增大观测的试验样品数目才终止试验时，需要的试验样品数目有递增的趋势。

4) 在相同的生产者风险参数条件下，随着消费者风险参数的增加，需要的试验样品数目有递减的趋势。

4. 结论

Table 1. The simulation results of acceptance sampling plans with α = 2

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