Statistical process control is often used interchangeably with statistical quality control SQC. A popular SPC tool is the control chart , originally developed by Walter Shewhart in the early s. A control chart helps one record data and lets you see when an unusual event, such as a very high or low observation compared with "typical" process performance, occurs. Control charts attempt to distinguish between two types of process variation :.
Various tests can help determine when an out-of-control event has occurred. However, as more tests are employed, the probability of a false alarm also increases. Statistical quality control SQC is defined as the application of the 14 statistical and analytical tools 7-QC and 7-SUPP to monitor process outputs dependent variables.
Statistical process control SPC is the application of the same 14 tools to control process inputs independent variables. In , Dr. Kaoru Ishikawa brought together a collection of process improvement tools in his text Guide to Quality Control.
Known around the world as the seven quality control 7-QC tools , they are:. In addition to the basic 7-QC tools, there are also some additional statistical quality tools known as the seven supplemental 7-SUPP tools:. The yellow zone is more than 1 but less than 2 Standard Deviations from Average The purple zone is more than 2 but less than 3 Standard Deviations from Average The red zone is more than 3 Standard Deviations from Average The blue lines show the specification limits for the launcher simulation.
If we drag the specifications to put them at the border of yellow and purple the percentage OK is recalculated. The percentage OK figure now shows how many of the results are within 2 Standard Deviations from Average. You see it is So, we now know that for a normal distribution, the majority of results will be less than one Standard Deviation from Average.
However, we also know that there will be a small number of results more than 3 times Standard Deviation from Average. We cannot tell WHEN these extreme results will happen, but we know that they will happen sometime.
These percentages tell us approximately what has happened in the past. Also, the percentages given above for the normal distribution are only true over the very long term. It would be wrong to suggest that we can tell with confidence what the measurements will be in any one particular batch of goods. In lesson 2, we used a section of data to calculate control limits for a process. In that example, the process was stable in the early stages and we used data from that period to calculate the control limits.
In this lesson we are going to investigate what happens if the process is unstable while producing the data which is used to calculate control limits. We ran a simulation of a process which is unstable in the early stages. You now see that the process is indicating instability even though the data used to calculate the control limits contains instability.
This ability of Shewhart control charts to detect special causes of variation, even when these special causes are present in the data used to calculate the control limits, is very important.
Most industrial processes are not naturally in a state of statistical control. The control limits are set at 3 times sigma from the average. Sigma is similar to standard deviation. This sigma is calculated based on the average range of the subgroups range is the maximum value minus the minimum value or in other words based on the within subgroup variation. The reason that the Xbar chart detects special variation is because the control limits are calculated using an estimate of standard deviation based on the average subgroup range.
Since the subgroups are taken from consecutive products, this means that all the variation between subgroups is filtered out. When using control charts it is important to ensure that subgroups contain mostly common cause variation. Normally this can be done by measuring a small number of consecutive products for each subgroup, and having a time gap between the subgroups.
Sometimes it is not possible to take consecutive measurements from a process which can be grouped in a subgroup. For example, there is no variation if we take consecutive measurements eg temperature or the pH value of a bath. In this type of chart we plot the individual measurements on one graph and the differences between the consecutive measurements on the other graph, this is called the Moving Range sometimes only the individual points are shown, the moving range chart is omitted.
If we run a process with is unstable in the early stages and we chart the individual values we see the control chart below. We see that the chart is able to detect both disturbances in the average as well as disturbances in the range. The chart shows some instability, both by having some points outside the control limits and because there are long runs in the data.
A run is where a number of consecutive results are all above average or all below average. Lets look at how control limits for individual value chart are calculated:. During an implementation we will also implement control charts where removing instability is not the highest priority because it is not the most critical characteristic. In that case we may use different ways to calculate limits. This advanced subject is outside the scope of this training.
Lesson 5 — Binomial control charts. In lesson 2 we looked at Xbar and Range control charts. In lesson 4 the X individual value chart was introduced. In both these cases, we used variable or measurement data. This is data which comes from a continuous scale.
