SPC - Statistical Process Control - Facilitation

 

   

Organisational Metrics
Product and Process Specifications
SPC Charting and Tools

Organisational Metrics

A key component of SPC implementation and facilitation is the reporting structure and ensuring the metrics gathered are key to the strategic and operational outcomes of the organisation whether they are delivering either a product or a service. Transparency is paramount for success tracking, impact analysis and adherence to organisational key performance indicators. Organisational reporting structures may be in place but an SPC program of data collection lends itself directly to the concept of Hoshin Kanri and the reporting that subsequently follows it.

The discipline of Hoshin Kanri is intended to help an organization:

• Focus on a shared goal
• Communicate that goal to all leaders
• Involve all leaders in planning to achieve the goal
• Hold participants accountable for achieving their part of the plan

The broader SPC program should take each process and be analysed with its relationship to business strategies, customer requirements, regulatory requirements and operational requirements. This ensures process metrics are directly related to the required outcomes of the organisation. A robust view of each measure when related to neighbouring processes and parent processes will set up a clear data reporting line and opportunity for further analysis. Once set up and agreed the collected data can be anlaysed by SPC using organisational KPI.

Adherence to KPI through SPC allows the organistion to report measureable success provided all KPI and metrics are linked to business strategies, customer requirements, regulatory requirements and operational requirements. Each metric within the organisation should be able to link to the higher level KPI of the shared goal of the organisation. In a multidimensional organisation KPI should be aligned along customer lines and will allow the Voice of Customer to be represented in SPC data - this is achieved in the initial process to' organisational requirement analysis. For assistance in obtaining organisational metrics robustly connected to organisational requirements please contact Quality One.

Product and Process Specifications

Product and Process Specifications are robustly determined through design and process engineering collaboration within the APQP process.

Determining Product and Process Specifications
SPC is placed in the Product and Process Validation phase of APQP. The characteristics measured by the SPC section of the APQP Process are delivered by a robust view throughout the product build which culminates in the Production Control Plan which delivers the requirements of the items to be measured whose output is SPC. This is well defined set of tools that delivers the key characteristics to be measured by the organisation.

Robust tools leading to SPC
In practical terms robustness in product development flows through from VOC (Voice of Customer) to the chosen SPC charts. The following question set applies to test the robustness of the SPC data.
Q. Why is there a chart with that characteritic?
A. The Production Control Plan asks for it
Q. Why does the Production Control Plan asks for it
A. The PFMEA identified the characteristic as high severity with the measure as a specific control
Q. Why did the PFMEA have the characteristic at a high severity
A. The Characteristics Matrix aligned the process step with the critical characteristic from the DFMEA Failure Mode
Q. Why was this process step highlighted in the Characteristics Matrix
A. The highlighted failure mode in the DFMEA has a relationship (potential for escape) at that process step
Q. Why was the failure mode highlighted in the DFMEA?
A. The failure mode of the functional requirement has an effect of failure at critical or significant levels
Q. Why was the function required as part of the design?
A. Engineering Specifications deemed the function required
Q. Why was the function deemed required?
A. The VOC (Voice of Customer) had a product requirement that needs the function
Q. Why did the VOC have the product requirement?
A. The customer requested the need, want or desire for the product to deliver the output or outcome.
For assistance in ensuring robustness in your organisations SPC measurements please contact Quality One.

For an organisational view of required metrics the measurements obtained from the APQP process can be determined as customer, regulatory and operational requirements being measured at the production processes within the organisational process hierarchy.

SPC Charting and Tools

Data Definitions For Proper Chart Selection
Choosing the correct chart for a given a situation is the first step in every analysis. There are just a few charts to choose from, and determining the appropriate one requires following some fairly simple rules based on the underlying data. These rules are described in the flowchart below:

Control charts are divided into two groups:
Variable Charts
Variable charts are based on variable data that can be measured on a continuous scale. For example, weight, volume, temperature, or length of stay. These can be measured to as many decimal places as necessary.
Individual, average, and range charts are variable data charts.
Attribute Charts
Attribute charts are based on data that can be grouped and counted as present or not. Attribute charts are also called count charts and attribute data is also known as discrete data. Attribute data is measured only with whole numbers. Examples include:

• Acceptable vs. non-acceptable
• Forms completed with errors vs. without errors
• Number of prescriptions with errors vs. without
• The number of green, blue, yellow or red cars

When constructing attribute control charts, a subgroup is the group of units that were inspected to obtain the number of defects or the number of defective items.
Defect and reject charts are used for attribute data.
Variable Data Charts – Individual, Average, and Range Charts
Variable data requires the use of variable charts. Variable charts are easy to understand and use.

