Fuzzy multiple deferred state variable sampling plan

Article type: Research Article

Authors: Afshari, Robab | Sadeghpour Gildeh, Bahram^{; *}

Affiliations: Department of Statistics, International Campus, Ferdowsi University of Mashhad, Mashhad, Iran

Correspondence: [*] Corresponding author. Bahram Sadeghpour Gildeh, Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Tel.: +98 51 38805684; E-mail: [email protected].

Abstract: Traditional multiple deferred state (MDS) sampling plan by variable is not able to decide about lots of products whose proportion parameter (p) is uncertain. In this study, fuzzy MDS (FMDS) variable sampling plan is proposed when p is not precise for the inspection of normally distributed quality characteristics in two cases known and unknown standard deviation. The plan parameters are obtained by the optimization problem, in which the objective function is considered to minimise sum of the fuzzy producer’s and consumer’s risks and the constraints are formulated by use of two-point approach under the specific fuzzy values of the producer’s and consumer’s risk, indexed by fuzzy limiting and acceptable quality levels. The proposed plan includes variable fuzzy single sampling plan (FSSP) as a special case. The obtained results show that the operating characteristic curve of FMDS variable plan seems to be closer to the ideal one with smaller required average sample number compared to variable FSSP. An industrial example is presented to illustrate the proposed plan in real applications.

Keywords: Statistical quality control, multiple deferred state sampling plan, fuzzy numbers arithmetic, variable sampling plan, producer’s risk and consumer’s risk

DOI: 10.3233/JIFS-17907

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2737-2752, 2018