Attribute data comes from discrete counts. For example:. With attribute type data, in order to choose the correct type of control chart, we have to look at the way the data was generated. If we know in advance that the set of data will exhibit the characteristics of Binomial data or Poisson data then these types of charts should be used. Binomial data is where individual items are inspected and each item either possesses the attribute in question or it does not. Each bead scooped is either blue or it is not blue — so if we create a stream of samples taken from the box and we count the number of blue beads in the samples, then we can assume that the resulting data will be Binomial type data.
The random variation of Binomial data acts in a particular way, because of this we can calculate where to put the control limits. All we need to know is the average of the data set and the sample size. It is used when we know we have Binomial data and the sample size does not change. If we have binomial data but the sample size is not constant, then we cannot use a np chart.
We will now use the simulation to add new samples to the data we have already started, but we will change the sample size:. When the sample size is not constant for every scoop we have to convert counts to a rate or proportion.
We convert to a rate by dividing the attribute count by the sample size. You will notice that there is a step in the control limit lines at the point where the sample size changed.
The purpose of the control limits is to show the maximum and minimum values that we can put down to random common cause variation. Any points outside the limits indicate that something else has probably occurred to cause the result to be further from the average.
As we have said before, the random common cause variation of Binomial data acts in a particular way. The variation with large sample sizes is smaller than the variation with small sample sizes. We can use the simulation to demonstrate this. Look at the results in the Data Table and keep in mind that the proportion of red beads in the box has not changed.
In rare cases like in this simulation we can even have 4 and we have a false alarm. Look again at the results in the Data Table. Look at the way the points which correspond to the small sample size samples 60 — 90 vary up and down, then compare this with the variation with the large sample size after Keep in mind that we are not looking at absolute numbers here, we are looking the proportion of the sample which is red.
Look at the position of the control limits for the small subgroupsize and the large subgroupsize. This illustrates one of the basic points about using control charts for attributes. Small subgroupsizes produce control charts which are not sensitive because there is so much random common cause variation in small sample sizes.
Large sample sizes produce more sensitive control charts. What this means is that if a process has a special cause of variation acting on it from time to time, it may not produce any points outside the control limits if the sample size is small. The same special cause of variation is more likely to produce points outside the control limits if we use a large sample size.
Notice that the limits have to be separately calculated for each subgroupsize. The example given is for sample number 1 subgroups 1 to Criteria for binomial data:. We can only use an np chart or a p chart if we know in advance that the data produced will be binomial data.
The full conditions which have to be satisfied before we can consider a set of data to be Binomial are:. For example, we might want to count the number of blemishes on a surface. The only difference is the way the control limits are calculated: Look at how the limits are calculated.
Notice that the sample size is not used anywhere in these calculations. The rate is simply the attribute count divided by the sample size or area of opportunity for the sample. Look at how the limits are calculated. Notice that the control limits are tighter for larger areas of opportunity. The X individual value control chart with attribute data:. In a lot of cases the Binomial or Poisson charts are not appropriate because one of the conditions is not applicable.
Control limits for X charts are empirical limits based on the variation in the data and these are almost always valid. First we will generate some data:. If we cannot be confident that the data we have fulfills the conditions to be binomial or Poisson data, then we can usually rely on an X chart to do a pretty good job. We now have a non constant sample size. Sometimes X charts should be rate charts when the sample size is not constant and sometimes they should not — it depends on what the measurement represents.
In our case the number of red beads scooped is definitely dependent on the sample size so we should look at an X chart based on rates. The p chart and the X rate chart are both showing proportions and the control limits have been calculated using scoops 1 — Compare the two charts. Look at the data and the control limits before and after the change of sample size the change was at subgroup number Because we have not changed the number of beads in the box, we are looking at the results of a stable process so in theory control charts should not show any points outside the control limits.
There is always more random common cause variation with small sample sizes and you can see that the points on both charts jump up and down more after we change to a smaller sample size. Because the control limits on a binomial chart are based on a theoretical knowledge of the way binomial data behave, the control limits change to accommodate the different sample sizes.
On X charts, the control limits are based on the variation between successive points in the data stream. When this variation changes due to altering the sample size, this can be misinterpreted as a process change.
X charts with low average:. When the average count is very small, another problem prevents us from using X charts. With attribute counts, the data can only take integer values such as 6, 12, 8 etc. Values such as 1. The discreteness of the values is not a problem when the average is large, but when the average is small less than 1 then the only values which are likely to appear are 0, 1, 2 and occasionally 3.
The whole idea of control charts is that we want to gain insight into the physical variations which are happening in a process by looking at the variation of some measurement at the output of the process. When the measurements are constrained to a few discrete values then the results are not likely to reflect subtle physical changes within the process.
For this reason X charts should not be used for attribute counts when the average count is low. Lesson 9 gives more information about using attribute control charts when the average count is low. Lesson 7 — Pareto chart. A Pareto chart helps us to identify priorities for tackling problems. The columns in the table represent 10 types of non-conformity or imperfection which can occur in Assembly M Each of the 25 rows contains the results of one inspection. In a Pareto chart, the categories of data are shown as columns and the height of each column represents the total from all the samples.
The order of the columns is arranged so that the largest is shown on the left, the second largest next and so on. Since these counts usually represent defects or non-conformities, the biggest problems are therefore the categories on the left of the chart. Our Pareto chart makes it immediately obvious that the most frequent problem is Smidgers appearing on the assembly.
It is common practice on Pareto charts to superimpose a cumulative percentage curve. At each point on this curve you can see the percentage of the overall number of non-conformities or imperfections which are caused by the categories to the left of the point. This is best illustrated by example. We have added a red line for the second defect Scrim pitted. If we concentrate our efforts on reducing the number of smidgers and pitted scrims, then even if we are only partially successful, we are likely to make a substantial difference to the number of assembles which we have to send for rework.
Of course, all types of problems do not have an equal impact in terms of cost or importance. So if we know the cost of putting right each type of problem, then it is better to draw the Pareto chart with the column heights representing the total cost. We are now looking at the total cost associated with each column total number multiplied by unit cost.
When the chart is showing costs, we get a different picture from the picture we get when it is showing numbers Although smidgers are the most common imperfection in assembly M, they are easy to remove — a quick wipe with a cloth is all that is needed. A pitted scrim, on the other hand, needs the assembly to be dismantled. A leaking gear housing is the big nightmare — but fortunately they are not very common.
Although we do not get many gear leaks, they are actually the second biggest problem in terms of costs. Smidgers do not cost the company a lot of money despite the fact that they occur in large numbers. So looking at Pareto chart for M costs, we should concentrate our efforts in eliminating pitted scrims and gear leaks. Although a Pareto clearly identifies the major cause of problems you also have to consider the amount of efforts required to solve a problem.
It might be that an issue is very easy to fix, so make sure you always briefly review all issues before you start to solve the most important problems. Pareto are used in a lot of different situations and can be adapted to get the right information. This Pareto is shown with the bars horizontally. With downtime analysis the total downtime is important but more information is required.
In this Pareto we see that a label is added with the total downtime in minutes but also the number of downtimes is given. One long downtime might require a different approach than a large number of short downtimes. In this Pareto the color of the bar indicates a downtime category. Lesson 7 summary:. Return to the index Lesson 8 — Scatter chart. When we want to reduce or eliminate a problem, we will need to come up with ideas or theories about what is causing the problem.
One way to check if a theory should be taken seriously is to use a scatter chart, also called regression analysis. To use a scatter chart, we first have to take a series of measurements of two things over a period of time. The two things that we would measure are the problem itself, and the thing that we think may be causing the problem. We then plot the measurements on a scatter chart.
The scatter chart will help us to see whether there is a mathematical relationship between two sets of measurements. Analysis using a Pareto chart showed that the problem of surface flaking of the plugs was costing the company a lot of money.
The team quickly found that everyone had a different opinion of what was OK and what was a flaker. The first job, therefore, was to come up with a good definition of a flaker which everyone could use. The process operators were shown how to use control charts and they started keeping a chart of the number of flakers produced in each batch. This chart showed that the process was unstable. Mary, one of the process operators on the team, said she always feels cold on days that they have a lot of flakers.
The process operators started keeping records of the air temperature at the time the plugs were made. At one of the team meetings Jack pointed out that on at least two occasions when the number of flakers was outside the control limits, it was raining.
