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A CCC‐ r chart for high‐yield processes
Author(s) -
Ohta Hiroshi,
Kusukawa Etsuko,
Rahim Abdur
Publication year - 2001
Publication title -
quality and reliability engineering international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 62
eISSN - 1099-1638
pISSN - 0748-8017
DOI - 10.1002/qre.428
Subject(s) - chart , x bar chart , \bar x and r chart , control limits , control chart , mathematics , statistics , function (biology) , fraction (chemistry) , mathematical optimization , computer science , process (computing) , evolutionary biology , biology , operating system , chemistry , organic chemistry
The cumulative count of a conforming (CCC) chart is used to monitor high‐quality processes and is based on the number of items inspected until observing r non‐conforming ones. This charting technique is known as a CCC‐ r chart. The function of the CCC‐ r chart is the sensitive detection of an upward shift in the fraction defectives of the process, p . As r gets larger, the CCC‐ r chart becomes more sensitive to small changes of upward shift in p . However, since many observations are required to obtain a plotting point on the chart, the cost is fairly high. For this trade‐off problem it is necessary to determine the optimal number of non‐conforming items observed before a point is plotted, the sampling (inspection) interval, and the lower control limit for the chart. In this paper a simplified optimal design method is proposed. For illustrative purposes, some numerical results for the optimal design parameter values are provided. The expected profits per cycle obtained using the proposed optimal design method are compared with those obtained using other misspecified parameter values. The effects of changing these parameters on the profit function are shown graphically. Copyright © 2001 John Wiley & Sons, Ltd.