Multiple dependent repetitive group sampling plan for Marshall-Olkin logistic-exponential distribution assuring percentile lifetime with applications

Abstract

Acceptance sampling plans are commonly utilized for planning, process control, and implementation of industrial data sets. In addition to this, they also provide a solution for process quality control. They could be used for executing a decision for acceptance or rejection of a lot. A good acceptance sampling plan can be formulated depending on the requirements of the project. Usually, the plan should follow a defined lifetime distribution. Hence, the appropriate plan would not only determine the plan parameters but would also be cost and time efficient. In this article, an attribute multiple dependent repetitive group sampling (MDRGS) plan is developed assuming that the lifetime of the product follows the Marshall-Olkin logistic-exponential (MOLE) distribution. The parameters of plan are examined by considering a two-point approach. The suggested plan is contrasted with the single sampling and repeated group sampling plans. Finally, the implementation of the proposed plan is discussed using industrial as well as simulated data sets. It is concluded that the proposed plan reduces the sampling inspection cost and time as compared to existing acceptance sampling plans.

Keywords:

• Average Sample Number (ASN)
• Acceptance sampling plan
• Operating Characteristic (OC) Function

Acknowledgement

The authors are deeply thankful to the editor in chief and anonymous referees for their invaluable constructive comments and suggestions, which helped clarify several ideas and improved the quality and presentation of this manuscript.

Nomenclature
$c_1$	=	Acceptance number for first sample
$c_2$	=	Combined acceptance number for first and second samples
$n$	=	Sample size
$i$	=	Number of successive preceding lots
$p_1$	=	Failure probability at a specific percentile ratio ${\mathrm{\gamma }}_c$
$p_2$	=	Failure probability at specific percentile ratio 1
AQL	=	Acceptance Quality Level
LQL	=	Limiting Quality Level
LTPD	=	Lot Tolerance Percent Defective
$\mathit{ASN}\left(p_1\right)$	=	Average Sample Number at a failure probability $p_1$
$\mathit{ASN}\left(p_2\right)$	=	Average Sample Number at a failure probability $p_2$
${\mathrm{\gamma }}_c$	=	Consumer’s risk
${ \mathrm{\gamma }}_p$	=	Producer’s risk
$t_q/t_q^o$	=	Percentile ratio of true to specified percentile life
$t_q$ & $t_q^o$	=	True and Specified percentile life
${\delta }_q^o$	=	Termination ratio
$t_o$	=	Experiment time
$\alpha$	=	Distribution’s shape parameter
$\theta$	=	Distribution’s shape parameter
$\lambda$	=	Distribution’s scale parameter
MOLE	=	Marshall-Olkin logistic-exponential
MDSR	=	Multiple dependent state repetitive
RGSP	=	Repetitive group sampling plan
MDRGS/MDSRGS	=	Multiple dependent state repetitive group sampling
DASP	=	Double acceptance sampling plan
SSP	=	Single sampling plan
GASP	=	Group acceptance sampling plan

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data sharing information statement

The data that underpins the study’s conclusions are presented in the application portion of the publication.