Basic tools of quality

Basic tools of quality

1. Control charts

   • It basically consists of the data of a process captured chronologically in a graph with established limits, which allows determining when a variation is not normal
   • Types of control charts
     • Graph X
       • Plot the process mean over time. Used to track the level of the process and detect the presence of special causes that affect the average.
     • Graph R
       • Plot the rate of the process over time. Used to track process variation and detect unexpected variation
     • Graph X-R
       • We use both types of plots when measuring the relationship of quality specifications with central tendency and dispersion. In this sense, we place one graph slightly above the other and analyze the behavior of each point.

2. Control charts for variables

   • Zone graph
     • Plots cumulative scores based on " zones " at 1, 2, and 3 standard deviations from the center line. Use it to detect an unexpected variation.
   • Graph S
     • It is used to monitor the variation (standard deviation) of the process when you have continuous data and subgroup sizes of 9 or more. This chart is used to monitor process stability over time so that you can identify and correct instabilities in a process.

3. Control chart by attributes

   • Graph P
     • In it we measure the percentage of defects per sample.
   • Graph NP
     • Unlike p, this value is not a fraction. It is the number of defective units in a sample.
   • Graph C
     • It is the number of defects per unit of production during a sampling period. In this case, the defects per product are counted, and we establish a value to define from how many defects a unit is defective.
   • Graph U
     • In it we measure the percentage of defects in a unit during a sampling period.

4. Frequency distribution

   • It is the way in which a series of observations is ordered in different groups, and normally in ascending or descending mode.
   • Types of frequency distribution
     • Absolute frequency
       • It is calculated by dividing the absolute frequency by the number of data.
     • Relative frequency
       • It is the number of observations that belong to each group.
     • Accumulated absolute frequency
       • It results from adding the absolute frequencies of a class or group of the sample (or population) with the previous one or the previous ones.
     • Cumulative relative frequency
       • It is the result of adding the relative frequencies

5. Measures of central tendency

   • Measures of central tendency are statistical measures that aim to summarize a set of values in a single value. The most commonly used measures of central tendency are: mean, median, and mode
   • Types of
     • Average or mean
       • It is calculated by adding a group of numbers and then dividing by the count of those numbers.
     • Median
       • It is a set is a value that is in the middle of the other values, that is, when ordering the numbers from smallest to largest, it is exactly in the middle
     • Mode
       • It is the value that appears most frequently in a data set.

6. Measures of dispersion

   • The measures of dispersion measure the degree of dispersion of the values of the variable. In other words, dispersion measures seek to evaluate to what extent the data differ from each other.
   • Types of
     • Variance
       • The variability of a data set with respect to its mean. Formally, it is calculated as the sum of the squared residuals divided by the total number of observations.
     • Typical derivation
       • Provides information on the dispersion with respect to the mean. Its calculation is exactly the same as the variance, but taking the square root of its result.
     • Variation range
       • It is defined as the difference between the highest value of the variable and the lowest value of the variable.
     • Coefficient of variation
       • Its calculation is obtained by dividing the standard deviation by the absolute value of the set mean and is usually expressed as a percentage.

7. Statictics and parameters

   • Statistical
     • It is a numerical quantity calculated on the sample that summarizes its information on some aspect. It is used to approximate a parameter.
   • Parameters
     • It is a numerical quantity calculated on a population and summarizes the values that this takes on some attribute. Try to summarize all the information in the population in a few numbers (parameters) example: the average height of the subjects.