Five basic quality control tools | Introduction

The five main quality assurance tools are often referred to as the "five quality tools of TS". In fact, these five tools were developed by the AIAG-Automotive Industry North American Action Group (AIAG was initiated by three major US automotive concerns: Ford, GM, and Chrysler). The five main tools include APQP, FMEA, PPAP, SPC and MSA.

Today, we'll take a brief look at the five main instruments to help you get a macroscopic view of these five instruments from 10,000 meters.

1. APQP - Advanced Product Quality Planning

APQP is Advanced Quality Planning, which is a structured new product development tool that is essentially a project management tool. Development quality. APQP includes several steps: project planning and definition, product design and development, process design and development, product and process validation, feedback evaluation, and improvement. It is worth noting that these stages are not connected logically sequentially and are not completely parallel, but overlap each other in time, which helps to reduce the product development cycle.

2.FMEA-Failure Mode and Effect Analysis

FMEA is an analysis of possible failure modes and their consequences, which is a risk control tool. Any failure mode has three dimensions: severity S, frequency O, and detection D. Based on these three dimensions, we can quantify risks to identify the highest risk items and then formulate countermeasures in advance. The FMEA includes the system FMEA, the design FMEA, the manufacturing process FMEA, and the service FMEA.

3.PPAP Approval Process

PPAP, Manufacturing Part Approval Procedure, is a standardized design development reporting procedure (Reporting Procedure) that aims to ensure that the design requirements (drawings) are fully understood and the product continues to meet customer quality and requirements. Power requirements (beat). In terms of content, PPAP includes 18 documents with format requirements such as process flow diagram, PFMEA, control plan, product test report, dimension measurement, process capability analysis, PSW, etc.

4. SPC Statistical Process Control

SPC stands for Statistical Process Control, which is a widely used process control method (common control methods include error protection, full check, etc.) among which the representative control charting tools SPC X-Bar and R are used Chart Invented by Hume Hart in the 1920s. Different SPC control charts have different data requirements, for example X-Bar and R Chart require data to be in a normal distribution, otherwise it is difficult to achieve a good effect. When data is affected by many complex factors, it is often difficult to represent an ideal normal distribution or other distributions, so the use of SPC is also limited. In this case, using error protection is a good choice.

5. Analysis of the MSA measurement system

MSA, or System of Measurement Analysis, is a tool used to analyze errors in a system of measurement. It must answer the question: To what extent do the measured data correspond to the real data? Although we can never guarantee absolutely accurate data, if the collected data deviates too much, then the data will not be of analytical value. It can be seen that MSA is very critical. The MSA may include several aspects of the measurement system commonly used in Gage R&R, including repeatability and reproducibility analysis (repeatability and reproducibility). Gage R&R general data collection method: 3 people, 10 parts, and each person measures 3 times each part. The analysis method can adopt Minitab ANOVA analysis of variance.

__SPC | Concept__

A lot of friends have been posting SPC related posts for a while now and the last few tweets will be related to this topic.

So what is SPC?

SPC stands for Statistical Process Control, English Statistical Process Control, one of the best quality tools to come out in the last century. Generally speaking, SPC tools can be divided into broad sense and narrow sense.

The generalized SPC includes seven traditional quality tools (the magnificent seven):

1. Histogram Histogram

2. Checklist

3. Plato's Pareto Diagram

4. Causal fishbone diagram

5. Process flow diagram

6. Scatter plot

7. Control Chart

SPC narrowly refers to what we often refer to as a control chart, a graphical method of measuring, recording, evaluating, and monitoring key values of a manufacturing process's quality characteristics and whether the process is under control.

In addition to the well-known Shewhart control chart, there are actually many other control charts such as the CUSUM (Cumulative Sum Control Chart) control chart, the EWMA (Exponentially Weighted Moving Average Control Chart) control chart. et al. This series of tweets focuses on the more commonly used Humhart control chart and other parts of the seven core SPC tools that will be introduced in subsequent articles.

It should be added here that when we talk about "quality tools" we often focus more on the technical aspects of the tools, while ignoring the "environment" in which the tools are used. This one-sided knowledge often leads to inefficient use of tools. Although the 7 core quality tools mentioned above are an important part of the SPC, it cannot be said that the SPC is the 7 core tools because the SPC also needs a "continuous improvement and management support" environment. If the enterprise does not strive for a culture environment of continuous improvement and the top management does not strive for this culture environment, then the SPC cannot show its strength. At present, the SPC is not a real SPC. I think that "oranges grown in Huainan are oranges, oranges grown in Huaibei are oranges" is probably the reason.

