SPC#

Estimated time to read: 54 minutes

Statistical Process Control (SPC) is the use of statistical techniques to measure and control quality by monitoring a process or production method.

In SPC, quality data is collected in the form of product or process measurements or readings from various machines or equipments. The collected data is then used to evaluate, monitor and control a process. Hence, SPC tools and procedures can help you monitor process behavior, discover issues in internal systems, and find solutions for production obstacles.

This document will guide you through the setup and usage of SPC functionalities.

Overview#

In Critical Manufacturing MES, SPC is a set of statistical methods used to monitor a process. The SPC tools in use help to track the behavior of a process in order to identify trends and out-of-control situations. When SPC violations are identified, protocols and corrective actions can be triggered and tracked.

Concepts#

The main concepts related with the SPC module are described in the table below:

Table: SPC main concepts

The SPC object model revolves around the Chart object as can be seen in the following image:

graph LR
    A1[Parameter] --- Main[Chart]
    A2[Maintenance Activity] --- Main
    Main === L1[Logical Chart]
    L1 === L6[Data Point]
    L6 === L7[Data Point Context]
    L6 === L8[Data Point Reading]
    L8 === L9[Data Point Violation]
    Main === L2[Chart Rule]
    L2 === L4["Rule (SPC)"]
    L2 === L5["Rule (SPC Action)"]
    L2 --- A3[Protocol]
    Main ==== L3[Chart Context Information]
    C1[Resource Chart Context] -.- Main
    C2[Step Chart Context] -.- Main

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classDef mermaid_start color:#000, fill:#fafafa, stroke:#fafafa, color:#fafafa, stroke-width:0x, font-size:100%, visibility: hidden;
classDef mermaid_businessdata color:#000, fill:#65CDE8, stroke:#65CDE8, stroke-width:0px, font-size:100%;
classDef mermaid_nonbusinessdata color:#000, fill:#B7DEE8, stroke:#B7DEE8, stroke-width:0px, font-size:100%;
classDef mermaid_entity color:#000, fill:#FB9F53, stroke:#FB9F53, stroke-width:0px, font-size:100%;
classDef mermaid_entitylinked color:#000, fill:#FCD5B5, stroke:#FCD5B5, stroke-width:0px, font-size:100%;
classDef mermaid_context color:#000, fill:#B9CDE5, stroke:#B9CDE5, stroke-width:0px, font-size:100%;
classDef mermaid_optional color:#000, fill:#B7DEE8, stroke:#65CDE8, stroke-width:1px, font-size:100%, stroke-dasharray: 5 5;
class Main mermaid_entity
class A1,A2,A3,A4,A5,A6,A7,A8,A9,A10,A11,A12 mermaid_businessdata
class L1,L2,L3,L4,L5,L6,L7,L8,L9 mermaid_entitylinked
class C1,C2,C3,C4,C5,C6 mermaid_context
class N1,N2,N3,N4,N5,N6 mermaid_nonbusinessdata

click Main "../../userguide/business-data/chart"
click A1 "../../userguide/business-data/parameter"
click A2 "../../userguide/business-data/maintenance-plan"
click A3 "../../userguide/business-data/protocol"
click A4 "../../userguide/business-data/flow"
click C1 "../../userguide/administration/tables/smart-tables/resourcechartcontext"
click C2 "../../userguide/administration/tables/smart-tables/stepchartcontext"

Chart#

A Chart is an object that represents an SPC Chart. Depending on what is intended to be controlled and the sample size, the system currently supports eight different Chart types as listed in the table below. The difference between Variable Charts and Attribute Charts is that Variable Charts monitor continuous variables and typically track two indicators (e.g. Average and Range) while the Attribute Charts monitor discrete variables with a single indicator and are typically related with the number of defects.

Table: Critical Manufacturing MES SPC chart types

The next sub-sections describe each chart in more detail.

