ADMISSIBILITY OF LIFETIME PERFORMANCE INDEX WITH RESPECT TO WEIGHTED SQUARED-ERROR LOSS FUNCTION IN PARETO DISTRIBUTION UNDER PROGRESSIVE TYPE II RIGHT CENSORED SAMPLE

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Zakerzadeh Hojjatollah; SHEIKHALISHAHI MARYAM

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Journal: ADVANCES IN MATHEMATICAL MODELING Year:2014 | Volume:4 | Issue:1 Page(s): 71-84

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Title

ADMISSIBILITY OF LIFETIME PERFORMANCE INDEX WITH RESPECT TO WEIGHTED SQUARED-ERROR LOSS FUNCTION IN PARETO DISTRIBUTION UNDER PROGRESSIVE TYPE II RIGHT CENSORED SAMPLE

Author(s)

Zakerzadeh Hojjatollah | SHEIKHALISHAHI MARYAM | Issue Writer Certificate

Keywords

LIKELIHOOD RATIO TESTQ2

EMPIRICAL BAYES ESTIMATORSQ2

ADMISSIBLE ESTIMATORSQ2

LIFETIME PERFORMANCE INDEXQ2

PROGRESSIVE CENSORED SAMPLEQ2

Abstract

Process capability analysis is an effective means to measure the performance and potential capabilities of a process. Process capability analysis has the following benefits: continuously monitoring the process quality through process capability indices (PCIs) in order to assure the products manufactured are conforming to the specifications; supplying information on product design and process quality improvement for engineers and designer; and providing the basis for reducing the cost of product failures. In the manufacturing industry, process capability indices are utilized to assess whether product quality meets the required level. For instance, Montgomery proposed the process capability index CL (or CPL) for evaluating the lifetime performance of electronic components, where L is the lower specification limit, since the lifetime of electronic components exhibits the larger-the-better quality characteristic of time orientation. In lifetime testing experiments, the experimenter may not always be in a position to observe the lifetimes of all the products on test. This may be because of time limitation or other restrictions (such as lack of funds, lack of material resources, mechanical or experimental difficulties, etc.) on data collection. Therefore, censored samples may arise in practice. And, in an industrial experiment, products may break accidently. Therefore, in this paper, we consider the case of the progressive type II right censoring. In this paper, under the assumption of Pareto distribution, construct a maximum likelihood estimator, UMVUE and also, assuming the Exponential prior distribution and weighted squared error loss function, this study construct Bayes and Empirical Bayes estimator of CL based on the progressive type II right censored sample. An admissible estimator of CL is given for Pareto distribution with respect to the weighted squared-error loss function. The MLE and Bayes estimator of CL is then utilize to develop a confidence and credible interval. Moreover, we also propose a LIKELIHOOD RATIO TESTs and a Bayesian Test to assess the LIFETIME PERFORMANCE INDEX. Finally, we give one example to illustrate the use of testing procedure under given significance level.

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APA: Copy

Zakerzadeh, Hojjatollah, & SHEIKHALISHAHI, MARYAM. (2014). ADMISSIBILITY OF LIFETIME PERFORMANCE INDEX WITH RESPECT TO WEIGHTED SQUARED-ERROR LOSS FUNCTION IN PARETO DISTRIBUTION UNDER PROGRESSIVE TYPE II RIGHT CENSORED SAMPLE. ADVANCES IN MATHEMATICAL MODELING, 4(1), 71-84. SID. https://sid.ir/paper/243867/en

Vancouver: Copy

Zakerzadeh Hojjatollah, SHEIKHALISHAHI MARYAM. ADMISSIBILITY OF LIFETIME PERFORMANCE INDEX WITH RESPECT TO WEIGHTED SQUARED-ERROR LOSS FUNCTION IN PARETO DISTRIBUTION UNDER PROGRESSIVE TYPE II RIGHT CENSORED SAMPLE. ADVANCES IN MATHEMATICAL MODELING[Internet]. 2014;4(1):71-84. Available from: https://sid.ir/paper/243867/en

IEEE: Copy

Hojjatollah Zakerzadeh, and MARYAM SHEIKHALISHAHI, “ADMISSIBILITY OF LIFETIME PERFORMANCE INDEX WITH RESPECT TO WEIGHTED SQUARED-ERROR LOSS FUNCTION IN PARETO DISTRIBUTION UNDER PROGRESSIVE TYPE II RIGHT CENSORED SAMPLE,” ADVANCES IN MATHEMATICAL MODELING, vol. 4, no. 1, pp. 71–84, 2014, [Online]. Available: https://sid.ir/paper/243867/en

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