History of the development and use of SPC

The earliest control chart was the P-chart-P-chart, proposed by Dr. Hume Hart of Bell Telephone Laboratories in the United States in 1924. Later such control charts became known as Hume Hart control charts. If you count according to the Hume Hart P-chart, the SPC theory has been around for almost a hundred years.

When the SPC theory was founded, it coincided with the Great Depression in the United States, and no one cared about the theory at the time. Later, during World War II, the SPC theory showed its talents by helping the US military improve the quality of weapons, so after the war it became popular all over the world. However, after World War II, the US had no competitors, and their products flourished all over the world, and SPC did not receive wide attention in the US.

Japan was taken over by the United States after being defeated in World War II. To help Japan recover from the war, the US military invited Deming to Japan to lecture on SPC theory. In 1980, Japan took the leading position in the world in terms of quality and labor productivity, one of the important reasons was the application of the theory of SPC. In 1984, the Nagoya Institute of Technology in Japan surveyed 115 small and medium-sized factories in various industries in Japan and found that each factory used an average of 137 control charts.

Deming lectured on SPC in Japan

Therefore, whether in Europe, America or Japan, SPC is a very important tool for quality improvement, so everyone needs to deeply understand SPC, apply SPC, and promote SPC.

A few important concepts related to SPC

1. Option

Just as no two leaves are the same in the world, any factory, no matter how advanced, will always have some differences in the same product coming off its production line, and that difference is variation. For example, the length of a batch of qualified bolts produced on the same production line cannot be exactly the same.

2. General reasons and special reasons

Similar to the bolt example above, why can't two identical hamburgers be guaranteed to have the same weight? This is because the process of preparing hamburgers cannot guarantee the absolute weight of each hamburger and there will always be small differences. Just as customers, we can accept such differences. We call the cause of this universal, innate, and acceptable change the general cause.

But if one day you buy two identical hamburgers and find that there are no added vegetables in the middle of one of the burgers, this is no longer an ordinary, ordinary change, but a change caused by some special reason, such as an operational error of an employee. This change is often unacceptable to customers. We call the cause of this non-universal, non-congenital and abnormal variation a special cause.

Would you agree to a burger without vegetables?

3. Controlled and uncontrolled

If a process has only variations due to common causes, we say that the process is under statistical control. If there are variations in the process due to special reasons, we say that the process is out of control.

The purpose of a control chart is to help us identify and eliminate special causes of process variability, i.e., a process that turns a process from uncontrollable to controllable.

It is emphasized here that "controlled" process does not mean "meets design specifications" and "uncontrolled" does not mean "out of specification". Being controlled by whether the specification meets or not is two different things.

Controlled and meets specification (blue control limit, red specification limit, same below)

Controlled but out of specification

4. Central limit theorem

The Central Limit Theorem is an important theoretical foundation for SPC.

This theorem looks like this: “Assume that X1, X2, ..., Xn are n mutually independent and identically distributed random variables. The overall distribution is unknown, but its mean and variance exist. When the sample size is large enough, the distribution of the sample mean will approach a normal distribution."

How to understand? For example, regardless of the weight distribution of 30-year-old men in China, we randomly select the weights of N people and calculate their average, then when N is large enough, the average weight of N people W will be close to a positive distribution of states.

Some people involuntarily ask how big is "big enough"? Remember: if the overall distribution is symmetrical, the effect is ideal for N>=5; if the overall distribution is skewed, usually N>=30 is considered large enough.

This theorem also has an important consequence: the distribution of the sample mean will be narrower than the distribution of the population

, n — sample size.

5. Smart sampling

In the central limit theorem, we talked about sampling. So what is sampling and why do we need to sample?

Sampling is a method of selecting a representative sample from the population under study. In the theory of SPC, the sample takes into account: 1) savings, that is, cost factors; 2) some quality characteristics can only be studied by sampling, such as quality data that must be obtained through destructive experiments.

It is clear that sampling involves risk. If the sampling is unreasonable, the result will be "a glimpse of a leopard in the tube", which is why we call it rational sampling.

Rational sampling includes several questions: sample size, sample frequency, type of sample (continuous sample, random sample, or other structured sample). For accessIn order to achieve the goal of statistical process control, the sampling plan should ensure that: within-sample variation contains nearly all of the variation due to common causes; there was no variation due to special causes in the subgroup, that is, the influence of all special causes is limited to the time period between samples.

