ARL-unbiased control charts for the monitoring of exponentially distributed characteristics based on type-II censored samples

Abstract

AbstractIn this paper, the problem of monitoring process data that can be modelled by exponential distribution is considered when observations are from type-II censoring. Such data are common in many practical inspection environment. An average run length unbiased (ARL-unbiased) control scheme is developed when the in-control scale parameter is known. The performance of the proposed control charts are investigated in terms of the ARL and standard deviation of the run length. The effects of parameter estimation on the proposed control charts are also evaluated. Then, we consider the design of the ARL-unbiased control charts when the in-control scale parameter is estimated. Finally, an example is used to illustrate the implementation of the proposed control charts.Keywords: exponential distributionaverage run lengthprocess controlunbiased control charttype-II censoringAMS Subject Classification: Primary: 62P30Secondary: 62F10 AcknowledgementsThe authors thank the Editor, the Associate Editor and the referees for their detailed comments and suggestions, which helped improve the manuscript.FundingThe work of Guo is sponsored by 'Foundation of Ministry of Education of China [Grant No. 13YJC910005 and No. 13YJC910010]', 'Philosophy and Social Science Research Project in Zhejiang Province of China [Grant No. 13NDJC055YB]', 'National Statistical Research Plan Project [Grant No. 2012LY163]', and 'Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics)'. The work of Wang is supported by 'the National Natural Science Foundation of China under the contract number [11371322]' and 'Zhejiang Provincial Key Research Base for Humanities and Social Science Research (Statistics)'. The work by M Xie was supported by 'National Natural Science Foundation of China under the contract number [71371163]'