Articles by Results

Explaining SPC - Applying SPC

Posted by Graham Cripps on Mon, Aug 03, 2015 @ 12:45 PM

Applying SPC

graham_cripps_dec_2010_formal-3

 

Statistical Process Control (SPC) is like many tools used in Continuous Improvement (CI) and Quality Control methodologies in that it is not something that you would use for every process. It is also true to say that we don't just apply it to processes that have variable data, as there are other forms of SPC charts available for use (which we will discuss later in this article).

 

Dependant upon which industry you are applying SPC in, there may well be industry standards to be considered, for example supply chain control systems. Therefore, in this article, we will make general recommendations on how you might approach the application of SPC.

Selecting Processes For SPC

SPC should not be applied as a scattergun approach but reserved for processes that are:

  • Critical (as defined by the FMEA process)
  • Producing critical outcomes (as defined by the FMEA process)
  • Known to have reliability issues (out of control conditions)
  • Critical to customer satisfaction (internal or external)

In all cases, it is better to control process parameters rather than the process outcomes. In other words, if the process parameters that make the outcome reliable are known then why risk making reject parts?

For example to produce a 'good' spot weld, the process parameters that can be controlled are:

  • Tip condition
  • Power (Amps)
  • Dwell time
  • Tip to anvil pressure
  • Substrate condition

Get all of these right and the spot weld is guaranteed!

Planning to implement SPC requires the involvement of the team and ensuring that everyone understands their role and are trained in the requirements for this. The plan also needs to reflect why SPC is to be applied to the process in question.

The plan should include:

  • Understanding the process paramters and common cause variation
  • Sample size
  • Sampling frequency
  • Measurement system analysis
  • Data collection and analysis responsibilities
  • Training requirements (where necessary)
  • Timing

When planning to set up SPC on a process, there are a few rules that need to be observed including data source - the data to be collected should be from one source only. In other words avoid collecting data from:

  • More than one process
  • More than one tool
  • More than one mould or cavity
  • More than one measuring station

Calculating Control Limits

Control Limits should not be calcuated, in the first instance, until such time as all of the common causes of variation have been experienced, such as:

  • Changes of shift
  • Normal changes in the environment (internal and external)
  • Change of supply of materials (under normal circumstances)
  • Cutting tool sharpening (after tool wear)
  • Autonomous maintenance
  • Change of operator
  • Change of person taking the measurement

In any event a minimum of twenty sub-sets of data will need to be collected

Once the control limits have been calculated, thay should not be re-calculated until something has changed, that is to say a special cause has taken place, process re-set, tooling changes or other significant event.

We have have experienced, in some organisations, the recalculation of the control limits after every SPC sheet has been completed, this should not be done unless the completion coincides with a significant event, as above.

Other Control Charts

There are two types of data that can come from a process.

1. Variable Data: something that can be measured (length, volume, mass for example), which has been the focus of this series of articles.

2. Attribute Data: something that can be observed, for example presence of components, marks, blemishes, go / no go conditions.

For variable data there are two charts in common use:

X-bar and R Charts (see here for downloadable version of blank and completed)

X and R Charts (individuals and moving range). These are used where small amounts of data are available or sampling frequency is required to be relatively high.

With attribute data the following charts are available for use:

P-Chart - for inconsistent sample sizes and non-conforming uits

N-Chart - for inconsistent sample sizes and non-conformities (faults)

C-Chart - for constant sample sizes and non-confirmities (faults)

Np-Chart - for constant sample sizes and non-confirming units

For more information about how these charts are appplied, or for assistance in your SPC efforts please contact either myself, Graham Cripps on graham.cripps@resultsresults.co.uk or Julie Camp on julie.camp@resultsresults.co.uk

 

Answers to Capability Exercise are here!

 

 

Topics: Continuous Improvement, Statistical Process Control, SPC

SPC - Understanding Capability

Posted by Graham Cripps on Mon, Jul 27, 2015 @ 12:12 PM

SPC - Understanding Capability

Having capable processes is critical to any improvement initiative. in this article we will look at what capability means and how to measure it.

In previous articles we have looked at process output and how the data can be used to control the process. Having this data available means that you can also calculate capability.

We will look at the prime capability indices:

C- Process potential capability

Cpk – Ongoing process capability

First, let us look at what capability is. By definition process capability is a ratio, over time, of how the process meets the specification. However the process must be stable and in control, that is that there are no special causes or variation present.

Process potential capability is a ratio and calculated by:

Cp = USL – LSL
          6σ

SPC_B6_P1

 

This diagram shows the upper and lower specification limits and a process that is centered whereby + / - 3σ falls within these limits. Where 6σ is equal to the specification then the process has a potential capability of 1.0. However, there is a possibility that 0.27% will fall outside specification limits.

 

 

SPC_B6_P2

 

In the graphic to the right we have three centered processes, each with a different process spread. From the top the spread is less than the specification, therefore the C will be greater than 1.

The middle example has a spread equal to the specification

The lower process has a spread greater than the specification therefore the C will be less than one (eg not capable).

 

 

 

In many cases the process spread will not be centered about the centre of the specification so we need a method for calculating capability in these circumstances.

SPC_B6_P3

 

This graphic shows that we need to calculate the capability for each half of the process spread, where the process capability is calculated by taking the lesser of CPKL (capability lower) and CPKU (capability upper). The calculations for these are:

CPKL = X – LSL and CPKU = USL – X
              3σ                            3σ

 

 

The following three examples are provided to aid your visualisation of capability for three process outputs.

SPC_B6_P4

 

Here the process is centered so the CPKL and CPKU are the same.

 

 

 

SPC_B6_P5

 

In this example the potential Cp is 1.00, or the process spread is equal to the specification limits. However, if we take into consideration the location of the data relative to the specification, the Cpk is 0.00

 

SPC_B6_P6

 

In this final example we can see that the process spread is below the specification limit. Cp is still 1.00 but the Cpk is minus 1.00

 

There is a capability exercise available for download at the end of this article, which will provide an opportunity for you to practice using four examples (the answers will be provided for you to check against with article 7, be sure to watch out for this later this week!).

Recommended Target Cpk Values

There are some practical considerations when looking at process capability. These are due to:

  • The data used in the examples above is based on averages of sub-groups of data (averages, X-bar)
  • Allowing for process shift due to common causes of variation
  • Allowances for measurement accuracies
  • Allowing for the 0.23% probability of producing outside the + / - 3σ

There are some industry standards established and these should be established in all cases. However, as a rule of thumb, we can recommend that for initial capability the Cpk  should be between 1.60 and 1.80. For ongoing capability, the Cpk  value should be between 1.40 and 1.60.

Download Your Capability Exercise

 

 

Topics: Continuous Improvement, Statistical Process Control, SPC

Interpreting An SPC X-bar And Chart

Posted by Graham Cripps on Thu, Jul 23, 2015 @ 03:29 PM

Interpreting An SPC X-bar And R Chart

In the last few articles we have looked at the basics behind SPC and the completion of an SPC chart. Now we have a completed chart we will look at how to interpret it. Firstly, however, we need to lay a few more foundations.

Types Of Distribution

We will cover the most common types, which are Gaussian, Bimodal and Skewed distributions. We will also consider the other descriptors, being the location (mean, mode and median) as well as spread.

SPC_B5_P1

Skewed Distribution - this is where the data is skewed to one side. the mode (highest occurring data point), the mean (or average) and median (middle number) do not coincide.

 

 

 

 

 

SPC_B5_P3

 

 

Bimodal - here we have a distribution that typically contains two of something (two processes, two tools or cavities, two measuring stations). As will be seen later, this can be misleading when trying to interpret the SPC chart. It is important to ensure that data is collected from one source only.

 

SPC_B5_P3

Gaussian - a distribution that is equally dispersed about the mean value. The mean, mode and median values are the same. In SPC we use this form of distribution by taking several samples (the sub-group), as this will tend any distribution towards a Gaussian curve. This enables probability to be assessed. 

 

 

The problem with some processes is that they do not behave in a way that presents the data in a normal (Gaussian) distribution. As mentioned in previous articles, we use sub-groups of data, which have the tendency to present the data in a normalised format.

Control Limits

Control limits are calculated based upon what the process is generating. As previously mentioned, control limits should only be calculated when the process is devoid of special causes of variation, and when all the normal causes of variation have been included. This includes but is not limited to:

  • Changes of shift
  • Normal changes in the environment (internal and external)
  • Change of supply of materials (under normal circumstances)
  • Autonomous maintenance
  • A minimum of twenty data sub-sets

This applies to both control limits for range (R) and for averages (X-bar) of sub-sets.

Interpreting The Sample X-bar And R Chart

As part of the last SPC article you will have given access to a sample chart (if you have not yet downloaded this you can find it here). We will be referring to this chart during the remainder of this article so having it to hand will be useful.

The sample chart has been produced based on data from a machining operation, producing a small shaft.

The 7 Point Rule

Well, not really a rule, more of a recommendation. However, in the article titled 'Probability And SPC', we discussed what we can expect from a process under normal conditions.

SPC_B5_P4The possible outcomes could be any one of the following eight:

  • All above the mean
  • All below the mean
  • All within the +/- 1 σ
  • All within the +/- 2 σ
  • In one half of the distribution
  • All going up
  • All going down
  • In the outer 1/3 area

 

 

The 7 Point Rule suggests that under normal circumstances we would expect that each sub-set of data would not  have more than seven successive points that are in one of the eight possible outcomes.

This is based upon the probability of this occuring of 1 / 128 or 27

In other words, each data set has two possible outcomes, either a repeat of one of the above possible outcomes or any other outcome.

For example, if the last data set was in the +/- 1 σ area, you would not expect to see a further six based upon the probablity theory.

The Range Plot

SPC_B5_P5

In this example we can see there are no seven points that could be considered to be 'out of control' conditions.

Out of control conditions are those situations that are brought about due to a change. A special cause of variation is present.

The X-bar Plot

Again this is taken from the chart previously provided

SPC_B5_P6

 

At first sight all would appear to be good. However, there are a number of successive points within the +/- 1 σ area, this would need further investigation.

In this example, the control limits have been calculated based upon the first set of twenty sub-sets of data, so 'Whats the problem?' you may ask.

SPC_B5_P7

 

We have seen a lot of instances where the individual data values have not been plotted as part of the SPC chart.

Not plotting this information, as in this case, can lead to misinterpretation of the X-bar plot.

Here we can see that there are two distinct distributions of the individual data points, in other words a bimodal distribution. As previously stated, this cannot be used in an X-bar and R chart, as it will be masked by the process of calculating the mean values of each sub-set of data.

The investigation would need to centre on what has caused this bimodal distribution (special cause)

This example clearly shows the need for plotting of the individuals

Summary

Reviewing the example X-bar and R chart shows how powerful this tool can be for reviewing the control of processes.

We have used an example of a manufacturing machining process but SPC is just as applicable to many other processes, not just manufacturing. In fact, any process from which data can be gathered can be controlled using SPC.

Download Your Calculations Sheet Here!

 

Topics: Continuous Improvement, Statistical Process Control, SPC

SPC - Collecting & Plotting Data

Posted by Graham Cripps on Thu, Jul 16, 2015 @ 01:00 PM

SPC - Collecting & Plotting Data

Data Collection

When planning to set up SPC on a process there are a few rules that need to be observed:

  • Data source* - the data to be collected should be from one source only, in other words avoid collecting data from:
    • More than one process
    • More than one tool
    • More than one mould or casting cavity
    • More than one measuring station
  • Data Type - data must be variable data (something that can be measured)
  • Characteristic - should be restricted to those that are critical in terms of customer satisfaction, or identified as critical as part of the FMEA output.

* Date that is collected from more than one source will contain the variance between the two sources and will make it difficult (if not impossible!) to predict outcomes. It can even be misleading, in terms of interpretation of the completed SPC Chart. This will be fully explained in the next article 'Interpreting The Chart'

For the purpose of this exercise we will use some data that is from a manufacturing process, the diameter of a small shaft. The data is arranged from top to bottom, starting in the top left corner (1.071, 1.032, 1.164 etc).

The measurements are taken approximately every thirty minutes and five consecutive samples are taken each time

SPC_B4_P1

The shaft specification is 1.100 mm diameter + / - 0.010mm.

Plotting Data

We will now go through the process of filling in the data and calculating the various parameters to enable the results to be plotted, we will cover step by step. The plotting will take place in three areas as shown below:

SPC_B4_P2

 

SPC_B4_P3

 

Step 1: For each sub-group record the individual values then calculate the mean value of this sub-group.

Example:   (1.071+1.032+1.164+1.041+1.064) ÷ 5 = 5.372 ÷ 2 = 1.0744 ( X-bar).

 

 

 

Step 2: Calculate the range of this sub-group.

Example: 1.164 (largest Number) – 1.032 (smallest value) = 0.132

Note: When beginning a new SPC project it is best to run at least twenty sub-groups before attempting to plot the data. This will allow you to select the best fit for the graphs (more about this in the next article).

