Control Charts simply explained - Statistical process control - Xbar-R Chart, I-MR Chart,...

Summary

This video script introduces control charts as statistical tools for monitoring and controlling processes by tracking key variables over time. It explains the purpose of control charts, such as identifying trends and unusual patterns, and provides an example using an x-bar R chart in a fulfillment center. The script also discusses different types of control charts for continuous and discrete data, including x-bar R, I-MR, NP, P, C, and U charts, and how to choose the appropriate chart based on data format and variability.

Takeaways

• 📊 Control charts are statistical tools used for monitoring and controlling processes by tracking key variables over time.
• 🔍 They help identify trends, shifts, or unusual patterns that may indicate a problem with the process.
• 📈 A decision tree can be used to determine the appropriate type of control chart based on the format of the available data.
• 📚 An example of an x-bar R chart is used to monitor the average processing time in a fulfillment center to ensure efficiency.
• 📝 Data for control charts is obtained by taking random samples and measuring key variables, such as processing time in the given example.
• 📉 The x-bar chart involves plotting mean values over time, with the center line representing the overall mean and control limits indicating process variation boundaries.
• 📌 The upper control limit (UCL) and lower control limit (LCL) are typically set at three standard deviations from the mean, representing the process's upper and lower variability thresholds.
• 🔢 Sigma, or standard deviation, can be calculated in different ways, with some methods being more accurate or straightforward.
• 📉 The R chart, often used alongside the x-bar chart, plots the range of values each day to provide additional insight into process variability.
• 🔄 The individual moving range (IMR) chart is used when there is only one observation per point in time, plotting the difference between consecutive points.
• 🔢 Discrete data control charts, such as the NP, p, C, and u charts, are used for processes with defects or events counted, and they can accommodate both constant and variable sample sizes.

Q & A

What are control charts and why are they important?

Control charts are statistical process control tools used to monitor and control processes by tracking the performance of key variables over time. They are important because they help identify trends, shifts, or unusual patterns that might indicate a problem with the process, providing crucial information about the stability of the process.

How does a control chart differ from a decision tree?

A control chart is a tool for monitoring process stability and identifying issues, while a decision tree is a flowchart-like structure used to help decide which control chart to use based on the format of the available data. The decision tree guides the selection of the appropriate control chart.

What is an x-bar (x̄) R chart and how is it used?

An x-bar (x̄) R chart is a type of control chart used to monitor the average (x̄) and range (R) of a process over time. It is used to ensure that the process remains stable and within acceptable limits, such as the average processing time in a fulfillment center.

How is the data for an x-bar (x̄) R chart collected?

Data for an x-bar (x̄) R chart is collected by taking random samples of the process at regular intervals. For example, in a fulfillment center, the processing time of five orders per day could be measured over a period of 25 days.

What are the three lines on an x-bar (x̄) R chart and what do they represent?

The three lines on an x-bar (x̄) R chart are the center line, the upper control limit (UCL), and the lower control limit (LCL). The center line represents the mean value of all data points, the UCL is set at three standard deviations above the mean and indicates the upper boundary of process variation, and the LCL is set at three standard deviations below the mean, representing the lower bound of process variation.

What is the difference between control limits and specification limits?

Control limits are based on process variability and statistical calculations, indicating the natural variation within a process. Specification limits, on the other hand, are defined by customer requirements or engineering tolerances and represent the acceptable range of product characteristics from a quality perspective.

What is an I-MR chart and when is it used?

An I-MR chart, which stands for individual moving range chart, is used when there is only one observation at each point in time. It plots individual data points over time and uses the moving range (the difference between consecutive points) to monitor process stability.

How is the moving range calculated in an I-MR chart?

The moving range in an I-MR chart is calculated as the difference between consecutive data points. For example, if the first and second data points are 10 and 11, respectively, the moving range would be 1.

What are the types of control charts for discrete data?

Control charts for discrete data include the np chart (for constant sample size and one defect per unit), the p chart (for variable sample size and one defect per unit), the c chart (for multiple defects per unit and constant sample size), and the u chart (for multiple defects per unit and variable sample size).

When would you use an np chart instead of a p chart?

An np chart is used when monitoring the number of defects in a process with a constant sample size and one defect per unit, such as when counting the number of defective light bulbs produced each day with a sample of 10 bulbs.

How can you create control charts for discrete data using a data tab?

To create control charts for discrete data using a data tab, you can input your data into a table, select the appropriate variables, and use statistical process control tools to automatically generate the desired control chart, such as an np, p, c, or u chart.