The sample size (subgroup size) affects the sensitivity of the control chart. The larger the sample, the smaller the average shift that can be detected. Generally speaking, it is recommended to take at least 4-5 contiguous parts for measurement data and generally at least 500 samples for count data (20-25 groups, each group contains at least 25 data).

There is a lot of content, so I'll stop here for today.

The above seems to represent only some of the basic concepts, but understanding these concepts is very important for mastering the theory of SPC. In the next article, we will look at the theoretical part of the Humhart control chart and answer questions such as:

Continuing the previous article, today we will break down the Humhart Control Chart (hereinafter referred to as the "Control Chart") with a few classic questions to understand what exactly is SPC?

In order to understand the SPC theory, we will first look at the concept of the normal distribution.

The normal distribution, also known as the Gaussian distribution (Gaussian distribution), is a very important probability distribution in mathematics, physics and engineering and has a great influence on many aspects of statistics. low at both ends, high in the middle, symmetrical on the left and right, because the curve is bell-shaped, so people often call it the bell curve, as shown in the figure below.

Let's skip the theoretical formula of the normal distribution function, let's understand some of the characteristics of the normal distribution with examples:

Suppose the weight of adult rabbits in the forest is normally distributed, the average weight is u, and the standard error is σ. Then, according to the probability density function of the normal distribution, we can conclude that about 68% of the rabbit's body weight will be in the range -σ~+σ, and about 95.5% of the rabbit's body weight will be in the range -2σ~+2σ, about 99 .73% of the rabbit's weight will be in the -3σ~+3σ range, and the thinnest 0.135% and the fattest 0.135% will be outside +/-3σ.

If we place all the rabbits on a flat surface according to their weight, we can roughly draw a nice bell curve.

The purpose of the above content is to tell everyone that in the example "about 99.73% of the weight of the rabbits will be in the range -3σ to +3σ", and in the SPC control chart "99.73% of the landing points will beI'm in the range -3σ~+3σ", the logic is the same.

First question:

"The X-histogram control limit calculation is an average of +/- 3 sigma, so 99.73% of the points will fall within the upper and lower control limits. But according to Six Sigma, even an ideal process that reaches the Six Sigma level , there will also be some points that fall between 3 sigma and 6 sigma. So why are we analyzing the cause and developing corrective actions for points outside +/- 3 sigma, even within the six sigma range?"

Do you have the same confusion?

First, this question is logically dubious, but it's a good question nonetheless. Why? Before we go any further, let's see what a control chart looks like.

The figure above shows a relatively common X-bar chart: the horizontal axis represents the sample number (or sample time), the vertical axis represents the quality characteristics of the sample, the center line represents the average of the quality process. characteristics (mean), upper and lower control limits UCL/LCL (upper/lower control limit) are calculated as the mean +/- 3 times the standard deviation of the sample.

If the bit is outside the upper and lower control limits, it means that the process has a special cause and is out of control, then we must analyze and eliminate the special cause.

"Even though it's an ideal process to achieve six sigma, some points will fall between 3 sigma and 6 sigma and be accepted, so why is there more than +/- 3 times the sample standard deviation (sampling means) control limit and action to be taken?"

The answer is that the control limits on the control chart are not specification limits, and a point suddenly outside the control limits does not mean that the process output is outside the specification, but that the process output may be drifting and action is required.

Actually, the person who asked this question confused the control limit (mean +/- 3x sample standard deviation) on the control chart with the mean +/- 3x standard deviation of the process to be monitored. control card Actually it's two things.

If you haven't figured it out yet, let's look at the previous rabbit example combined with the central limit theorem mentioned in the previous article. The total body weight of rabbits is normally distributed. If we randomly sample rabbits, each time 9, and calculate the average, then these sample means form a new normal distribution (small red bell curve in the figure below), and this standard deviation of the new distribution will be be 1/3 of the population standard deviation (1√9).

In accordance with the derivation of the central limit theorem, it can be seen that only for a single-valued sliding range diagramshe I-MR Chart control limit can be 3 times the sigma limit of the process. In addition, the control limits will be narrower than 3 times the sigma limit.

Second question:

Why is a sample size of 4 or 5 recommended?

