7QC Tools: My bitter experience with statistical Process Control (SPC)!

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I just want to share my experience in SPC.

In general, I have seen that people are plotting the control chart of the final critical quality attribute of a product (or simply a CQA). But the information displayed by these control charts is historical in nature i.e. the entire process has already taken place. Hence, even if the control chart is showing a out of control point, I can’t do anything about it except for the reprocessing and rework. We often forget that these CQAs are affected by some critical process parameters (CPPs) and I can’t go back in time to correct that CPPs. The only thing we can do is to start a investigation.

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HENCE PLOTTING CONTROL CHARTS IS LIKE DOING A POSTMORTEM OF A DEAD (FAILED) BATCH.

Instead, if we can plot the control chart of CPPs and if these control charts shows any out of control points, IMMEDIATLY WE CAN FORECAST THAT THIS BATCH IS GOING TO FAIL or WE CAN TAKE A CORRECTIVE ACTION THEN AND THERE ITSELF. This is because CPPs and CQA are highly correlated and if CPPs shows an out of control point on its control chart, then we are sure that that batch is going to fail.

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Hence, the control charts of CPPs would help us in forecasting about the output quality (CQA) of the batch because, the CPP would fail first before a batch fails. This will also help us in saving the time that goes into the investigation. This is very important for the pharmaceutical industry as everyone in the pharmaceutical industry knows, how much time and resource goes into the investigation!

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I feel that we need to plot the control chart of CPPs along with the control chart of CQA, with more focus on the control chart of CPPs. This will help us in taking timely corrective actions (if available) or we can scrap the batch, saving downstream time and resource (in case no corrective action available).

Another advantage of plotting the CPP is for looking for the evidence that a CPP is showing a trend and in near future it will cross the control limits as shown below, this will warrant a timely corrective action of process or machine.

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CQA: Critical Quality attribute

CPP: Critical Process Parameter

OOS: out of specification


7QC Tools: How to Extract More Information from the Scatter Plot?

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We saw the use of scatter plot for understanding the correlation between two variables in earlier blogs.

Now let’s see what we can do to extract more information from the scatter plot. Let’s take the earlier example, X7 Vs, Y

Picture35The graph above indicates no correlation, which is also evident by the R2 value of 0.0465. However, if we look carefully, it appears that most of the observations (blue circle) is trying to show some trend but, the two points (outside the blue circle) is influencing that trend in their  direction!

Now question to be asked is whether these two outlier or influential points is because of typo error or there are some special causes associated with these observations? Let’s assume that an investigation was carried out and it was found that there was no typo error but these points appeared as exception because of some special causes. What we should do now?

Since these two observation are because of some special causes hence, it is appropriate to ignore these points and re-construct the scatter plot as shown below.

Picture36The re-constructed scatter plot starts showing a trend of negative correlation between the above two variables.

Another way of extracting information is by dividing the scatter plot into four quadrant by plotting the mean of X and Y. After that we can focus on the quadrant where there is maximum concentration of observations.

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Another way of analyzing scatter plot is by augmenting it by regression analysis, where we can have a quantitative equation describing the relationship between the variables. This can easily be done with excel sheet. This will be discussed in subsequent blog.

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

7QC Tools: How to Draw a Scatter Plot?

 

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Option-1: using Excel sheet

Select the columns whose scatter plot is to be constructed and then go to Menu bar and select “insert” followed by scatter plot as shown below

Picture28 Picture30For displaying R2 value

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Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

 

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Let’s take the of scatter plot of X3 Vs. Y from the previous example

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We can see that there is a very weak correlation between  X3 Vs. Y as the scatter plot is almost horizontal to the X-axis. Now manipulate the Y-axis, instead of starting from zero, start the Y-axis from 20 and in another scatter plot start it from 37. See what happens

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This is called as misuse of statistics, initially there seems to be no correlation between X3 and Y, but as you change the Y-axis, there seems to be a strong correlation, even though R2 value remains constant.

It always better to quote the R2 values along with the scatter plot.

Second issue with Scatter Plot is that it represents the correlation between the two variables which may or may not have a cause and effect relationship. What we want to say is that, the two variables are correlated by chance but in reality, they don’t affect each other. Hence, after scatter plot we need to establish the cause and effect relationship between X and Y by deliberately varying X and measuring its effect on Y. This is done more systematically with the help of Design of Experiments (DoE).

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Also see

Car Parking & Six-Sigma

7QC Tools: Scatter Plot

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In general after preparing flow chart there is a brainstorming session, and the outcome of this brainstorming session is the fish-bone diagram which in-turn list down the probable parameters or causes that can affect your quality parameter. At this step all parameters thus collected are only suspects (unless proven guilty!) and their role in affecting the quality parameters needs to be proved in order to held them guilty. In this regard historical data of all suspects (probable parameters or causes) are collected and their effect on the quality parameter is evaluated using scatter plot.

This evaluation can be dome by expert using ANOVA, Regression etc. but a visual tool was required which can tell a shop-floor person that a given parameter is affecting the quality attributes or not? In this regard scatter plot comes handy where you plot a given parameter against the quality attributes.

In real case scenario, we end-up with huge data base as shown below, where X1 to X8 represents the process parameters (suspects) and y represents the quality attribute of interest.

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By visual inspection of the above data, it becomes difficult to analyze the effect of X on Y, situation becomes worse if data is larger. Hence, scatter plot is a visual tool that gives qualitative correlation between X and Y.

Let’s look at the scatter plot of X1 and X2 Vs. Y

Picture22X-Axis represents X and Y-axis represents Y. we can see that in scatter plot of X1 Vs. Y, as the value of X1 increases, Y also increases. Whereas in X2 Vs. Y, there is no apparent correlation. Hence, we can conclude that X1 is affecting the Y and there is no effect of X2 on Y. We can also quantify the effect by calculating R2 values. R2 values can vary from -1 to +1. The values close to +1 indicates strong positive correlation whereas values close to -1 indicates strong negative correlation.

Scatter plot of all X Vs. Y are given below along with R2 values.

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Looking at the scatter plot given above, any shop-floor person can tell that X1, X3 and X5 are affecting the Y in positive way whereas, X4 and X8 are affecting the Y in negative way. Also X2 and X6 doesn’t have any effect on Y.

Related Blogs

7QC Tools: Flow Chart, Know Your Process Thoroughly

7QC Tools: Fish Bone or Ishikawa Diagram

7QC Tools: How to Extract More Information from the Scatter Plot?

7QC Tools: How to Draw a Scatter Plot?

7QC Tools: Scatter Plot — Caution! Misuse of Statistics!

7QC Tools: Scatter Plot

7QC Tools — How to Prioritize Your Work Using Pareto Chart?

7QC Tools — How to Interpret a Histogram?

7QC Tools — How to Draw a Histogram?

7QC Tools — Histogram of Continuous Data

7QC Tools — Histogram of Discrete Data

7QC tools — Check List

Excellent Templates for 7QC tools from ASQ

What are Seven QC Tools & How to Remember them?

Also See

Car Parking & Six-Sigma