Average and Range#

The Average and Range chart is described in the table below:

Table: Average and Range chart properties

Average and Standard Deviation#

The Average and Standard Deviation chart is described in the table below:

Table: Average and Standard Deviation chart properties

Median and Range#

The Median and Range chart is described in the table below:

Table: Median and Range chart properties

Individuals and Moving Range#

The Individuals and Moving Range chart is described in the table below:

Table: Individuals and Moving Range chart properties

Fraction Defective#

The Fraction Defective chart is described in the table below:

Table: Fraction Defective chart properties

Number Defective#

The Number Defective chart is described in the table below:

Table: Number Defective chart properties

Number of Defects per Unit#

The Number of Defects per Unit chart is described in the table below:

Table: Number of Defects per Unit chart properties

Number of Defects#

The Number of Defects chart is described in the table below:

Table: Number of Defects chart properties

Logical Charts#

A Chart consists of many Logical Charts. A Logical Chart is automatically created by the system for each unique combination of Chart context keys. For example, if there is a parameter to be monitored across ten machines (Resources), it is not necessary to create ten different Charts; it is only necessary to create one Chart and define the Resource as a Chart context key. This mechanism allows the same Chart to be re-used across Steps, Equipment (Resources), Products and so forth. A Chart can have many context keys. In addition to the context keys, a Chart can have defined additional mandatory context information. Non mandatory context can always be supplied.

When a Logical Chart is first created (by posting data to a particular context key combination or by explicitly creating it), the system will automatically create the Logical Chart inheriting all the properties that are defined at the Chart level. However, each Logical Chart will maintain a set of its own properties as listed in the table below:

Table: Logical Chart properties

Chart Statistics#

The Chart statistics described below, are calculated based on all the data points that are visible in the GUI for the Logical Chart. Deleted and Excluded data points are not included in these calculations. All formulas apply to the indicator one only.

Some Chart statistics use a single value for specification limits and control limits. Because the specification limits (Lower, Target, Upper) as well as Centerlines and Control Limits (Lower Control Limit and Upper Control Limit) may change from data point to data point, changes in these values will be handled based on the value defined in the configuration entry Cmf/System/Configuration/SPC/MultipleDataPointsStatistics/CalculationMode/ that can have two values:

• Average (default and used if no value is present) - uses the average of the values for the considered data points (default). The considered data points are only the ones that contains the required values (Lower Specification Limit, Target Specification Value, Upper Specification, Lower Control Limit, Centerline and Upper Control Limit).
• Last - uses the values (Lower Specification Limit, Target Specification Value, Upper Specification, Lower Control Limit, Centerline and Upper Control Limit) from the last data point, if the values are defined for the data point.

Table: Chart Statistics

Data Points#

Every time data is posted to SPC a data point is created. A data point stores many properties including the readings that are part of the Data Point. The most important properties are shown in the table below:

Table: Data Point properties

The state of a Data Point results in a different graphical representation and it has an effect on how it is considered for statistics and for SPC rules as shown in this table:

Table: Data Point state effect

Point Statistics#

The point statistics that are displayed in the GUI are described in the table below. The statistics are calculated based on a single data point considering the all the data point readings and are applicable only to variable charts.

Table: Point Statistics

Step and Resource Chart Contexts#

A Chart can be attached to a Step or to a Resource via the Step Chart Context and Resource Chart Context, respectively. The purpose of these contexts is to:

1. Resolve the right of SPC Charts to be used based on the Material or Resource Context;
2. Enable automatic EDC data feed to SPC.

The Step Chart Context can be defined as described in the table below:

Table: Step Chart Context

The Resource Chart Context defined for a state transition of the resource is as described in the table below:

Table: Resource Chart Context

SPC Rules#

SPC rules are used to detect SPC violations. A Chart can have many SPC rules. An SPC rule tests a particular indicator for a specific pattern. It is also possible to specify for each Chart SPC rule an Exception Protocol to be opened and an action to be executed automatically whenever that SPC rule pattern is detected.