The team asked the lab for help to test the theory that rain was a factor. One of the engineers pointed out that it was actually raining that very day but there were very few flakers. Nevertheless he still suggested that it might be a good idea to measure the moisture content of the main ingredient.
Because each plug is either a flaker or it is not a flaker, the chart we should use is a binomial chart. The data is out of control because some points are outside the control limits. There are also runs of 10 consecutive points above and below the average line — these also indicates instability. On this chart, the number of flakers is on the vertical axis and the air temperature is on the horizontal axis.
For each row in the data table, a dot is put where the two values meet. In a scatter chart, if the measurements on the horizontal axis are not related in any way to the measurements on the vertical axis, then the dots will appear at random, with no pattern visible. If there is a mathematical relationship between them then the dots will tend to group into a fuzzy line or curve.
In this case there does not seem to be any pattern to the points on the scatter chart. We can conclude, therefore, that there is no correlation between air temperature and the number of flakers produced.
This means that we can say that the air temperature is not a factor in producing flakers. On this scatter chart we see flakers on the vertical axis and moisture content on horizontal axis. There appears to be a correlation between the two sets of numbers because we can see the dots have formed into a fuzzy line.
This chart is showing that flakers increase when the moisture content increases. This still does not prove that one causes the other. There could be a third factor which causes BOTH to change at the same time. Still, we seem to have a clue here. The equation for this line is shown at the top right of the chart. The R-squared figure is a measure of how well the data fits the line.
If R-squared is 0 or near 0 then there is no correlation between the data on the two axes so the line and the equation has no relevance. Now look again at the scatter of the temperature. You can now see the best fit line through these points. The R-squared value is low showing that there is no correlation between the two sets of data.
One simple way to express the reaction plan is to create a flow chart with a reference number, and reference the flow chart on the SPC chart. Many reaction plans will be similar, or even identical for various processes. Following is an example of a reaction plan flow chart:. A control plan should be maintained that contains all pertinent information on each chart that is maintained, including:. The control plan can be modified to fit local needs. A template can be accessed through the Control Plan section of the Toolbox.
The area circled denotes an out-of-control condition, which is discussed below. After establishing control limits, the next step is to assess whether or not the process is in control statistically stable over time.
This determination is made by observing the plot point patterns and applying six simple rules to identify an out-of-control condition. When an out-of-control condition occurs, the points should be circled on the chart, and the reaction plan should be followed. When corrective action is successful, make a note on the chart to explain what happened. If an out-of-control condition is noted, the next step is to collect and analyze data to identify the root cause. Several tools are available through the MoreSteam.
You can use MoreSteam. Remember to review old control charts for the process if they exist - there may be notes from earlier incidents that will illuminate the current condition.
After identifying the root cause, you will want to design and implement actions to eliminate special causes and improve the stability of the process. You can use the Corrective Action Matrix to help organize and track the actions by identifying responsibilities and target dates. The ability of a process to meet specifications customer expectations is defined as Process Capability, which is measured by indexes that compare the spread variability and centering of the process to the upper and lower specifications.
The difference between the upper and lower specification is know as the tolerance. After establishing stability - a process in control - the process can be compared to the tolerance to see how much of the process falls inside or outside of the specifications. Note: this analysis requires that the process be normally distributed. Distributions with other shapes are beyond the scope of this material. The first step is to compare the natural six-sigma spread of the process to the tolerance.
This index is known as Cp. Cp is often referred to as "Process Potential" because it describes how capable the process could be if it were centered precisely between the specifications. A process can have a Cp in excess of one but still fail to consistently meet customer expectations, as shown by the illustration below:.
The measurement that assesses process centering in addition to spread, or variability, is Cpk. Think of Cpk as a Cp calculation that is handicapped by considering only the half of the distribution that is closest to the specification.
Cpk is calculated as follows:. The illustrations below provide graphic examples of Cp and Cpk calculations using hypothetical data:. So Cpk is 0. Without reducing variability, the Cpk could be improved to a maximum 1. Further improvements beyond that level will require actions to reduce process variability.
The last step in the process is to continue to monitor the process and move on to the next highest priority.
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