Individual Charts – I chart
The I chart is also referred to as an individual, item, i, or X chart. The X refers to a variable X.

Individual charts plot the process results varying over time. Individual observations are plotted on the I chart, averages are not plotted on this type of chart. Individual charts are used to plot variable data collected chronologically from a process, such as a part’s measurement over time.
These charts are especially useful for identifying shifts in the process average. When monitoring a system, it is expected that equal numbers of points will fall above and below the average that is represented by the centerline. Shifts or trends can indicate a change that needs to be investigated.
The individual control chart is reserved for situations in which only one measurement is performed each time the data is collected, where it is impractical or impossible to collect a sample of observations. When there are not enough data points to calculate valid control limits, an individual chart functions as a simple run chart.
Average Charts – X-bar Chart
Average charts are made by plotting averages of individual measurements on the chart. The average chart is called the X-bar chart because, in statistical notation, a bar or line over the variable (X) symbolizes the average of X. “X-bar” is a shorthand way of saying “the average of X”.
An X-bar chart is a variable control chart that displays the changes in the average output of a process. The chart reflects either changes over time or changes associated with a categorical data variable. The chart shows how consistent and predictable a process is at achieving the mean.
X-bar charts measure variation between subgroups. They are often paired with either Standard Deviation (S) or Range (R) charts, which measure variation within subgroups.

Range Chart – R-Chart
The Range chart can be combined with I charts and X-bar charts. The chart names combine the corresponding chart initials. Range charts measure the variation in the data. An example is the weather report in the newspaper that gives the high and low temperatures each day. The difference between the high and the low is the range for that day.

Moving Range Chart – MR Chart
This type of chart displays the moving range of successive observations. A moving range chart can be used when it is impossible or impractical to collect more than a single data point for each subgroup.
This chart can be paired with an individual chart, which is then called an Individual Moving Range (IR) chart. An individual chart is used to highlight the changes in a variable from a central value, the mean. The moving range chart displays variability among measurements based on the difference between one data point and the next.

Individual And Range Charts – IR Charts
This pair of variable control charts is often offered together for quality control analysis. The Individual chart, the upper chart in the figure below, displays changes to the process output over time in relation to the center line which represents the mean. The Moving Range chart, the lower chart in the figure below, analyzes the variation between consecutive observations, which is a measure of process variability.

Average & Range Charts – X-Bar And R Charts
Variable and Range control charts are often displayed together for quality control analysis. The X-bar chart, the upper chart in the figure below, is a graphic representation of the variation among the subgroup averages, the R chart, the lower chart in the figure below, looks at variability within these subgroups.
The variation within subgroups is represented by the range (R). The range of values for each subgroup is plotted on the Y-axis of the R chart. The centerline is the average or mean of the range.

X-Bar Standard Deviation Charts – X-Bar And S Charts
This pair of variable control charts is often displayed together for quality control analysis. The X-bar chart, the upper chart in the figure below, displays the variation in the means between the subgroups. The s chart, the lower chart in the figure below, looks at variability within these subgroups.
In this pair of charts, the variation within subgroups is represented by the standard deviation. The standard deviation is plotted on the y-axis, and is a measure of the spread of values for each subgroup. The centerline is the average or mean of these sub-group standard deviations.

It is possibe to choose a standard deviation chart, i.e. an s-chart, instead of the Moving Range chart. The Range chart is often used because the standard deviation is a more accurate and therefore more difficult measurement. Now that computers are automatically calculating the standard deviation, the s-chart can be used in all situations. This is called the X-bar S chart.
A standard deviation formula is used to calculate the differences in the data. This calculation can be used in cases where the subgroup sample size is large and sampling methods support the modeling of the data as normal distribution.
Process Capability Chart – cp Chart
Process capability analysis is used to adjust the process until virtually all of the product output meets the specifications. Once the process is operating in control, capability analysis attempts to answer the question: Is the output meeting specifications, or is the process capable? If it is not, can the process be adjusted to make it capable?
The process capability chart contains a normal curve superimposed over a histogram of the data, followed by several statistics. A process is said to be capable if its output falls within the specifications virtually 100% of the time.
Note: Specification Limits are the boundaries, or tolerances, set by management, engineers or customers which are based on product requirements or service objectives. Specification Limits are NOT established by the process itself, and may not even be possible within the given process.
One goal of Statistical Process Control is to determine if specifications are in fact possible in the current process. If the following statements are true, a process capability chart can be an appropriate tool for measuring the inherent reproducibility of the process and monitoring the degree to which it can meet specifications:

• The process is stable and in control.
• The data are normally distributed.
• Specification limits fall on either side of the centerline.
• You are investigating whether your process is capable of meeting specifications.