Continuing from the previous article, we know that as the sample size n increases, the control limit will get narrower and narrower, which means that if the process fluctuates slightly, it can go beyond the control limit, that is, the control graph will become more and more sensitive. A small sample size will reduce the sensitivity of the control chart, i.e. there is a risk that the process has shifted and cannot be detected.

The four plots from top to bottom in the figure below simulate the sensitivity of the control chart to anomaly detection when the sample subgroup is n=1,2,5,12.

The blue curve in the figure represents the original process, and the red curve represents the process after the mean shift. Looking at the first figure, we found that the areas covered by the two curves overlap to a large extent, that is, if the post-migration process is discretized, then the result has a high probability of hitting the pre-migration process. control limits, which means that the control chart cannot detect abnormality. As n increases, the sensitivity of the control chart increases, but the economy will decrease, therefore, considering all aspects, it is more appropriate to define the subgroup size as 4 or 5. Of course, if necessary, you can choose a larger value of n to improve the detection ability, as shown in the last figure above .

Third question:

"The upper and lower control limits of the control chart are calculated as the mean +/-3 times the standard deviation of the sample, so why not +/-4 or +/-2 times?"

Actually, a control chart is an alarm system. In any alarm system, there are two types of risks: the first type of risk is the risk of false positives, which we denote by α, and the second type of risk is the risk of false positives. the risk of missed alarms, which we will denote by β.

α risk: Even when the process is in a controlled state, some points may go out of control for random reasons. At this time, it is considered that the process is out of control in accordance with the rules. This judgment is wrong, and the probability of its occurrence is equal to α. In the 3σ mode α=0.27%. as shown below.

β risk: even if the process is abnormal, some points are still within the control limits. If such a product is retrieved, it will be erroneously judged to be normal, resulting in a type 2 error, i.e. no signaling. The probability of making a Type II error is denoted as β. as shown below.

How to reduce the loss caused by two types of errors? Adjusting the distance between UCL and LCL can increase or decrease α and β. If the distance increases, α decreasedecreases and β increases, otherwise α increases and β decreases. Therefore, no matter how you adjust the interval between the upper and lower control limits, two kinds of errors are inevitable.

One solution is to determine the optimal distance between UCL and LCL according to the principle of minimizing the total loss caused by two errors. Experience has shown that the 3σ method proposed by Shewhart is better, and in many cases the 3σ method is close to the optimum separation distance.

Because the design idea of a conventional control chart is to first determine the probability α of making a type 1 error, and then determine the probability β of making a type 2 error.

Determining CL, UCL and LCL using the 3σ method is equivalent to determining α = 0.27%; in statistics, α = 1%, 5%, and 10% are commonly used at three levels, but Shewhart, in order to increase user confidence, the α of the ordinary control chart is set especially small, so that β is relatively large, which requires the addition of a second type of discrimination criterion. Even if the points are within the control limit, if the location of the points is not random, then there are anomalous factors.

Therefore, there are two types of discrimination criteria for conventional control charts, namely discrimination when the point exceeds the control limit, and discrimination if the location of the points within the control limit is not random.

Okay, that's the end of the introduction on how the SPC works.

Actual SPC fightAbout SPC The first two articles discussed the what and why, respectively, introduced the related concepts of SPC and a few general issues related to the SPC logic.

Today we will talk about how and how to use SPC control charts.

1. Introduction to Halmehart Control Chart Types

For the steps involved in creating an SPC control chart, let's look at the flowchart:

In the figure above, the yellow lane is for quantitative data, including four control charts:

1. X-Bar & R Chart - Mid Range Control Chart

The most commonly used and basic control chart, the object of control is a case of measuring values such as long hair, weight, strength, cleanliness, time and production.

2. I & MR Chart - Single Value Moving Range Chart

The sensitivity of this graph is lower than the other three graphs, and it is mainly used in the following cases: 1) automatic detection (testing for each product); 2) destructive sampling, high cost; 3) uniformity. samples such as chemical and other processes, multiple sampling is useless.

3. X-Bar & S Chart - Mean Standard Deviation Control Chart

Similar to the average range chart, except that instead of the range chart (R chart), it uses a standard deviation chart (ddiagram S); range calculation is simple, so the R chart is widely used, but when the sample size is n>=9 When using the range to estimate population standard deviation performance, it is better to use the S-chart instead of the R-chart.

4. Xmed & R Chart - Medium Range Control Chart

It is also similar to the average range chart, except that the average chart has been replaced with a median chart; since the median can be read directly and is very simple, it is mainly used in areas where measurement data is required. be directly recorded in the control chart for the control case.

