Error type chart with simultaneous errors

1. What is an error type chart?

Our monitoring system measures the parameters of telecommunications services at regular intervals, and based on the measured parameter values, automatically decides if there were service errors. For every monitored service, there is a chart on our dashboard, which displays in percents the ratio of error-detecting measurements to all measurements. Different service error types are displayed with different colors.

2. EASY CASE: Mutually exclusive error types

In most cases, one measurement can detect at most one service error type, so I could use stacked bar charts. This way the user can examine not just the percentage of different error types, but also the total percentage of errors, which is shown by the total height of the stack. Example chart with 6 possible error types:

enter image description here

The users like this solution.

3. MY PROBLEM: Simultaneous error types

In rare cases one measurement can detect more than one service error type, even all of them.

a) I cannot use stacked bar charts because the height of the stack would be misleading. For example, if there are 100 measurements, and 5 of them detects errors, but all of them detect the same 3 error types, then the top of the stack would be at 15%, while the total error ratio is 5%.

b) I also cannot use use unstacked bar charts, because at the smallest supported display resolution there are only 10-15 pixels for every time interval, so there would be only 1-2 pixels per bar if I put them next to each other.

c) Both problems could be solved by unstacked line charts. Here is an example with 7 error types:

enter image description here

Unfortunately the users don't like it, because "it's very hard to see the total error percentage". Although there is another chart which displays the total error percentage, they would still prefer being able to see its value on the error type chart. I could add yet another, possibly thicker chart line, which shows the total error ratio but in some cases there are 16 different error types and I'm not sure that adding a 17th line with a special meaning wouldn't make the chart too complex.

4. MY QUESTION: How could I display on the same chart not just the different error type ratios, but also the total error ratio in a meaningful way?

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