Question

explain the difference between control charts for nonconformity (c-chart) number of non confirming (np-chart) and fraction of non conforming (p-chart)

Answer 1

The control charts for nonconformities, usually assume that the occurrence of nonconformities in samples of constant size, is well modeled by the Poisson distribution.

Statistical process control charts are a graphical means to monitor a process or product in manufacturing or service applications. One category of control charts deals with data of attribute type. Specifically, these charts track nonconformities or defects obtained from samples chosen randomly from the process or product. When the size of the selected sample varies, the characteristic that is monitored is the number of nonconformities or defects per unit, through a control chart referred to as a u ‐chart. The occurrence of nonconformities or defects is assumed to be governed by a Poisson distribution. For a homogeneous Poisson distribution, the rate of occurrence of nonconformities or defects is assumed to be constant over a period of time or space or area or volume, depending on the context of the application.

An NP chart allows a researcher to keep track of whether a measurement process is within bounds or ‘out of control’. It records the number of non conforming units or defective instances in the measurement process.

The np=Chart is also known as the Number Defective Parts, and Number Non-Conforming Parts Chart For a sample subgroup, the number of defective parts is measured and plotted as a simple count. Statistically, in order to compare number of defective parts for one subgroup with the other subgroups, this type of chart requires that the subgroup sample size is fixed across all subgroups

Note that this chart tracks the number of defective parts, not the number of defects as done in the c-chart. Therefore there must be some yes/no decision of whether or not the sampled part meets production standards. A defective part does not indicate any magnitude of defectiveness (such as might be measured in one of the variable control charts), only that it is, or is not defective.

The proportion or fraction nonconforming (defective) in a population is defined as the ratio of the number of nonconforming items in the population to the total number of items in that population. The item under consideration may have one or more quality characteristics that are inspected simultaneously. If at least one of the characteristics does not conform to standard, the item is classified as nonconforming.

The fraction or proportion can be expressed as a decimal, or, when multiplied by 100, as a percent. The underlying statistical principles for a control chart for proportion nonconforming are based on the binomial distribution.