1. PTTE 434 Quality Organization & Management Lecture 7
Ch 11: Statistical Tools for Analyzing Data (Process Control Charts)

2. Chapter Overview Statistical Fundamentals Process Control Charts
Some Control Chart Concepts
Process Capability
Other Statistical Techniques in Quality Management

3. Some useful URLs on Control Charts
Stat Soft Quality Control Charts:
Free Quality. Org (Many free tools)
(Please Note: These tools are supported by MS Excel and Access and download best when MS Internet Explorer is used.)
Wikipidia on Control Charts
Six Sigma on Control Charts
Univariant and Multivariant Control Charts

4. Process Control Charts Slide 1 of 37
Process Charts
Tools for monitoring process variation.
The figure on the following slide shows a process control chart. It has an upper limit, a center line, and a lower limit.

5. Process Control Charts Slide 2 of 37
Control Chart (Figure 10.3 in the Textbook)
The UCL, CL, and
LCL are computed
statistically
Each point represents
data that are plotted
sequentially
Upper Control
Limit (UCL)
Center
Line (CL)
Lower Control
Limit (LCL)

6. Process Control Charts Slide 3 of 37
Variables and Attributes
To select the proper process chart, we must differentiate between variables and attributes.
A variable is a continuous measurement such as weight, height, or volume.
An attribute is the result of a binomial process that results in an either-or-situation.
The most common types of variable and attribute charts are shown in the following slide.

7. Process Control Charts Slide 4 of 37
Variables and Attributes
Variables
Attributes
X (process population average) P (proportion defective)
X-bar (mean for average) np (number defective)
R (range) C (number conforming)
MR (moving range) U (number nonconforming)
S (standard deviation)

8. Process Control Charts Slide 5 of 37
Central Requirements for Properly Using Process Charts 1.
You must understand the generic process for implementing process charts.
You must know how to interpret process charts.
You need to know when different process charts are used.
You need to know how to compute limits for the different types of process charts. 2. 3. 4.

9. Process Control Charts Slide 6 of 37
A Generalized Procedure for Developing Process Charts
Identify critical operations in the process where inspection might be needed. These are operations in which, if the operation is performed improperly, the product will be negatively affected.
Identify critical product characteristics. These are the attributes of the product that will result in either good or poor function of the product.

10. Process Control Charts Slide 7 of 37
A Generalized Procedure for Developing Process Charts (continued)
Determine whether the critical product characteristic is a variable or an attribute.
Select the appropriate process control chart from among the many types of control charts. This decision process and types of charts available are discussed later.
Establish the control limits and use the chart to continually improve.

11. Process Control Charts Slide 8 of 37
A Generalized Procedure for Developing Process Charts (continued)
Update the limits when changes have been made to the process.

12. Process Control Charts Slide 9 of 37
Understanding Control Charts
A process chart is nothing more than an application of hypothesis testing where the null hypothesis is that the product meets requirements.
An X-bar chart is a variables chart that monitors average measurement.
An example of how to best understand control charts is provided under the heading “Understanding Control Charts” in the textbook.

13. Process Control Charts Slide 10 of 37
X-bar and R Charts
The X-bar chart is a process chart used to monitor the average of the characteristics being measured. To set up an X-bar chart select samples from the process for the characteristic being measured. Then form the samples into rational subgroups. Next, find the average value of each sample by dividing the sums of the measurements by the sample size and plot the value on the process control X-bar chart.

14. Process Control Charts Slide 11 of 37
X-bar and R Charts (continued)
The R chart is used to monitor the variability or dispersion of the process. It is used in conjunction with the X-bar chart when the process characteristic is variable. To develop an R chart, collect samples from the process and organize them into subgroups, usually of three to six items. Next, compute the range, R, by taking the difference of the high value in the subgroup minus the low value. Then plot the R values on the R chart.

15. Process Control Charts Slide 12 of 37
X-bar and R Charts

16. Process Control Charts Slide 13 of 37
Interpreting Control Charts
Before introducing other types of process charts, we discuss the interpretation of the charts.
The figures in the next several slides show different signals for concern that are sent by a control chart, as in the second and third boxes. When a point is found to be outside of the control limits, we call this an “out of control” situation. When a process is out of control, the variation is probably not longer random.