Step 3: Calculate the average of all the averages for X. This is the sum of all the averages divided by the number of sub- groups:

SPC_B4_P7

Step 4: Calculate the average for the ranges (R-bar). This is the sum of all the ranges for each sub group divided by the number of sub groups:

SPC_B4_P8

 

 

Step 5: Determine the scales for plotting:

  • The range values
  • The X-bar values

Step 6: Plot the range values and the X-bar values

Plot of the range values R

SPC_B4_P4

Plot of the average values X-bar

SPC_B4_P5

Step 7: Calculate and plot the control limits for range R and sub-group averages X-bar

SPC_B4_P6

 

There is a completed  example chart, using the data provided in this article, that can be downloaded (see below) that will enable you to follow this example.

This will also be referred to in the next article

 

 

Step 8: Plot the individual vales. To do this you will need to determine the intervals and the scale for plotting. Remember, the individuals should not be compared to the plot of X-bar as these are the average values of the sub-groups.

In the next article we will be discussing how to interpret an example of a completed chart.

SPC X-bar & R Chart (Completed) Download

Topics: Continuous Improvement, Statistical Process Control, SPC

SPC - Probability And SPC

Posted by Graham Cripps on Mon, Jul 13, 2015 @ 02:39 PM

Probability And SPC

Welcome to the third article in the 'Explaining SPC' series, written by our Subject Specialist Graham Cripps.

 

Probability is the statistical method for predicting the chances of a single or series of events actually happening.

For example, if I toss a coin in the air, assuming no other influences are present, I can predict that I will get either heads or tails - two possible outcomes from one event. This can be expressed as:

  • The probablity of a head is 1/2
  • The probability of a tail is 1/2

If I now consider having two coins that are tossed then the outcome could be the same for each coin. However, if we consider that the outcome we are looking for is all heads, then we can see that the outcomes could be:

SPC_B3_P1

We can see that we have four possible outcomes so the probability of one of these is 1/4 (or 1/2 x 1/2).

If we had seven coins, the probability of getting all heads, or any other outcome, would be:

1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 x 1/2 = 1/128

This is usually written as 27 (2 to the power of 7). In other words, two possible outcomes from seven different coins.

Variation

Variation is present in all things - be it manufacturing a shaft, filling a milk bottle or formulating ink colour, there will be some degree of variation.

There are two types of causes of variation:

  • Common Causes
  • Special Causes

Common Causes are due to the natural variation, always present in and around a process, under normal running conditions. These will include those coming from man, machine, measurement, materials, equipment, methods and environment (both internal and external environments).

Special Causes are due to a change condition, something has changed in or around the process that is abnormal.

A process that has only common causes present is said to be in control. In other words, the outcome of a process can be predicted within the realms of probability.

SPC can only be applied on a process that is in control as predicting special causes of variation is not feasible.

So let us take a look at how SPC can predict an outcome based upon the output of the process itself.

SPC - Predicting Outcomes

A process has been measured for a few days. The data gathered is based upon a sample size of five taken every hour. The data has been plotted on a histogram and we have calculated the mean of the data (mean of all the means, X-bar), the range and the distribution (the sigma value or σ)

SPC_B3_P2This diagram describes the past process output, based upon the data gathered. If we consider plus or minus three sigma (+ - 3σ), it is a function of a normal distribution that 68.27% falls within the cente third, 95.45% within the centre two thirds and 99.73% within + - 3σ.

Only 0.23% of all data falls outside of + - 3σ.

Finally, the data is equally spread about the mean.

These statistical facts form the basis of the application theory of SPC

Let me explain how this works. For any set of sample data from now on (sample of five) we can predict that the data points will follow these patterns.

So the likelihood that seven sets of consecutive samples behave outside of these patterns (i.e. one single outcome repeated from eight possible outcomes) then the probability against would be 1 / 128.

The eight possible outcomes for sub-group values are:

  • All above the mean
  • All below the mean
  • All within the + - 1σ
  • All within the + - 2σ
  • In one half of the distribution
  • All going up
  • All going down
  • In the outer 1/3 area

We will come back to this again in future articles

Download Your SPC Dice Plotting Exercise

As always please let us know if you have any questions or feedback, you can call us on 01371 859 344 or contact by email us on julie.camp@resultsresults.co.uk 

Topics: Continuous Improvement, Statistical Process Control, SPC

SPC - The Basic Statistics Behind SPC

Posted by Graham Cripps on Thu, Jul 09, 2015 @ 03:04 PM

SPC - The Basic Statistics Behind SPC

This is the second article in our SPC Blog series, aiming to provide a background to the statistics behind Statistical Process Control (SPC) for variable data.