Outlines

00:00

📊 Introduction to Control Charts

This paragraph introduces control charts as statistical process control tools used to monitor and control processes by tracking key variables over time. It explains the purpose of control charts, which is to identify trends, shifts, or unusual patterns indicating process problems. The paragraph also mentions the use of a decision tree to select the appropriate type of control chart based on data format. An example of an Xbar-R chart in a fulfillment center is provided to illustrate the monitoring of average processing time, including how to collect data, calculate mean values, and plot the chart with control limits. The difference between control limits and specification limits is highlighted, with control limits being based on process variability and statistical calculations, while specification limits are set by customer requirements or engineering tolerances.

05:03

📈 Exploring Different Types of Control Charts

The second paragraph delves into the variety of control charts, starting with the Xbar-R chart and moving on to the I-MR chart, which is used when only one observation per time point is available. The I-MR chart calculates and plots the moving range between consecutive points. The paragraph then discusses control charts for discrete data, differentiating between charts for one defect per unit (NP chart) and multiple defects per unit with constant or variable sample sizes (C and U charts, respectively). Examples from light bulb manufacturing and car production illustrate the application of these charts. The paragraph also explains the difference between constant and variable sample sizes and how they affect the choice of control chart.

10:04

🛠️ Creating Control Charts for Discrete Data

The final paragraph focuses on creating control charts for discrete data, such as defects in a process. It outlines the steps for creating control charts using data, including selecting the appropriate type of chart based on the nature of the data (e.g., constant or variable sample size). The paragraph provides guidance on using online tools to create control charts by inputting measured values and specifying sample sizes. It concludes with a mention of the availability of instructions for creating various control charts, encouraging viewers to explore these resources further.

Keywords

💡Control Charts

Control charts are statistical tools used in process control to monitor and control processes by tracking key variables over time. They are essential in identifying trends, shifts, or unusual patterns that may indicate a problem with the process. In the video, control charts are discussed as a means to provide information about the stability of a process, with examples given to illustrate their application in quality management.

💡Statistical Process Control

Statistical Process Control (SPC) is a method of quality control that uses statistical methods to monitor and control a process. It is the overarching concept within which control charts are used. The video script emphasizes the importance of SPC in maintaining the efficiency of processes, such as in a fulfillment center, by using control charts to monitor key performance metrics.

💡Trends

In the context of control charts, trends refer to a tendency for data points to consistently increase or decrease over time. Detecting trends is crucial as they may signal a systemic change in the process that could affect quality. The video mentions that control charts help identify trends, which is vital for maintaining process stability.

💡Shift

A shift in control charts indicates a sudden change in the process that results in the process mean moving away from its expected value. The video script explains that shifts can be identified using control charts, which is important for quickly addressing process issues before they lead to significant deviations in product quality.

💡Unusual Patterns

Unusual patterns on a control chart are deviations from the expected behavior that do not follow a predictable pattern and may suggest a special cause of variation. The video script discusses how control charts can reveal these patterns, which can be critical for diagnosing process anomalies.

💡Xbar-R Chart

The Xbar-R chart is a type of control chart used for variables data when multiple observations are taken at each point in time. It is composed of an Xbar chart, which tracks the mean, and an R chart, which tracks the range. The video provides an example of using an Xbar-R chart to monitor the average processing time in a fulfillment center.

💡Mean

The mean, or average, is a measure of central tendency calculated by summing all the values in a data set and dividing by the number of values. In the context of control charts, the mean is used as the center line for the chart, representing the expected value of the process. The video script describes calculating the mean from daily order processing times to create an Xbar chart.

💡Upper and Lower Control Limits (UCL and LCL)

UCL and LCL are the upper and lower bounds of process variation on a control chart, typically set at three standard deviations from the mean. They help determine whether the process is in statistical control. The video script explains that these limits indicate the boundaries of normal process variation and are essential for interpreting control charts.

💡Standard Deviation

Standard deviation is a measure of the amount of variation or dispersion in a set of values. It is used in control charts to calculate control limits. The simplest way to calculate sigma, a common term used to represent standard deviation in SPC, is mentioned in the video script, which is crucial for determining the UCL and LCL.

💡Specification Limits

Specification limits are the boundaries defined by customer requirements or engineering tolerances that a product or process must meet. They differ from control limits, which are based on process variability. The video script clarifies the distinction between specification limits and control limits, emphasizing their importance in quality management.