Attribute Data Charts
Attribute data represents particular characteristics of a product or system that can be counted, not product measurements. They are characteristics that are present or not present. This is known as discrete data, and is measured only with whole numbers. Examples include:

• Acceptable vs. non-acceptable
• Forms completed with errors vs. without errors
• Number of prescriptions with errors vs. without

Attribute data has another distinctive characteristic. In quality control analysis, this countable data falls into one of two categories:

• Defects data is the number of nonconformities within an item. There is no limit to the number of possible defects. Defects charts count the number of defects in the inspection unit.
• Rejects data where the entire item is judged to conform to product specifications or not. Rejects charts count the number of rejects in a subgroup.

One way to determine what type of data you have is to ask, “Can I count both the occurrences AND non-occurrences of the defective data?” For example, you can count how many forms have errors and how many do not, however you cannot count how many errors were NOT made on the form. If you can count both occurrences and non-occurrences, you have rejects data. If the non-occurrences cannot be determined, then you have defects data.
For example:
If you are counting the number of errors made on an insurance form, you have an example of the defects per form. There is no limit to the number of defects that can be counted on each form.
If you are counting the total number of forms that had one or more errors, then you have a count of the rejected units. This is either one or zero rejects per unit.

Summary Of Defects vs. Rejects Data

• Defects charts are attribute charts for cases in which the possible occurrences are infinite or cannot be counted. They count the number of non-conformities within an item.
• Rejects charts are attribute Data charts for the cases in which rejected whole units are counted. These figures can be described as ratios instead of just counts.

Subgroup Size – Constant or Changing?
Subgroup size is another important data characteristic to consider in selecting the right type of chart. When constructing attribute control charts, a subgroup is the group of units that were inspected to obtain the number of defects or the number of rejects.To choose the correct chart, you need to determine if the subgroup size is constant or not. If constant, for example 300 forms are processed every day, then you can look at a straight count of the defective occurrences. If the subgroup size changes, you need to look at the percentage or fraction of defective occurrences.
As an example:
An organization may have a day in which 500 insurance forms are processed and 50 have errors vs. another day in which only 150 are processed and 20 have errors. If we only look at the count of errors, 50 vs. 20, we would assume the 50 error day was worse. But when considering the total size of the subgroup, 500 vs. 150, we determine that, on the first day, 10% had errors while, the other day, 13.3% had errors.
Now that we understand the different types of attribute data, let’s move on to the specific charts for analyzing them. There are four different types of attribute charts. For each type of attribute data, defects, and rejects, there is a chart for subgroups of constant size and one for subgroups of varying size.
To finish:

• Defects Charts count the number of defects within the inspection unit.
• Rejects Charts count the number of rejected units in a subgroup.

Defects Charts
The two defects charts are the c chart and the u chart. The c refers to count of defects in a subgroup of constant size. The u is a per unit count within a variable size subgroup.
c Chart – Constant Subgroup Size
A c chart, or Count chart, is an attribute control chart that displays how the number of defects, or nonconformities, for a process or system is changing over time. The number of defects is collected for the area of opportunity in each subgroup. The area of opportunity can be either a group of units or just one individual unit on which defect counts are performed. The c chart is an indicator of the consistency and predictability of the level of defects in the process.
When constructing a c chart, it is important that the area of opportunity for a defect be constant from subgroup to subgroup since the chart shows the total number of defects. When the number of items tested within a subgroup changes, then a u chart should be used, since it shows the number of defects per unit rather than total defects.

u Chart – Varying Subgroup Size
A u chart (u is for Unit) is an attribute control chart that displays how the frequency of defects, or nonconformities, is changing over time for a process or system. The number of defects is collected for the area of opportunity in each subgroup. The area of opportunity can be either a group of items or just one individual item on which defect counts are performed. The u chart is an indicator of the consistency and predictability of the level of defects in the process.
A u chart is appropriate when the area of opportunity for a defect varies from subgroup to subgroup. This can be seen in the shifting UCL and LCL lines that depend on the size of the subgroup. This chart shows the number of defects per unit. When the number of items tested remains the same among all the subgroups, then a c chart should be used since a c chart analyzes total defects rather than the number of defects per unit.

