Plano de amostragem dupla baseado no Cpk para aceitação de lotes

Abstract

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.