The orange path is for count data, which also includes four control charts:

1. P Chart -- P Control Chart

A control object is an event related to quantitative indicators of quality, such as the proportion of unqualified products or the proportion of qualified products.

2. np Chart -- np control chart

The object of control is the number of unqualified products. Since division is required to calculate the proportion of non-qualified products, the graph is relatively simple for equal sample sizes.

3. c chart --c control chart

It is used to control the number of defects in a machine, a component, a specific length, a specific area, or any specific unit, such as the number of sand holes in a casting, the number of machine hardware failures, etc. .

4. u-chart --u-control chart

If you change the sample size, you should convert it to defects per unit and use the u control chart.

Second, the steps involved in creating a control chart

The above 8 control charts are Halmehart control charts, among which the two most commonly used charts are X-Bar & R and I & MR. But no matter which schedule you choose, do the following:

Step 1

Determine the type of control chart based on the data type and sample design.

Step 2

Calculate process averages and control limits using collected data.

Step 3

Calculates the graph scale and plots the data points, process average, and control limits on the control chart.

Step 4.

Find uncontrolled points:

- a. Determine why the situation got out of hand.

-b. Fix process issues such as sampling design, data collection methods, etc.

- c. If a specific cause is identified, remove the out-of-control point and add an additional number

Stronghold replaces.

- d. Recalculate process averages and control limits.

- e. Rescale and plot modified data points, process mean and control limits.

On

-f. go onrepeat the sampling process until all required points are under control. This will install the correct

Process mean and control limits.

Notes: we refer to the control chart before step 4-d above as the control chart for analysis (stage I); the control card after d is called the control card for control (stage II). The analysis control chart stage is the process stage Parameters are unknown, and the control chart stage for control is the stage at which the process parameters are known.

Control chart for analysis

– Control charts for analysis mainly analyze whether the process is stable and controllable, whether it is in a statistically stable state and technical In the steady state of the technique, the data analyzed at this time is often the data of a certain period of time, such as a week or a month; one of the main tasks of charts.

Control chart for control

When the process reaches the "statistical steady state and technical steady state" defined by us, the control line of the control chart for analysis can be expanded as a control chart for control. This extended line of control is equivalent to the production legislation that goes into day-to-day management.

Third, the control chart option

We track the diameter of the shaft part using SPC. If its nominal size is 18.0mm, follow the above 4 steps:

Step 1

First, decide on the type of control chart: variable data that is easy to get, so be sure to select X-bar chart and R-chart.

Step 2

Collect data and calculate initial means and control limits. As shown in the table below, we have collected m = 25 subgroups, the size of each subgroup is n = 5, for a total of 125 data.

According to the following formulas, you can get the upper and lower control limits of the X-Histogram and R-Chart, respectively.

Step 3

Start drawing graphs, pay attention to the appropriate scale of the graph.

Step 4

Fortunately, we found no outliers indicating that the process itself is stable and manageable, and the analysis phase is complete, so we can expand the control limit and proceed to subsequent monitoring of the process.

In many cases, there will be abnormal points before Step 4, i.e., in the "analysis stage", and abnormal points may also appear in the subsequent "control stage", so how to "distinguish"?

Fourth, Control Chart Differences

During the development of control charts over the past hundred years, various types of discrimination criteria have been proposed, such as:

There may therefore be some differences in the discriminatory principles listed in different sources, and which are discriminantThe principles we choose to use can be determined according to our own situation. Today we present 8 different criteria in Minitab (combined with the following figure for understanding):

Principle 1

Any point outside the control bounds

Principle 2

2 out of 3 points are in zone A or outside it

Principle 3

4 out of 5 points are in zone B or outside it

Principle 4

15 consecutive points are within 1 standard deviation of the center line (both directions)

Principle 5

8 consecutive points more than 1 standard deviation from the center line (either way)

Principle 6

Nine consecutive dots are on the same side of the center line

Principle 7

6 points in a row up or down

Principle 8

Successive 14 dots change up and down alternately

Actually, the contents of the SPC can be discussed in more detail. In addition to the Humhart control chart above, there are the CUSUM Cumulative Sum Control Chart, the EWMA Exponentially Weighted Moving Average Control Chart, etc. Due to space constraints, the control chart application is presented here SPC and I hope it will be helpful for everyone.