Resumo:
Sampling inspection has reduced operational efforts in companies during the
acceptance/rejection process of lots of items from external and/or internal suppliers of finished
and/or in-process products. Sampling plans based on sample estimates of the process capability
index (Cpk) have been the focus of recent studies. Within this line of research, a double sampling
plan based on sample estimates of Cpk is proposed. In this plan, a random sample is selected
from each lot, and with the observations of this sample of size 𝑛𝑛1, 𝐶𝐶 ̂ 𝑝𝑝𝑝𝑝1, a sample estimate of
the Cpk index, is obtained. If 𝐶𝐶 ̂ 𝑝𝑝𝑝𝑝1, is lower (higher) than a threshold 𝑘𝑘1(𝑘𝑘2), the lot will be
rejected (accepted). Otherwise, a new sample of size 𝑛𝑛2 will be randomly drawn from the same
lot. A second estimate, 𝐶𝐶 ̂ 𝑝𝑝𝑝𝑝2, of the Cpk index will then be obtained with the observations of
this second sample, and finally, the values of 𝐶𝐶 ̂ 𝑝𝑝𝑝𝑝1 and 𝐶𝐶 ̂ 𝑝𝑝𝑝𝑝2 will determine the
acceptance/rejection of the lot. Double sampling based on sample estimates of the Cpk index
presents itself as an interesting alternative to the double sampling plan by attributes of the
NBR 5426 standard, due to a significant reduction in the number of items inspected per lot; on
average, the reduction is around 71%. It also shows, on average, a 21% reduction in the number
of items inspected compared to the single sampling plan based on Cpk. This decrease in the
average sample size required for the acceptance or rejection of lots, promoted by the double
sampling plan based on Cpk, results in lower use of operational resources such as labor, time,
and cost during the industrial lot inspection process. This achievement aligns with the
Sustainable Development Goals (SDGs), particularly SDG 9 (Industry, Innovation, and
Infrastructure) and SDG 12 (Responsible Consumption and Production), contributing to the
promotion of a more efficient, responsible, and innovative industry.
