1. Statistical Process Control
Short Run SPC

2. Statistical Process Control
Consider a machine making two different types of parts. We want
to measure the capability of the machine.

3. Short Run SPC
Many products are made in smaller quantities than are practical to control with traditional SPC
In order to have enough observations for statistical control to work, batches of parts may be grouped together onto a control chart
This usually requires a transformation of the variable on the control chart, and a logical grouping of the part numbers (different parts) to be plotted.
A single chart or set of charts may then cover several different part types

4. DNOM Charts Deviation from Nominal
Variable computed is the difference between the measured part and the target dimension
where: Mi is the measured value of the ith part
Tp is the target dimension for all of part number p

5. DNOM Charts Part A has nominal target value TA = 50
Part B has nominal target value TB = 25

6. DNOM Charts
The computed variable (xi) is part of a sub-sample of size n
xi is normally distributed
n is held constant for all part numbers in the chart group.
Charted variables are x and R, just as in a traditional Shewhart control chart; and control limits are computed as such, too:

7. DNOM Charts

8. DNOM Charts

9. DNOM Charts

10. DNOM Charts
Usage:
A vertical dashed line is used to mark the charts at the point at which the part numbers change from one part type to the next in the group
The variation among each of the part types in the group should be similar (use a hypothesis test or a norm prob plot)
Often times, the Tp is the nominal target value for the process for that part type
Allows the use of the chart when only a single-sided specification is given
If no target value is specified, the historical average (x) may be used in its’ place

11. Standardized Control Charts
If the variation among the part types within a logical group are not similar, the variable may be standardized
This is similar to the way that we converted from any normally distributed variable to a standard normal distribution:
Express the measured variable in terms of how many units of spread it is away from the central location of the distribution

12. Standardized Charts – x and R
Standardized Range:
Plotted variable is
where: Ri is the range of measure values for the ith sub-sample of this part type j
Rj is the average range for this jth part type

13. Standardized Charts – x and R
Standardized x:
Plotted variable for the sample is
where: Mi is the mean of the original measured values for this sub-sample of the current part type (j)
Tj is the target or nominal value for this jth part type

14. Standardized Charts – x and R
Usage:
Two options for finding Rj:
Prior History
Estimate from target σ:
Examples:
Parts from same machine with similar dimensions
Part families – similar part tolerances from similar setups and equipment

15. Standardized Charts – Attributes
Standardized zi for Proportion Defective:
Plotted variable is
Control Limits:

16. Standardized Charts – Attributes
Standardized zi for Number Defective:
Plotted variable is
Control Limits:

17. Standardized Charts – Attributes
Standardized zi for Count of Defects:
Plotted variable is
Control Limits:

18. Standardized Charts – Attributes
Standardized zi for Defects per Inspection Unit:
Plotted variable is
Control Limits: