14-1 Control Charts for Variation and Mean

• Process data are data arranged according to some time sequence. They are measurements of a characteristic of goods/services that result from some combination of equipment, people, materials, and conditions.

• A run chart is a sequential plot of individual data values over time. One axis (usually the vertical axis) is used for the data values, and the other axis (usually the horizontal axis) is used for the time sequence.

• A process is statistically stable (or within statistical control) if it has only natural variation, with no pattern, cycles, or unusual points

• Random variation is due to chance, it is the type of variation inherent in any process that is not capable of producing every good or service exactly the same way each time

• Assignable variation results from causes that can be identified (such as defective machinery or untrained employees)

• A control chart (or Shewhart chart or process-behavior chart) of a process characteristic consists of values plotted sequentially over time, and it includes a centerline as well as a lower control limit (LCL) and an upper control limit (UCL).

  • The centerline represents a central value of the characteristic measurements, whereas the control limits are boundaries used to separate and identify any points considered to be significantly high or significantly low

• Two types of control charts: R charts used to monitor variation, x bar charts used to monitor means

• R charts are plots of the sample ranges instead of individual samples values, and it is used to monitor the variation in a process

• A process is not statistically stableor is out of statistical control if one or more of the following criteria are satisfied:

  • There is a pattern, trend, or cycle that is obviously not random

  • There is at least 1 point above the UCL or at least one point below the LCL

  • Run of 8 rule: There are at least 8 consecutive points all above or all below the centerline

• An x bar chart is a plot of the sample means, and it is used to monitor the center in a process

14-2 Control Charts for Attributes

• A control chart for p (or p chart) is a graph of proportions of some attribute (such as whether products are defective) plotted sequentially over time, and it includes a centerline, a LCL, and an UCL.

• Requirements for a control chart for p:

  • The data are process data consisting of a sequence of samples all of the same size n

  • Each sample item belongs to one of two categories (such as defective/not defective)

  • The individual sample data values are independent

• Notation for a control chart for p:

  • p bar = estimate of the proportion of defective items in the process = total number of defects found among all items sampled / total number of items samples

  • q bar = estimate of the proportion of process items that are not defective = 1-p hat

  • n = size of each individual sample or subgroup

• We use p bar for the centerline because it is the best estimate of the proportion of defects from the process

• Upper and lower control limits of a control chart for a proportion p are based on the actual behavior of the process, not the desired behavior. Upper and lower control limits are totally unrelated to any process specifications that may have been decreed by the manufacturer.