Variable data is derived from anything that can be measured and includes length, diameter, hardness, distance, volume, mass and gloss levels to name but a few.

Basic Statistics are used to convert large amounts of data into a more meaningful form. For me, this is about making pictures from numbers.

SPC requires information or data to be described using three terms:-

  • Location - where the data is located on a line of continuum
  • Spread - the smallest to largest measurement taken
  • Distribution - the way the data is located relative to a central data value

Location - Measures Of Central Tendency

Central tendency describes the location of a set of data. The three descriptors are mean, mode and median.

  • MEAN is the arithmetic mean or average
  • MODE describes the most frequently occurring value
  • MEDIAN is the value of the middle value when all the data is arranged in ascending order

The following two slides illustrate the calculations for all three of these measures (Mean, Mode and Median)

SPC_B2_P1       SPC_B2_P2

 

Where these measures are useful depends on the data set you are using. For example we will use the mean value and sub-group size of 5 samples. Having sub-group samples means we can take advantage of the central limit theorem to be abe to manage data analysis from normalised values.

This provides the advantage of reviewing the data as a normally distributed set of data (more about this in the next article)

Spread

This is simply the difference between the largest and smallest data points or measurements.

Distribution - Measure Of Dispersion

Measures of dispersion define the spread of data and the overall shape of the data. 

If we consider a simple histogram then we can see that there is more than one measure needed to describe the data set.

 

SPC_B2_P3This diagram shows a typical histogram for a linear set of data. This type of graph is very useful for visualising small or large sets of data points, in terms of the distribution, and can be produced using Microsoft Excel.

However, for us to analyse this data further, we would need to overlay a distribution curve for this data.

 

 

 

 

SPC_B2_P4

 

This diagram illustrates three sets of data, all centred on the same value, but the spread and shape of the data sets vary (the spread is the difference between the highest data value and the lowest data value)

You will also notice that, although the last two data sets share the same location and the same spread, the shape is different.

 

 

 

So we use three descriptors to describe the data:

  • location
  • spread
  • shape of the data

Summary

Location is defined by the mean, mode or median value (the diagram above shows the mean for a normal distribution)

Spread is defined by the range (R) value for the data (difference between the highest and latest data points in absolute values).

Shape of the data is defined by the variance (the average of the squared differences from the mean) and is commonly referred to as the sigma (σ) value.

Download your 6σ Conversion Chart 

Topics: Continuous Improvement, Statistical Process Control, SPC

SPC - Understanding Statistical Process Control

Posted by Graham Cripps on Mon, Jul 06, 2015 @ 12:07 PM

Understanding Statistical Process Control (SPC)

Having reviewed feedback from visitors to our website we have found that we get a lot of requests for information on Statistical Process Control (SPC).

SPC_blog_chart_1We will be launching a series of articles during the next couple of weeks that aim to provide a foundation understanding of SPC and it's application, this will hopefully help you make an informed choice about whether SPC is the correct tool for you!

Our intention is to provide a solid foundation for understanding SPC, the terminology, metrics and uses of SPC along with  useful resources which can be downloaded and customised to suit your specific requirements, the first of which (X-bar and R chart) is available below.

My job takes me into all types of business, and I often find SPC charts being displayed, but when I ask the client they are either not correctly used or not correctly interpreted.

SPC_blog_chart_2The articles will be broken down into small bite size offerings that can be used for future reference. We will also be making available the relevant resources, including an SPC chart, calculation sheets and a table of constants along with some recommended further reading.

 

The information will be split into the following articles for ease:

  • The basic statistics behind SPC (for variable data)
  • Probability and SPC
  • Collecting and plotting data (using the X-bar and R chart)
  • Interpreting the chart, including the seven points rule
  • Understanding capability
  • Applying SPC

The article structure will be on our website so if there is something that interests you, keep an eye out!  You can sign up to receive notifications to our Blogs here and our Facebook page can be found here.

If there are any SPC questions we haven't answered, or for any queries or feedback, let us know either via the contact form here or by emailing julie.camp@resultsresults.co.uk

 

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Topics: six sigma, Statistical Process Control, SPC

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