SPC rules can be system rules or user defined rules. The system rules are based on the Specification Limits as well as on the Nelson and Western Electric Rules and are described in the table below:

Table: System SPC Rules

In addition to the system rules above, the following user defined rules are also available out of the box.

Table: User Defined SPC Rules

The applicability of an SPC rule to an Indicator as well as to a particular Chart or Chart Type is given by the generic table ChartRuleScope. By default the system ships with the configuration shown below:

Table: Default generic table ChartRuleScope configuration used for scope resolution

Point Selection#

Only the points that have not been deleted or excluded should be taken into account for the calculation of the SPC rules. Also, if the configuration value for /Cmf/System/Configuration/SPC/ChartRules/FilterByControlLimits is set to true, the selection of the points that can be counted for the rule calculation must take the following caveats into account:

For all charts:

• Consider only the points that have the same value for Centerline 1 as the last point.

For Variable charts:

• If the value for Standard Deviation in the last point is not null, consider only the points that have the same value for Standard Deviation as the last point;
• If the value for Standard Deviation in the last point is not null, consider only the points that have the same value for Centerline 2 as the last point.

Zones#

The sigma regions mentioned in the SPC rules are always based on the centerline and the control limits, regardless of whether the limits are defined manually or automatically as shown in the figure below. The upper sigma zones are calculated by dividing the difference between the upper control limit and the centerline by three. Conversely, the lower sigma zones are calculated by dividing the difference between the centerline and the lower control limit by three.

SPC Actions#

It is possible to define an SPC action to be triggered when an SPC rule is violated. For example, it is possible to put the Material on hold, put the Equipment down, request Maintenance, send an Alarm or send an Email. The system comes with three SPC Actions as shown in the table below, but it is possible to create any desired SPC Action. For information on how to create an SPC Action, please refer to the Developer Guide ⧉.

Table: System SPC Actions

Control Limits#

The Control Limits - Upper Control Limits (UCL) and Lower Control Limits (LCL) - are the Voice of the Process (VOP) and often referred in SPC terminology as UAL (Upper Action Limit) and LAL (Lower Action Limit). The control limits vary from chart type to chart type. In some cases, they are fixed over time, and for other cases they are variable (to account for differences in the sample size).

Automatic and Manual Control Limits#

Ideally, the Control Limits are defined based on historical data. In Critical Manufacturing MES, when using automatic control limits, it is necessary to define the centerline and in the case of variable charts also the standard deviation. Using the Chart specific statistical formulas, the system calculates automatically the upper and lower control limits based on the chart type, sample size and using the control chart constants tables described in Appendix A - Control Chart Constants at the end of this page.

It is also possible, but not recommended, to configure a Chart to use manual control limits in which case the user must define them manually. When defining the control limits manually, it is possible to define the upper control limit, the centerline and the lower control limit for Indicator 1 and Indicator 2 (for variable charts).

Automatic Control Limit Recalculation#

When using automatic control limits, at the Chart level it is possible to configure that the control limits (centerlines) must be recalculated every time after a certain number of data points by enabling the Auto-Calculate option in the Chart. There are two parameters that affect this recalculation: the Auto-Calculate Window Size (when to recalculate), and the Auto-Calculate Data Point Size (how many data points to consider in the recalculation) as shown in the figure below:

The system can also be configured to simply collect data points and then, after a certain number of configured data points, calculate and set calculate the centerline (and also the standard deviations in case of variable charts). This is achieved by activating the Learning Mode either in the Chart or in the Logical Chart. When activating the Learning Mode it is also possible to configure the system to stop recalculating the centerline (and standard deviation for variable charts) after a certain number of data points.

Specification Limits#

The Specification Limits -- Upper Specification Limit (USL), Target Specification Value (TSV) and Lower Specification Limit (LSL) are the Voice of the Customer (VOC). The Specification Limits are optional and can be defined for the Chart and for each Logical Chart.