Rejects Charts
The two types of Rejects charts are the p chart and the np chart. The name of the p chart stands for the Percentage of rejects in a subgroup. The name of the np chart stands for the Number of rejects within a p-type chart. You can also remember it as “not percentage” or “not proportional”.
A mnemonic to remember that the p chart and its partner, the np chart, represent Rejects data is to think of P as a “pea” and a canning plant that is rejecting cans of peas if they are not 100% acceptable. As p and np are a team, you should be able to recall this with the same story.
np Chart – Number of Rejects Chart for Constant Subgroup Size
An np chart is an attribute control chart that displays changes in the number of defective products, rejects or unacceptable outcomes. It is an indicator of the consistency and predictability of the level of defects in the process.
The np chart is only valid as long as your data are collected in subgroups that are the same size. When you have a variable subgroup size, a p chart should be used.

p Chart – Percentage Chart for Varying Subgroup Size
A p chart is an attribute control chart that displays changes in the proportion of defective products, rejects, or unacceptable outcomes. It is an indicator of the consistency and predictability of the level of defects in the process.
Since a p chart is used when the subgroup size varies, the chart plots the proportion or fraction of items rejected, rather than the number rejected. This is indicated by the shifting UCL and LCL lines that depend on the size of the subgroup. For each subgroup, the proportion rejected is calculated as the number of rejects divided by the number of items inspected. When you have a constant subgroup size, use an np chart instead.

Histograms
Now you can put the data from the check sheets into a histogram. A histogram is a snapshot of the variation of a product or the results of a process. It often forms the bell-shaped curve which is characteristic of a normal process.
The histogram helps you analyze what is going on in the process and helps show the capability of a process, whether the data is falling inside the bell-shaped curve and within specifications.
A histogram displays a frequency distribution of the occurrence of the various measurements. The variable being measured is along the horizontal x-axis, and is grouped into several ranges of measurements. The frequency of occurrence of each measurement is charted along the vertical y-axis.

Histograms depict the central tendency or mean of the data, and its variation or spread. A histogram also shows the range of measurements, which defines the process capability. A histogram can show characteristics of the process being measured, such as:

• Do the results show a normal distribution, a bell curve? If not, why not?
• Does the range of the data indicate that the process is capable of producing what is required by the customer or the specifications?
• How much improvement is necessary to meet specifications? Is this level of improvement possible in the current process?

Pareto Charts
The Pareto chart can be used to display categories of problems graphically so they can be properly prioritized. The Pareto chart is named for a 19th century Italian economist who postulated that a small minority (20%) of the people owned a great proportion (80%) of the wealth in the land.
There are often many aspects of a process or system that can be improved, such as the number of defective products, time allocation, or cost savings. Each aspect usually contains many smaller problems, making it difficult to determine how to approach the issue. A Pareto chart or diagram indicates which problem to tackle first by showing the proportion of the total problem that each of the smaller problems comprise. This is based on the Pareto principle: 20% of the sources cause 80% of the problem.
A Count Pareto chart is a vertical bar graph displaying rank in descending order of importance for the categories of problems, defects or opportunities. Generally, you gain more by working on the problem identified by the tallest bar than trying to deal with the smaller bars. However, you should ask yourself what item on the chart has the greatest impact on the goals of your business, because sometimes the most frequent problem as shown by the Pareto chart is not always the most important. SPC is a tool to be used by people with experience and common sense as their guide.
This is a Pareto chart of defect types.

Once a major problem has been selected, it needs to be analyzed for possible causes. Cause-and-effect diagrams, scatter plots and flow charts can be used in this part of the process.
Probability Plots
In order to use Control Charts, the data needs to approximate a normal distribution, to generally form the familiar bell-shaped curve.
The probability plot is a graph of the cumulative relative frequencies of the data, plotted on a normal probability scale. If the data is normal it forms a line that is fairly straight. The purpose of this plot is to show whether the data approximates a normal distribution. This can be an important assumption in many statistical analyses.

Although a probability plot is useful in analyzing data for normality, it is particularly useful for determining how capable a process is when the data is not normally distributed. That is, we are interested in finding the limits within which most of the data fall.
Since the probability plot shows the percent of the data that falls below a given value, we can sketch the curve that best fits the data. We can then read the value that corresponds to 0.001 (0.1%) of the data. This is generally considered the lower natural limit. The value corresponding to 0.999 (99.9%) is generally considered the upper natural limit.
Note that to be more consistent with the natural limits for a normal distribution, some analysis is chosen between 0.00135 and 0.99865 for the natural limits.
Scatter Diagrams
The Scatter diagram, or plot, is another problem analysis tool. Scatter plots are also called correlation charts.
A Scatter plot is used to uncover possible cause-and-effect relationships. It is constructed by plotting two variables against one another on a pair of axes. A Scatter plot cannot prove that one variable causes another, but it does show how a pair of variables is related and the strength of that relationship. Statistical tests quantify the degree of correlation between the variables.

In this example, there appears to be a relationship between height and weight. As the student gets taller, generally speaking they get heavier.