💡I-MR Chart

An I-MR chart, which stands for Individual-Moving Range chart, is used when there is only one observation per time point. It plots individual data points over time and uses the moving range (the difference between consecutive data points) as its statistical basis. The video script explains the use of I-MR charts in situations where multiple observations at each time point are not available.

💡Discrete Data

Discrete data refers to data that are separate and distinct, often counting the number of occurrences of specific events. In the context of control charts, discrete data is used to monitor the number of defects or events in a process. The video script discusses control charts for discrete data, such as the C chart and U chart, which are used for different scenarios of defect occurrences.

💡Constant Sample Size

Constant sample size refers to taking the same number of observations in each sample during data collection. This is in contrast to variable sample size, where the number of observations can change. The video script uses the example of sampling light bulbs to explain the use of constant sample size in control charts like the NP chart.

💡Variable Sample Size

Variable sample size means that the number of observations in each sample can vary. This is applicable when the sample size is not fixed, such as in the case of a machine randomly sorting out items for inspection. The video script discusses the use of variable sample size in control charts like the p chart, where the number of defects per unit is counted with a varying number of units sampled.

💡Defects per Unit

Defects per unit is a measure used in quality control to count the number of defects found in each unit of production. The video script explains that this metric is used in control charts for discrete data, such as the C chart and U chart, to monitor the quality of products like car bodies or software releases.

💡Control Chart for Discrete Data

A control chart for discrete data is a type of control chart used when the data collected are counts of discrete events, such as defects. The video script discusses different types of control charts for discrete data, including the np chart, p chart, and c chart, each used under different conditions of defect occurrence and sample size.

Highlights

Control charts are statistical process control tools used to monitor and control processes by tracking key variables over time.

They help identify trends, shifts, or unusual patterns indicating potential process problems.

A decision tree is provided to determine the appropriate type of control chart based on data format.

The x-bar R chart is an example of a control chart used in quality management to monitor average processing time.

Data for control charts is obtained by taking random samples and measuring key variables like processing time.

The x-bar chart involves plotting mean values over time with calculated upper and lower control limits.

The upper control limit (UCL) and lower control limit (LCL) are set at three standard deviations from the mean.

Sigma can be calculated in different ways, with the simplest being the standard deviation of all data.

Control limits are based on process variability and statistical calculations, distinct from specification limits defined by customer requirements.

The R chart extends the x-bar chart by plotting the range of values each day to monitor process stability.

The individual moving range (IMR) chart is used when only one observation per time point is available.

The IMR chart calculates and plots the difference between consecutive points instead of a range.

Discrete data control charts monitor the number of defects in a process, with options for one defect per unit or multiple defects.

The NP chart is used for monitoring the proportion of defective units with a constant sample size.

The p chart is used when there is one defect per unit but with a variable sample size.

The C chart is used for monitoring the total number of defects per unit when multiple defects are possible.

The u chart is suitable for monitoring defects per unit with a variable sample size and multiple defects.

Control charts for discrete data can be created online using data input and selecting the appropriate variables.

A list of control charts with instructions on how to create them is provided for both continuous and discrete data.

