Rectifying inspection for PAOSQLL scheme based on variable repetitive group sampling plan

The concept of the quality loss derived by Taguchi has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of non-conforming items. Since the variable single sampling plan having the desired operating characteristics indexed by the quality loss was proposed in 1997, various kinds of sampling plans indexed by the quality loss have been considered. Among them, there are two kinds of rectifying variable single sampling (RVSS) plans indexed by the quality loss. In the RVSS plans, two inspection schemes called the acceptance quality loss limit (AQLL) scheme and the permissible average outgoing surplus quality loss limit (PAOSQLL) scheme have been formulated. Note that the concepts of the AQLL and PAOSQLL schemes in the RVSS plans indexed by the quality loss are equivalent to those of the lot tolerance percent defective (LTPD) and the average outgoing quality limit (AOQL) schemes in the traditional rectifying attribute single sampling plans, respectively. On the other hand, in the sampling plan having the desired operating characteristics, an attribute repetitive group sampling plan was proposed for the purpose of reducing the average sampling number in the inspection. Recently, by applying the repetitive group sampling to the rectifying variable sampling plan for the AQLL scheme, the rectifying variable repetitive group sampling (RVRGS) plan for the AQLL scheme has been considered for the purpose of reducing the average total inspection (ATI). However, the RVRGS plan for the PAOSQLL scheme has not been investigated yet. Accordingly, the RVRGS plan for the PAOSQLL scheme must be investigated to complete the RVRGS plans indexed by the quality loss. In this article, the RVRGS plan for the PAOSQLL scheme is addressed. Then, the design procedure in the RVRGS plan for the PAOSQLL scheme is proposed for the purpose of reducing ATI. Through some numerical investigations, the effectiveness to reduce ATI by the RVRGS plan for the PAOSQLL scheme is confirmed.