## 7QC Tools: Interpretation of Control Charts Made Easy

Amrendra RoyVisual Inspection of the Control Charts for Unnatural Patterns

Besides above famous rules, there are patterns on the control charts that needs to be understood by every quality professionals. Let’s understand these patterns using following examples. It would be easier to understand them if we can imagine the type of distribution of the data displayed on the control chart.

###### Case-1: Non-overlapping distribution

As a production-in-charge, I am using two different grades of raw material with different quality attributes (non-overlapping but at the edge of the specification limits) and I am assuming that the quality attributes of the final product will be normally distributed i.e. I am assuming that most of final product will hit the center of the process control limits.

If the quality of the raw material is detrimental to the quality of the final product then my assumption about the output is wrong. Because the distribution of the final product quality would take a bimodal shape with only few data at the junction of the distribution. Same information would be reflected onto the control chart with high concentration of data points near the control limits and fewer or no points near the center. Here is the control chart of the final product

In this completely non-overlapping distribution, there will be **unusual long connecting arms** in the control charts. There will be **absence of points near the central line**.

If we plot the histogram of this data set and go on increasing the number of classes, the two distribution would get separated.

So, whenever we see a control charts with the data points concentrated towards the control limits and no points at the center of the control charts, immediately we should assume that it is a mixture of two non-overlapping distribution. *Remember long connecting arms and few data points at the center of the control chart.*

###### Case-2: Partially overlapping distribution

Assume this scenario: A product is being produced in my facility in two shifts by two different operators. Each day I have two batches, one in each shift. There is a well written batch manufacturing record indicating that the temperature of the reactor should be between 50 to 60 °C. The control chart of a quality attribute of the product is represented by following control chart.

We can see that the data points on the control chart are arranged in an alternate fashion around the central line. The first batch (from the 1^{st} shift) is below the central line and next batch (from the 2^{nd} shift) is above the central line. This control chart shows that even we are following the same manufacturing process, there is a slight difference in the process. It was found that the 1^{st} shift in-charge was operating towards 50 °C and the 2^{nd} shift in-charge was operating towards 60 °C. This type of alternate arrangement is indication of **stratification** (due to operators, machines etc.) and is characterized by short connecting arms.

There are the cases of partially overlapping distribution resulting in a bimodal distribution, which means that there will be few points in the central region of the control charts but, majority of the data points would be distributed in zone C or B. In such cases, it would be appropriate to plot the histogram with groups (like operator, shift etc).

###### Case-3: Significant Overlapping distribution

If there is significant overlap between the two input distributions then it would be difficult to differentiate them in the final product and the combined distribution would give a picture of a single normal distribution. Suppose the operators in the above case-2 were performing the activity at 55 °C and 60 °C respectively. This would result in an overlapping distribution as shown below

###### Case-4: Mixture of unequal proportion

As a shift-in-charge, I am running short of the production target. What I did to meet the production target was to mix the current batch with some of the material produced earlier for some other customer with slightly different specification. I hoped that it wouldn’t be caught by the QA!. The final control chart of the process looked like

We can see from the control chart that if two distributions are mixed in an unequal proportions then the combined distribution would be an unsymmetrical distribution. In this case one-half of the control chart (in present case the lower half) would have maximum data points and other half would have less data points.

###### Case-5: Cyclic trends

If one observe a repetition of the trend on the control chart, then there is a cyclic effect like sales per month of the year. Sales in some of the specific months are higher than the sales in some other months.

###### Case-6: Gradual shift in the trend

A gradual change in the process is indicated by the change in the location of the data points on the control charts. This chart is most commonly encountered during the continuous improvement programs when we compare the process performance before and after the improvement program.

If it is observed that this shift is gradual on the control charts, then there must be a reason for the same, like wear and tear of machine, problem with the calibration of the gauges etc.

###### Case-7: Trend

If one observe that the data points on the control charts are gradually moving up or down, then it is a case of trend. This is usually cause by gradual shift in the operating procedure due to wear and tear of machines, gauges going out of calibration etc.

###### Summary of unnatural pattern on the control charts

Unnatural pattern |
Pattern Description |
Symptom in control chart |

Large shift (strays, freaks) |
Sudden and high change | Points near and or beyond control limits |

Smaller sustained shift |
Sustained smaller change | Series of points on the same side of the central line |

Trends |
A continuous changes in one direction | Steadily increasing or decreasing run of points |

Stratification |
Small differences between values in a long run, absence of points near the control limits | A long run of points near the central line on the both sides |

Mixture |
Saw-tooth effect, absence of points near the central line | A run of consecutive points on both sides of central line, all far from the central line |

Systematic Variation or stratification |
Regular alternation of high and low values | A long run of consecutive points alternating up and down |

Cycle |
Recurring periodic
movement |
Cyclic recurring patterns of points |

For the case study see next blog