17. Process Control Charts Slide 14 of 37

18. Process Control Charts Slide 15 of 37
Control Chart Evidence for Investigation (Figure in the textbook)

19. Process Control Charts Slide 16 of 37
Control Chart Evidence for Investigation (Figure in the textbook)

20. Process Control Charts Slide 17 of 37
Control Chart Evidence for Investigation (Figure in the textbook)

21. Process Control Charts Slide 18 of 37
Implications of a Process Out of Control
If a process loses control and becomes nonrandom, the process should be stopped immediately.
In many modern process industries where just-in-time is used, this will result in the stoppage of several work stations.
The team of workers who are to address the problem should use a structured problem solving process.

22. Process Control Charts Slide 19 of 37
X and Moving Range (MR) Charts for Population Data
At times, it may not be possible to draw samples. This may occur because a process is so slow that only one or two units per day are produced.
If you have a variable measurement that you want to monitor, the X and MR charts might be the thing for you.

23. Process Control Charts Slide 20 of 37
X and Moving Range (MR) Charts for Population Data (continued)
X chart. A chart used to monitor the mean of a process for population values.
MR chart. A chart for plotting variables when samples are not possible.
If data are not normally distributed, other charts are available.

24. Process Control Charts Slide 21 of 37
g and h Charts
A g chart is used when data are geometrically distributed, and h charts are useful when data are hypergeometrically distributed.
The next slide presents pictures of geometric and hypergeometric distributions. If you develop a histogram of your data, and it appears like either of these distributions, you may want to use either an h or a g chart instead of an X chart.

25. Process Control Charts Slide 22 of 37
h and g Distributions (Figure in the textbook)

26. Process Control Charts Slide 23 of 37
Control Charts for Attributes
We now shift to charts for attributes. These charts deal with binomial and Poisson processes that are not measurements.
We will now be thinking in terms of defects and defectives rather than diameters or widths.
A defect is an irregularity or problem with a larger unit.
A defective is a unit that, as a whole, is not acceptable or does not meet specifications.

27. Process Control Charts Slide 24 of 37
p Charts for Proportion Defective
The p chart is a process chart that is used to graph the proportion of items in a sample that are defective (nonconforming to specifications)
p charts are effectively used to determine when there has been a shift in the proportion defective for a particular product or service.
Typical applications of the p chart include things like late deliveries, incomplete orders, and clerical errors on written forms.

28. Process Control Charts Slide 25 of 37
np Charts
The np chart is a graph of the number of defectives (or nonconforming units) in a subgroup. The np chart requires that the sample size of each subgroup be the same each time a sample is drawn.
When subgroup sizes are equal, either the p or np chart can be used. They are essentially the same chart.

29. Process Control Charts Slide 26 of 37
np Charts (continued)
Some people find the np chart easier to use because it reflects integer numbers rather than proportions. The uses for the np chart are essentially the same as the uses for the p chart.

30. Process Control Charts Slide 27 of 37
c and u Charts
The c chart is a graph of the number of defects (nonconformities) per unit. The units must be of the same sample space; this includes size, height, length, volume and so on. This means that the “area of opportunity” for finding defects must be the same for each unit. Several individual unites can comprise the sample but they will be grouped as if they are one unit of a larger size.

31. Process Control Charts Slide 28 of 37
c and u Charts (continued)
Like other process charts, the c chart is used to detect nonrandom events in the life of a production process. Typical applications of the c chart include number of flaws in an auto finish, number of flaws in a standard typed letter, and number of incorrect responses on a standardized test

32. Process Control Charts Slide 29 of 37
c and u Charts (continued)
The u chart is a graph of the average number of defects per unit. This is contrasted with the c chart, which shows the actual number of defects per standardized unit.
The u chart allows for the units sampled to be different sizes, areas, heights and so on, and allows for different numbers of units in each sample space. The uses for the u chart are the same as the c chart.