Transcripts

this video is about control charts first

we discuss what control charts are and

why you need them then we are going to

explore the different types of control

charts so what are control charts

control charts are a type of statistical

process control tool used to Monitor and

control processes by tracking the

performance of key variables over time

they help identify Trends shift

or any unusual patterns that might

indicate a problem with the process

therefore control charts give important

information about the stability of the

respective process depending on the

format in which the data is available

different types of control charts will

be used to find out which one is right

for you you can use this decision tree

we will go through this decision Tree in

more detail later don't worry it's not

complicated but what are control charts

used for to understand this let's first

look at an example of an xar R chart

let's say we work in quality management

at a fulfillment center in a fulfillment

center products are stored packed and

shipped to customers the primary purpose

of a fulfillment center is to ensure

that orders are processed efficiently

therefore the stability of this process

should be monitored for the this purpose

the time from order receipt to shipment

is measured so our objective is monitor

the average processing time to ensure it

stays within acceptable limits of course

we need data to monitor the process to

obtain data we take a random sample of

five orders per day so at the first day

we measure a processing time of five

orders for example the processing time

for the first order was 12 minutes the

processing time for the second order was

14 minutes and so on and so forth

similarly we measure the processing time

on the second day on the third day and

so on let's say we measure the times on

a total of 25 days but how do we get an

expired chart with this data to do this

we first calculate the mean values of

the five orders from all 25 days now we

can create the xar chart to do this we

plot The 25 Days on the xaxis and the

mean values we just calculated on the Y

AIS so we have the first point the

second the third and so on and so

forth now we are almost finished we only

need to calculate these three lines the

center line is simply the mean value of

all values so we just calculate the mean

value of all points the red lines are

the upper and lower

limits the upper control limit UCL is

the threshold above the central line

usually set at three deviations from the

mean it indicates the upper boundary of

process variation the lower control

limit LCL is the threshold below the

central line also set at three standard

deviations from the mean it represents

the lower bound rate of process

variation note there are different ways

to calculate the sigma some are a more

accurate approximation others are a more

straightforward way to calculate it the

simplest way to calculate Sigma is to

calculate the standard deviation of all

data in addition keep in mind that there

is a difference between control limits

and specification limits control limits

are based based on process variability

and statistical calculations whereas

specification limits are defined by

customer requirements or engineering

tolerances now we have the so-called xar

chart in most cases the xar chart is

extended by the r chart R stands for

range to create the r chart we simply

calculate the range of each day for

example on day one the low lowest value

is 12 and the highest is 15 so we get

the range of three we can now plot these

values 3 3 3 5 and so on until the end

three if you want to calculate an xar R

control chart with data tap simply copy

your data into this table and click on

statistical process control now you only

need to select the variables below and

you will get an xar R chart your data

can also be available in such a

format now we know what an xar chart is

but what about the other types let's

start with the IMR chart the IMR chart

stands for individual moving range chart

but what is the difference with the xar

r chart in the case of the xar r chart

we have several observations at each

point in time if if we do not have

several observations at each point in

time but only one we use an IMR chart so

to create the IMR chart we simply draw

the corresponding value at each point in

time since we have only one value per

point in time we cannot calculate the

range therefore we use a moving range in

the moving range chart we calculate and

plot the difference between the conse

itive points such as the difference

between two successive points between a

first and second point for example we

have a difference of one between the

second and the third point we have a

difference of two so we entered a point

at two here to create an IMR chart with

data tab copy your measured values into

this table again if you now simply click

on one variable an IMR chart will be

created automat ically now that we've

discussed the control chart for

continuous data what if we have discrete

data in the control charts of the

discrete data we look at the number of

defects in a process here we

differentiate between one defect per

unit or several defects per unit we'll

go through what that means in a moment

in addition in both cases we

differentiate between constant sample

size and variable sample size let's say

you work for a company that manufactures

light bulbs now you want to monitor the

proportion of defective bulbs produced

each day to do this you take a random

sample of 10 light bulbs each day and

count the number of defective light

bulbs the first day two were defective

on the second one on the third three and

so on and so forth okay hopefully in

reality there are far fewer defects and

Sample should therefore be larger in

this case we have one defect per unit a

bulb is either defective or not and we

have a constant sample size so we use an

NP chart so the NP chart is used to plot

the defect counts over time to identify

Trends or shifts in a defect rate on the

first day for example two lamps were

defective on the second day one was

defective and so on now the question is

what is the difference between constant

sample size and variable sample size in

our example with the lamps we took a

constant sample size every day now we

could also have a machine that randomly

sorts out a lamp from time to time one

day it sorts out 155 lamps the next day

180 lamps then 121 one and so on and so

forth in this case our sample would

contain a different number of lamps each

day and we would have a variable sample

size to get the error rate we then have

to divide the number of 40 lamps by the

number of randomly drawn lamps so we

have one def fact per unit and a

variable sample size we therefore use a

p chart to create a p chart we need two

columns one with the samp example size

and one with the number of defs found

with these values we can now calculate

the proportions and plot the values what

about multiple defects per unit let's

say a car production plant wants to

monitor the number of defects found in

each car body produced to maintain high

quality standards each day one car body

produced is inspected and the total

number of defects per car body is

recorded in this case we use the C chart

to draw the C chart we simply need the

number of defects found per car for

example four defects were found in the

first car so we enter a point at four

but what is an example of a u chart

there we have several defects per unit

and variable sample size imagine a

software development team wants to

monitor the number of B Max per software

release the individual releases are of

course different in size one way to

measure the scope is to measure the

number of lines of code added so we have

a column with the number of lines of

code and the number of reported box this

allows us to calculate the Box per line

of code with this data we can now create

a up plot of course you can also create

a control chats online with data step

for discrete data to do this simply

click on attributive now you can either

select one or more effects select the

measured values and then either specify

a constant sample size or specify the

variable with the sample size the

correct control chart will then be

displayed automatically below you can

see a list of the control charts with

instructions on how to create them

thanks for watching and I hope you

enjoyed the video