Real Time Statistical Process Control enables the operators running the process to know when action is required, as described in

In this second article we will analyse some of the Out-Of-Control situations we can detect and the corresponding corrective actions required.

SPCimr.xlsx

### Individuals and Moving Range SPC charts

In sheet A we have collected process yield data every hour during several shifts.

Since we collect a single value each hour we are using the pair:

• chart for individuals
• moving range chart

The individuals chart has the actual values and the MR chart the absolute values of the change between two consecutive values.

In both charts we automatically apply the Western Electric rules for Out-Of-Control symptoms and the alert will appear in the corresponding column: N - W for the individuals chart and Y - AH for the MR chart.

When any of these alerts appear the corresponding point in the chart will be colored:

• In red: upward symptom
• In green: downward symptom

### Process Change

Looking at the charts above, the individuals chart shows green dots from 10:00 to 16:00 and red dots between 1:00 and 3:00 during the night. We can notice a jump from 16:00 to 17:00 which might indicate the moment when the process has changed but this jump is not significant enough to declare it as a process change.

It is not until 1:00 that we have enough evidence to declare that the process has changed.

In this case, since we are measuring yield, an increase in yield is an improvement.

So we can say that process yield has improved sometime between 16:00 and 1:00. With this information we should now investigate what happened during this period of time that caused this improvement.

How much have we improved?  If we compute the average between 6:00 and 16:00 we get an average yield of 93. And from 17:00 to 11:00 the next day 118. So we can estimate an average yield increase of 25.

### Process Improvement Symptoms

Let's now analyse the alerts in our sheet A:

The -4 values in the individuals chart indicate 4 out of 5 consecutive values 1 sigma below the center line: values significantly below the average. The value -9 at 14:00 means that the last 9 values were below the center line: same interpretation.

The values 9 starting at 1:00 mean that from 17:00 to 3:00 all values have been above the center line: yield has significantly increased.

Finally, value 1 in moving range indicates that a significant change has occurred in the yield at 5:00. Looking at the individuals chart we see it corresponds to an increase.

### Slow Trend

Let's interpret the charts in sheet B:

We notice that there is an upward trend in yield as shown by the green dots up to 6:00 in day 11 followed by red dots starting at 12:00 until the end.

The alert in the MR chart on 4:00 corresponds to a significant one time decrease in yield so we can interpret it as a false alarm.

The interpretation of this situation is that we have a continuous process improvement starting around 11:00 on day 11 maybe due to some ongoing improvement actions.

Let's now look at the alerts:

They confirm a significant yield increase starting around 12:00 of day 11.

### Variation Increase

We now analyse sheet C:

An increase in yield variation is visible in the individuals chart but no alarms are visible.

The MR chart, on the other hand, is meant to detect this variation, and so it does.

Variation is significantly below the center line, as shown by the green dots before 20:00 and a significant increase is shown by the red dots starting at 3:00 on day 11.

If we only measure averages, as we often do, this problem would remain undetected.

Variation is always a bad thing for our process, so we can say our process has got worse starting around the end of day 10.

Yield variation will eventually cause inefficiencies, late deliveries and accumulation of WIP so this problem needs to be addressed before these side effects start to appear.

### Day of the Week Effect

Let's now analyse the example in sheet D:

Here we are collecting daily production data and we notice that our average production is 400 and our charts are not detecting any significant changes in the process.

On the other hand we can see a repetitive cycle of 7 days which, of course, corresponds to a week.

If we look in our calendar the days of lowest production we realize they correspond to Sundays and the next lowest to Saturdays.

This is telling us that maybe there is significant seasonal trend within each week.

In order to check that we have added column AT to our spreadsheet where we calculate the day of the week corresponding to each date with this formula:

=DIASEM(A3;2)

Where A3 holds the date and "2" is to start counting the week on Monday.

We can now do an ANOVA of our Production Vs Day of the Week with Minitab:

We can now confirm that there are significant differences among the different days of the week: Wednesdays and Fridays we have the highest productions. On Thursdays, for some reason, it is significantly lower and, of course, it is lowest on Saturdays and Sundays.

### Shift Change Effect

We have been suspecting that we have a drop in production at the start of a shift, so we have collected data of hourly production in sheet E to check this effect. These are the resulting charts:

In this case, just like in the previous one, there is no indication of Out-Of-Control but we can see peaks in the MR chart which correspond to the start of each shift.

To see how significant are these differences we add a column with the hour of the shift: 6:00, 14:00 and 22:00 are hour 1 of the shift.

Now we do an Anova in Minitab of Production Vs Shift Time:

We notice that production in the last hour of the shift is significantly higher than the average and in the first hour it is significantly lower.

We would need to analyse the root cause of this effect which represents an inefficiency in our process.

One possible cause may be to try to ship as much product as possible at the end of the shift in order to meet the  target. And, to do that, operators are moved to the end of the line. The side effect is that we leave an empty line for the next shift so some operators will have no work until the line fills up.

### Conclusions

Real Time SPC is a useful tool for operators in order to control their process by making the required adjustments as soon as needed but without over-reacting.

Control charts are useless if analysis and corrective actions are not done in real time.

Operators need to be trained to do this analysis and to know what corrective action needs to be done and when.