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# Control Limits

## Question

Q 77. If variation gradually increases in a process output, the control limits (in the control chart) will shift gradually and become wider. The process in such a case may seem to be in control through the entire period. How is such a phenomenon supposed to be addressed?

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For statistical Control charts, the control limits are formed by its own historical data. To answer the above question, let’s quickly recap the process of forming the control limits.

Typically the inputs based on past 30 or more data points are taken and the control limits are worked out using the formula depending upon the nature of the data and the appropriate control chart applied. I am skipping the elaboration of the control chart construction in this discussion.

(i)               Once the control limits are derived as above, this becomes a baseline situation, against which the readings are plotted subsequently. Since we keep the limits fixed based on the baseline inputs, if the variation increases, the points will start falling outside the control limits, or would start representing the runs that indicate that the process is no longer in control with respect to the baseline limits.

(ii)             Another scenario is if we do not fix the baseline limits, but the UCL and LCL keep revising themselves as when the data points are added into the control chart. In this case, if the variation increases, the control limits will keep widening and might give an illusion that the process continues to be in control.

As a matter of fact, the process can still be termed as “within statistical control” even with an increased variation, so long as the points are contained within those widened limits.

(iii)           Hence, to keep track of the changes in variation levels and at the same time to watch whether the process is within statistical control, “stages” can be defined for periods of the control chart run, and the control limits for each stage can be worked out. This will help us to graphically see any changes on the variations (distance between the control limits) and the extent of statistical control within each stage. Such an option is available in Minitab.

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Here is what i think; the answer lies in understanding the customer specification limits along with control limits. While we are monitoring the process using control chart, what is important is to keep a watch on the customer specifications. In a process where the variation is gradually increasing will in most occasions breach the customer specification, which fundamentally means we are not meeting customer requirement. So, maybe we should first get to meet the customer specification and then look at controlling the process…...

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Based on the equations below, it is very clear that as the standard deviation increases, the UCL and LCL would shift widely(as the Variation is square of Std. deviation). So as the variation increases, the control limits also increase which would show that the process is in control despite the increase in variation. This can be addressed by making sure that the control limits are set based on the maximum allowable standard deviation and both the UCL & LCL to be made static and not variable based on the changing value of variation.

UCL = Avg + 3*Sigma

LCL = Avg - 3*Sigma

where Avg = average of all the individual values

Sigma = the standard deviation of the individual values.

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Control limits indicates voice of process.  They are based on the past performance. On the other hand specification limits are the voice of customer.  If variation increases and control limits shifts gradually and becoming wider but seems to be process is in control throughout entire period of process.

We can say that it is possible to a process to be incapable of meeting a specification while remaining in statistical control. Predictably,  We are making a product out of spec.

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Any matured process fall into one of the four states:

1. Ideal

2. threshold

3. brink of chaos

4. state of chaos

an ideal process is one where the variations are within the control limits, increase in the variation means standard deviation is increasing  and the the control limit X+- 3 sigma also increases at the same time. Therefore target should always be to stay within the control limits which is nothing but the voice of the process. We should always watch for the below in a control chart:

a. if an observation is outside the control limits

b. 9 points in a row above or below the center line

c. 6 points in a row steadily increasing or decreasing

Variation is present in output of every process. The degree of variation or distribution pattern of the output is an indicator of to what extent the process is matured. The six key process elements people, environment, material, machinery, method, and measurement impact the variation. If the variation is within a predictable range as mentioned at the starting which are nothing but the common causes of variation and over the period the process could still be brought down within the range after reducing the effect of common causes. on the contrary if we look for different ways to reduce the variation as defined by the customer we could never be able to reach an optimal solution because for a customer who is receiving an ordered food from zomato, +- 20 minutes could be a tolerance level where as for customer2 it could be +- 30 minutes. The question indicates variation level which sounds more like defined by the voice of the customer but by the voice of the process.

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