Using Product or Product Group Specification Limits#

It is common for the specification limits to be defined by Product or Product Group. This has the advantage of maintaining the specification limits where it belongs as well as it provides the benefits associated with versioning and change control. To enable Product or Product Group Specification Limits, it is necessary that the Chart has either the Product or the Product Group as context key. If that requirement is met, it is necessary to set the Specification Limits mode to Product. Once the Specification Limits mode is set to Product when creating a logical chart, the system will look for the Product (or Product Group) parameters of type Specification that match the Chart parameter as well as the Chart Product (or Product Group) values to set the specification limits automatically. In addition, if the Chart defines the Step as key, the Product Parameter Step must match the Chart Step key value as well.

Setting Up an SPC Chart#

In order to setup an SPC Chart it is necessary to follow the steps as described in this short table:

Table: SPC Setup steps

The second step, Create the Chart, is specific to SPC and is described below in more detail.

Create a Chart#

To create a Chart, it is necessary to select the appropriate control chart, the image that follows provides guidance on the selection. Nevertheless, the final decision is up to the process specialist based on the specific scenario that is intended to apply SPC control.

• It is better to use X̄ R charts than X̄ s charts when sample sizes are less than 4 [Stapenhurst 2005].
• Although X̄ R charts can be used when the subgroup size is not constant, it is not a good practice. In these cases, X̄ s charts should be used instead [Montgomery 2009].
• For c charts, if the average is large (>5), I-MR charts can be used [Stapenhurst 2005].
• For p charts, if p is near 0.5 and n>10, variable charts can be used [Stapenhurst 2005].

The table that follows describes the most important properties from the different Chart creation step General Data:

Table: SPC creation wizard General Data step important properties

Below you can see a description of the most important properties from the different Chart creation step Display:

Table: SPC creation wizard Display step important properties

Next follows a description of the most important properties from the different Chart creation step Limits:

Table: SPC creation wizard Limits step important properties

In the Context step of the SPC creation wizard, it is necessary to specify the context keys that define each Logical Chart. It is important to bear in mind that each unique combination of the context key values generates a new Logical Chart. In addition to the context keys, any context that is defined for the Chart and that is not marked as key will be treated as required context values (in addition to the context keys) that need to be supplied when posting data to the Chart.

Once the Chart is created, it is possible to manage the Rules using the Manage Rules transaction available in the Rules section. In the Manage Rules transaction, as shown in the figure below, it is possible to add many SPC Rules and for each rule it is possible to define an Exception Protocol to be opened automatically as well as to define a SPC Action to be executed automatically whenever the SPC rule detects a violation.

The option Allow user triggered protocols specifies whether the user can manually open or not a Protocol which is associated with the Chart.

Creating Logical Charts#

As stated earlier, a Logical Chart is created automatically every time a data point is posted to a unique Chart context key combination. Data can be posted manually using the Post Chart Data Point or Post Chart Data Point Aggregated transactions (see Posting Data Points to a Logical Chart) or automatically by configuring a Data Collection to send data automatically to SPC (see the section Integrating Data Collection with SPC).

A Logical Chart can also be created explicitly by using the transaction Manage Logical Charts.

Setting Chart Limits#

With the Set Chart Limits transaction it is possible to modify the specification and control limits for the chart and for the respective logical charts. The Set Chart Limits transaction also allows the modification of the Control limits mode and in case that the Chart Context Keys include the Product or the Product Group, it is also possible to change the Specification Limits mode.

• The Upper, Target and Lower Specification Limits can only be modified if the Specification Limits mode is Chart.
• The Upper and Lower Control Limits can only be modified if the Control limits mode is set to Manual.
• Using Learning Mode can also be enabled, allowing the user to decide whether the limits are set and used automatically when the centerlines are recalculated.

Enabling or Disabling a Chart#

A Chart can be enabled or disabled using the Enable Chart and Disable Chart transactions. When a Chart is disabled it is not possible to post data to any of its logical charts.

