Statistical Chart Selection
Commonality: Rational Subgroups, Control Limits, and Startup:
The charts differ in that each is based on different output variables.
a) First, p-chartinguses attribute data derived from a count of the number of nonconforming units in a subset of the units produced.
b) Second, demerit chartsplot a weighted sum of the nonconformities per item.
c) Third, u-chartingplots the number of nonconformities per item inspected; this method is described together with demerit charts.
d) Fourth, Xbar & R chartingcreates two charts based on continuous quality characteristic values.
e) A fifth, the relativelyadvanced “Hoteling’s T” method, is described in Chapter 8 and permits simultaneous monitoring of several continuous quality characteristics on a single chart.
- A “rational subgroup” is a selection of units from a large set, chosen carefully to represent fairly the larger set. An example of an “irrational subgroup” of the marbles in a jar would be the top five marbles.
- A rational subgroup would involve taking all the marbles out, spreading them evenly on a table, and picking one from the middle and one from each of the corners.
- All four SPC charting methods in this book make use of rational subgroups. In some situations, it is reasonably easy and advisable to inspect all units, not merely a subset.
- According to the above definition, complete inspection necessarily involves rational subgroups because the complete set is representative of itself.
- All charting methods involve calculating an “upper control limit” (UCL), “center line” (CL), and a “lower control limit” (LCL). The control limits have no simple relationship to upper and lower specification limits. They relate to the goals of charting to identify assignable causes and preventing over-control of systems. It is conceivable that, on some control charts, all or none of the units involved could be nonconforming with respect to specifications.
- Charting methods generally include a “startup phase” in which data is collected and the chart constants are calculated.
- In addition, all charting methods also include a “steady state” phase in which the limits are fixed and the chart mainly contributes through (1) identifying the occasional assignable cause and (2) discouraging people from changing the process input settings.
- When the charted quantities are outside the control limits, detective work begins to investigate whether something unusual and fixable is occurring.
- When a process is associated with charted quantities within the control limits, it is said to be “in control” even if it generates a continuous stream of nonconformities
Example (Chart Selection for Monitoring Retail Theft) which charting procedure is most relevant for monitoring retail theft?
Answer: A natural key output variable (KOV) is the amount of money or value of goods stolen. Since the amount is a single continuous variable. The usual inventory counts that are likely in place can be viewed as complete inspection with regard to property theft. Because inventory counts might not be gauge capable, it might make sense to institute random intense inspection of a subset of expensive items at the stores.