Lecture 42 is about the statistical process control. This is part of the control phase control phase has a significant role in the Six Sigma projects. In this lecture, I will describe about the objectives and benefits of SPC, control process performance, identifying spatial and common causes, selection of appropriate control charts, etc. In first module, we learnt that radiation is law of nature No production process is good enough to produce all items alike. controlling a process is nothing but controlling the variation. Process processes can be controlled by using statistical techniques.

It is commonly known as statistical process control. As we see basic steps of SPC are select the control subject, establish performance standards measure the actual performances compare with standard initiate corrective action. In traditional quality control, corrective action is taken when product or service does not meet the specification limit. This was known as the traditional goal post approach. In traditional approach, control limits carried no meaning for managers. It was water Sure, who stated for first that plus minus three sigma is the point where your process needs control.

Sure, pad invented the control charts. He framed control charts as a tool to identify the two reasons of variation. Common causes of variation special causes of variation. variation in the data represents the voice of process. Generally, variations are due to two types of causes. Special cause variation.

They are nothing but sporadic causes, such as tools breakage, machine breakdown, strike, absence of skilled employee, etc. absence of spatial causes, make a process stable control chart is the tool to identify spatial causes. Common causes variations are inherent to process or product design example are prevalent work procedures, policies, etc. aim of six sigma project is to remove the common causes of variation. Let us review the difference between traditional process control and statistical process control draw a control chart by plotting upper specification limit USL upper control limit UCL mean of the process, lower control limit LCL lower specification limit ls l. Now, plot the output characteristics of the process as shown on the screen. The output characteristics could either be the individual measurement of process outputs or the average measures of set of products.

Now connect the points with lines as shown We can see that there are two points going out of specification limits. Now, in traditional approach of process control, the corrective actions were initiated when the product characteristics crosses the specification limits. This is a kind of reactive approach. Now, sure we're stressed to managers that they should not wait things to cross the specification limits, the corrective action should be initiated immediately when the output measures cross the control limits. Let us learn about a different type of control chart and methods of selection the selection of control charts is purely based on the type of data it is going to deal. We have learned about two major types of data in measure face, which you recall absolutely right.

They are variable types of data and attribute types of data. Now, if we want to use control charts for variables identify whether rational subgrouping as possible or not if it is not possible To go for for a sampling data, then we will use the IMR chart I am our char stands for individual moving range chart for plotting the individual data data can be collected using rational sub grouping techniques. Then we can use either the x bar our chart stands for x bar and range chart or the x bar s jar stands for x bar standard deviation chart. Now, let us see the control charts for attributes, if we need to select the control chart for attributes, then identify first that what is controlled subject that we are interested for. If we are interested to control the defective units, then use NP chart for constant sample size and use v chart for where constant sample size is not possible.

Similarly, if we are interested to control defects, then use C char where constant sample size is possible And use your chart where constant sample size is not possible. Let us discuss about the variable control charts first at first the x bar and our chart which means average and range chart. In this chart the mean x bar and range bar are used together. This chart is used when subgroup sample size is less than 10. The steps for preparing this chart are step one is data collection that includes deciding the subgroups. size and number of subgroups K and subgroup frequency f. The number of samples should be enough to capture all sources of variation.

As a thumb rule, we can also collect data as 20 subgroups k consisting of five samples and our 25 subgroups k consisting of four samples and. Now, next step is to calculate the subgroup means and ranges we know to calculate the mean x bar, the range R is calculated as the difference between Between highest and lowest values. For example, take a set of data in one subgroup say as 9.99 10.0 for 9.98 9.99 and 9.95. Then, the mean and range of this subgroup are calculated as shown on screen. We got the subgroup mean as 9.97 and subgroup range as 0.15. Similarly, we got 20 or 25 Such means and ranges.

Now calculate the averages of these means as x double bar average of these ranges as our bar. Next step is to calculate upper and lower control limits for both X bar and our the calculation of control limits differ slightly, then what we learned in the process capability lecture. The upper control limit for means, the UCL x bar is equal to x double bar plus a two into our bar The lower control limit of means, l see l x bar is equal to x double bar minus a two into our bar. The upper control limit for ranges, UCL r is equal to d3 into our bar. And the lower control limit of ranges LC LR is, is equal to T four into our bar where a two, D three and D four are constants. There are standard tables Find out these constants for particular sample size these calculations are tedious and as usual, we will use Minitab to construct the control charts.

I will explain them in the next lecture. Let us learn about x bar s and I m our charts. x bar and s chart is known as average and standard deviation chart. This is used when subgroup size is more than or equal to 10 average or mean is calculated as similar to the x bar Our chart discussed in the previous slide here instead of range, we are using the standard deviations and the average of standard deviations to plot the control chart. Similarly, the IMR chart or the individual moving range chart is used where the rational sub grouping is not possible. This chart is plotted with individual values rather than the sample measures.

That's all for this lecture. We are going to discuss more about the control chart in the next lecture.