The chance and assignable cause terminology was developed by W. A. Shewhart. Now, common and special cause terminology is used.

Due to some reason, it may be possible that process mean shifts from one point to anor, and remain re for quite some time. This shifting of mean is called sustained shift of mean.

The general expression for LCL of a quality characteristic ?w? is given by,
LCL = ?_w – L?_w;
Where ?L? denotes distance of control limits from center line.

A scatter diagram is a very useful plot between two variables which affects manufacturing process. To identify any potential relationship between two variables, scatter diagram is a very useful tool.

We define ARL as reciprocal of probability of a point falling out of area between control limits. Here,
ARL=\(\frac{1}{p}=\frac{1}{0.0040}\)=250

It is property of a Pareto chart that, it does not automatically identify most important defects but only most frequent. There is no information about severity of defect.

The slope of OC curve varies inversely with sample size taken for control chart construction. The decrease in size of sample taken to construct a control chart will increase slope of OC curve.

As we know, UCL_3?=;n=5; ?=0.15, \(\overline{x}\) = 1.5; ?_x=0.0671{from question}
So, UCL_3?=1.5+3(0.0671)=1.7013.

Type I error is actually concluding process state being out-of-control when process state is in-control. The opposite conclusion gives conditions for Type II error.

Attributes are increased on discrete scale and y give results as eir conformity or non-conformity. So charts plotted for non-conformities and conformities are called Attributes control charts.