Eng. Mgt 385 Statistical Process Control Stephen A. Raper Chapter 7 – The Control Chart for Nonconformities

C-Charts “Every nonconforming article contains one or more nonconformities. Where it is appropriate to make a total count of the number of nonconformities (or errors or mistakes) in each article, or in each group of an equal number of similar articles, it may be reasonable to use a control-chart technique based on the Poisson distribution. This means using either a c chart or a u chart.”

C-Chart The c chart applies to the number of nonconformities in subgroups of constant size. Each subgroup for the c chart usually is a single article; the variable c is the number of nonconformities observed in one article. A c chart may be two or more articles. It is essential only that the subgroup size be constant in the sense that the different subgroups have substantially equal opportunity for the occurrence of nonconformities.

C-Chart “In many different kinds of manufactured articles, the opportunities for nonconformities are numerous, even though the chances of a nonconformity occurring in any one spot are small. Whenever this is true, it is correct as a matter of statistical theory to base control limits on the assumption that the Poisson distribution is applicable. The control limits for c charts are based on this assumption.”

C-Chart Where c-chart may be applied: –c is the number of nonconforming rivets in an aircraft wing or fuselage. –c is the number of breakdowns at weak spots in insulation in a given length of insulated wire subjected to a specified test voltage. –c is the number of surface imperfections observed in a galvanizes sheet or in a painted, plated, or enameled surface of a given area. –c is the number of imperfections observed in a bolt of cloth. –c is the number of errors made in completing a form.

C-Chart UCL =  c + 3 UCL =  c – 3 UCL = LCL = Although statistical theory may not absolutely apply, this charting technique has use in many situations.

C-Chart It stands to reason that setting up trial limits, establishing “in-control” limits, and interpretation of the limits is in line with previous discussions in chapters 4 and 6. Table G is useful but approximations may be used. Probability limits can be used and will be illustrated by example. Typical problems and examples follow.

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