33. Process Control Charts Slide 30 of 37
Other Control Charts
s Chart. The s (standard deviation) chart is used in place of the R chart when a more sensitive chart is desired. These charts are commonly used in semiconductor production where process dispersion is watched very closely.

34. Process Control Charts Slide 31 of 37
Other Control Charts (continued)
Moving Average Chart. The moving average chart is an interesting chart that is used for monitoring variables and measurement on a continuous scale.
The chart uses past information to predict what the next process outcome will be. Using this chart, we can adjust a process in anticipation of its going out of control.

35. Process Control Charts Slide 32 of 37
Other Control Charts (continued)
Cusum Chart. The cumulative sum, or cusum, chart is used to identify slight but sustained shifts in a universe where there is no independence between observations.

36. Process Control Charts Slide 33 of 37
Summary of Chart Formulas (Table 10.2 in the textbook)

37. Process Control Charts Slide 34 of 37
Some Control Chart Concepts
Choosing the Correct Control Chart
Obviously, it is key to choose the correct control chart. Figure in the textbook shows a decision tree for the basic control charts. This flow chart helps to show when certain charts should be selected for use.

38. Process Control Charts Slide 35 of 37
Some Control Chart Concepts (continued)
Corrective Action. When a process is out of control, corrective action is needed. Correction action steps are similar to continuous improvement processes. They are
Carefully identify the problem.
Form the correct team to evaluate and solve the problem.
Use structured brainstorming along with fishbone diagrams or affinity diagrams to identify causes of the problem.

39. Process Control Charts Slide 36 of 37
Some Control Chart Concepts (continued)
Corrective Action (continued)
Brainstorm to identify potential solutions to problems.
Eliminate the cause.
Restart the process.
Document the problem, root causes, and solutions.
Communicate the results of the process to all personnel so that this process becomes reinforced and ingrained in the operations.

40. Process Control Charts Slide 37 of 37
Some Control Chart Concepts (continued)
How Do We Use Control Charts to Continuously Improve?
One of the goals of the control chart user is to reduce variation. Over time, as processes are improved, control limits are recomputed to show improvements in stability. As upper and lower control limits get closer and closer together, the process improving.
The focus of control charts should be on continuous improvement and they should be updated only when there is a change in the process.

41. Process Capability Slide 1 of 4
Process Stability and Capability
Once a process is stable, the next emphasis is to ensure that the process is capable.
Process capability refers to the ability of a process to produce a product that meets specifications.
Six-sigma program such as those pioneered by Motorola Corporation result in highly capable processes.

42. Process Capability Slide 2 of 4
Six-Sigma Quality (Figure in the textbook)

43. Process Capability Slide 3 of 4
Process Versus Sampling Distribution
To understand process capability we must first understand the differences between population and sampling distributions.
Population distributions are distributions with all the items or observations of interest to a decision maker.
A population is defined as a collection of all the items or observations of interest to a decision maker.
A sample is subset of the population. Sampling distributions are distributions that reflect the distributions of sample means.

44. Process Capability Slide 4 of 4
The Difference Between Capability and Stability?
Once again, a process is capable if individual products consistently meet specifications.
A process is stable if only common variation is present in the process.

45. Determine characteristic How to choose the correct control chart
to be charted.
How to choose the correct control chart
Non-conforming
units? (% bad
parts)
Nonconformities?
(I.e., discrepancies
per part.)
Is the data
variable? NO NO
YES
YES
YES NO NO
Constant
sample size?
Is sample
space
constant?
Use m
chart.
Use
p chart.
YES
YES
Is it homogeneous,
or not conducive to
subgroup sampling?
(e.g., chemical
bath, paint
batch, etc.)
Use
c or m chart.
Can subgroup
averages be
conveniently
computed?
Use np or
p chart.
Use
median chart. NO NO
YES
YES
Use X - MR chart.
Next slide.

46. How to choose the correct control chart
Can subgroup
averages be
conveniently
computed?
(from previous page) NO
Use
median chart.
YES
Is the subgroup
size < 9? NO
Use .
X - R chart
YES
Can s be calculated
for each group? NO
Use .
X - R chart
YES
Use .
X - s chart