Histogram identified as being most helpful in troubleshooting issues related to quality and used to solve most quality-related issues

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Histogram represents a shape of a distribution curve superimposed on the bars to cross most of the bars at their maximum height.

If your data is from a symmetrical distribution, such as the Normal Distribution, the data will be evenly distributed about the center of the data.

If the data is not roughly evenly distributed about the center of the histogram, it is commonly called “skewed”.

If it appears skewed, you should understand the cause of the “skewness”.

If double or multiple peaks occur, look for the possibility that the data is coming from two different sources, such as two separate personnel groups, or two differently adjusted machines.

Normal Distribution is a continuous probability distribution that describes data that clusters around a mean or average.

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The graph of the associated probability density function is bell-shaped and symmetric in nature.

The shape of the normal distribution is determined by the average and standard deviation.

In, SPC, the normal distribution allows us to determine the probabilities of getting values beyond control limits.

The probabilities that a normally distributed variable will be within -

±1 standard deviation of the average is approximately 0.68 (i.e. 68% values will be within one SD),

± 2 standard deviation of the average is approximately 0.95 (i.e. 95% values will be within two SD),

± 3 standard deviation of the average is approximately 0.997 (i.e. 99.7% values will be within three SD).

QQ Plot is a graphical tool to help us assess if a set of data probably came from some theoretical distribution such as a Normal or exponential.

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A Q-Q plot is used to compare the shapes of distributions, providing a graphical view of how properties such as location, scale, and skewness are similar or different in the two distributions.

The main step in constructing a Q–Q plot is calculating or estimating the quantiles to be plotted.

If one or both of the axes in a Q–Q plot is based on a theoretical distribution with a continuous cumulative distribution function(CDF),

all quantiles are uniquely defined and can be obtained by inverting the CDF.

Box_chart provides a summary of the variation within and/or between categories.

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Box_chart determining if outliers are present in the data, and comparing processes.

The median is the middle value of the Box plot data, if it is not in the center of the box, it is an indication that your data is skewed.

If the median is closer to the bottom of the box, the data are positively skewed.

If the median is closer to the top of the box, the data is negatively skewed.

Control Chart consist of a central line (CL), upper control limit (UCL), lower control limit (LCL).

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Control charts consist of a central line (CL) denoting the average value of the statistic being plotted, it has 2 control limits on either side of the central line which are called upper control limit (UCL) and lower control limit (LCL). The control limits are determined statistically from the probability distribution of the sample statistic.

The purpose of control chart is to obtain a state of statistical control by locating and eliminating the assignable causes and then maintain the production in this state to ensure the manufacture of consistent products of acceptable quality.

For this purpose, the variation due to chance causes is estimated and then used as the basis for the detection of the variation due to assignable causes by plotting the sample statistic on the control chart.

When no assignable causes of variation are present in a process and it operates only under a system of non-assignable or chance causes, the process is said to be in a state of statistical control.

I-MR charts plot individual observations on one chart accompanied with another chart of the range of the individual observations - normally from each consecutive data point. This chart is used to plot continuous data.

PC Plot is a statistical measurement of a process’s ability to produce parts within specified limits on a consistent basis.

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To determine how our process is operating, we can calculate -Cp (Process Capability), -Cpk (Process Capability Index), or -Pp (Preliminary Process Capability) and -Ppk (Preliminary Process Capability Index), depending on the state of the process and the method of determining the standard deviation or sigma value.

The Cp value indicate that the process is capable to making parts within specifications and Cpk suggest that how the process is centered between the specification limits.

The Cp and Cpk calculations use sample deviation or deviation mean within rational subgroups.

The Pp and Ppk calculations use standard deviation based on studied data (whole population).

Interpretations