Using SPC Charts#

Chart Visualization#

When opening a Logical Chart, the system will display the Chart graphically using the Chart default Display options (refer to the Create a Chart for more information). The next figure shows a standard Chart visualization:

The color and shape of each data point provides meaningful information, as shown below:

Shape and color	Symbol	Comment	Exclusion	Violations
	Blue circle
	Grey circle		x
	Red circle			x
	Blue square	x
	Grey square	x	x
	Red square	x		x

Table: Data Point shape and color information

On the right side there are different Detail panels that are detailed in the following table:

Table: SPC Details Panels

• It is possible to revert to the default view by pressing the Reset View button.
• It is possible to export the Chart either as an image or as an Excel table by pressing the Export button.

The different Chart visualization options can be seen in the table below:

Table: Chart visualization options

Chart Operations#

For a Logical Chart, it is possible to perform the operations described in the table below:

Table: Chart operations

Posting Data Points to a Logical Chart#

To post a data point to a Chart it is necessary to use the Post Chart Data Point transaction as shown below. The Post Chart Data Point Aggregated transaction is available for variable charts and it allows the user to post just the summary of the data (sample size, indicator 1 value, indicator 2 value) and not the individual reading values as shown below:

• When calling the Post Chart Data Point transaction from the Chart, it is necessary to specify the Logical Chart keys. When calling the Post Chart Data Point transaction from the Logical Chart, the context keys are automatically supplied to the transaction.
• The mandatory context must always be filled. Additional supplementary context can also be supplied by pressing the Add button in the Context tab.
• When posting data to a Logical Chart for the first time, the Logical Chart is automatically created with the default settings for the Chart.
• If a comment is entered when posting the data, the comment will be automatically associated with the data point.
• Depending on the configured SPC rules for the chart, if an SPC violation is detected, a Protocol may be opened and/or a SPC Action may be executed automatically.
• The value for the readings must be provided and must comply with the minimum and maximum readings sample size definition for the chart. By default, the maximum number of readings are displayed, and the mandatory readings are marked with an (*) at the beginning. The name of the readings can be changed.
• The values for the Standard Deviation are read from the Logical Chart Standard Deviation at the time of the Data Point post. This value may not be the same as the one that is associated to the Chart Data Point Statistics.

Data Point Operations#

For a Data Point, it is possible to perform the operations described in the table below:

Table: Data Point operations

Integrating Data Collection with SPC#

It is possible to configure a Data Collection to feed data automatically to SPC. This is accomplished in the case of Material Tracking and Resource Tracking by matching Parameters in the Data Collection and in the Chart that are resolved for a context. For Material Tracking and Resource Tracking, Data Collection and Charts are resolved with the same context information. For all matching parameters from the Data Collection with a Chart parameter, the data will be fed automatically to an SPC. In the case of Maintenance Management, the integration is configured directly per Maintenance Activity. The table below provides a summary on how to integrate Data Collections with SPC and the figure provides an illustration of this integration.

Table: Data Collection and SPC Integration

When feeding data from EDC to SPC, the system will automatically supply as much context is available both for the Material and for the Resource. The table below lists the context that is supplied automatically by the system when sending data automatically from EDC to SPC. Note that the context matching between the system context and the Chart context is made by [Name] only.

Table: Data Collection system context supplied to SPC

When sending data automatically from a Data Collection to SPC there are three possible modes as shown in the table below. The mode is defined at the Data Collection level and applies to all the Data Collection Parameters.

Table: EDC system context supplied to SPC

Document References#

Here are the document references used in this document:

Table: Document references

Appendix A - Control Chart Constants#

List of the \(c_4\), \(c_5\), \(d_2\), \(d_3\) and \(e_1\) control chart constants ([Cano et al. 2015], [Montgomery 2009], [Walker et al. 2012], [Statsoft 2009], [Milivojevich 2015]).

Table: Constants for \(c_4\), \(c_5\), \(d_2\), \(d_3\) and \(e_1\)