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Content:

- 27 PROCESS CAPABILITY, NORMALLY DISTRIBUTED, PART 1
- 27 PROCESS CAPABILITY, NORMALLY DISTRIBUTED, PART 2
- 27 PROCESS CAPABILITY, NORMALLY DISTRIBUTED, PART 3
- 28 PROCESS CAPABILITY, NOT NORMALLY DISTRIBUTED
- 29 PROCESS CAPABILITY, BINOMIALLY DISTRIBUTED
- 30 PROCESS CAPABILITY, POISSON DISTRIBUTED

**27 PROCESS CAPABILITY, NORMALLY DISTRIBUTED
**In the 27th Minitab tutorial, we will accompany the quality team of Smartboard Company as they analyze the process capability of the die casting process for the production of skateboard axles as part of a quality improvement process. Before we get into the actual process capability analysis, we will first see which work steps are required in advance. We will see how the quality team uses the probability plot, and the associated Anderson- Darling test, to work out whether the sample data set available for the process capability follows the laws of normal distribution. We will learn how to use appropriate quality control charts to check whether the die casting process provides the necessary process stability, in the run-up to the actual process capability analysis. The core of this Minitab tutorial will be to get to know all relevant capability indicators within the framework of the process capability analysis, which relate to the overall process capability on the one hand, and the potential process capability on the other. In particular, we will get to know the central capability indicators CP, CPK, PP, or PPK, but also work on the so-called Taguchi Capability Index CPM, which belongs to the so-called second-generation capability indicators. We will use simple calculation examples to calculate the most important key figures step by step including manually, in order to understand how the capability figures shown in the output window are created in the first place. We will also understand what the z-benchmark performance indicator means, and how it relates to the sigma level. Using other performance indicators such as observed performance or expected performance, we will then also be able to assess process capability both, within and between subgroups. We will get to know the very useful Capability Six Pack function, which will help us very quickly, especially in turbulent day-to-day business to calculate all the necessary analyses, which are also required in advance of the actual process capability analysis in just a few steps. Based on the knowledge we have learned and the analysis results available, we will then be able to assess the process capability of our die casting process in a differentiated manner, and thus derive appropriate measures to improve process capability. Once the improvement measures have been implemented, we will finally carry out a new process capability analysis, and use the capability indicators to compare the improved process with the original unimproved process in detail.

MAIN TOPICS MINITAB TUTORIAL 27, part 1

- Fundamentals of standard regulations regarding process capability
- Basic principle and logic of the process capability definition
- Process yields versus process capability
- Process capability indices: PP, PPL, PPU, PPk
- Process capability for centered processes
- Process capability for non-centered processes

MAIN TOPICS MINITAB TUTORIAL Minitab Training 27, part 2

- Preparatory work for the process capability analysis
- Descriptive statistics as part of a process capability analysis
- Test for normal distribution, Anderson-Darling test
- Derivation of the probability plot from the probability function
- Process stability analysis: Xbar and R-chart
- Estimation methods for determining the standard deviation
- Key figures for overall process capability
- Key figures for potential process capability
- Total standard deviation vs. standard deviation within the subgroups
- Sigma level vs. process capability level
- Observed performance, expected performance overall, expected performance within
- Manual determination of the standard deviation for the potential process capability

MAIN TOPICS MINITAB TUTORIAL Minitab Training 27, part 3

- Manual derivation of key performance indicators
- Manual derivation of the standard deviation with the R-bar method
- Manual derivation of the „summarized standard deviation“
- Benchmark-Z (Sigma level)
- Working with the dot plot as part of a process capability analysis
- Extraction of data information as part of a process capability analysis
- Working with the „Capability Six Pack“ option

MAIN TOPICS MINITAB TUTORIAL 27, Part 2

- Preparatory work for the process capability analysis
- Descriptive statistics as part of a process capability analysis
- Test for normal distribution, Anderson-Darling test
- Derivation of the probability plot from the probability function
- Process stability analysis: Xbar and R-chart
- Estimation methods for determining the standard deviation
- Key figures for overall process capability
- Key figures for potential process capability
- Total standard deviation vs. standard deviation within the subgroups
- Sigma level vs. process capability level
- Observed performance, expected performance overall, expected performance within
- Manual determination of the standard deviation for the potential process capability

MAIN TOPICS MINITAB TUTORIAL Minitab Training 27, Part 3

- Manual derivation of key performance indicators
- Manual derivation of the standard deviation with the R-bar method
- Manual derivation of the „summarized standard deviation“
- Benchmark-Z (Sigma level)
- Working with the dot plot as part of a process capability analysis
- Extraction of data information as part of a process capability analysis
- Working with the „Capability Six Pack“ option

**28 PROCESS CAPABILITY, NOT NORMALLY DISTRIBUTED
**In the 28th Minitab tutorial, we visit the last process step of the die-casting process for the production of skateboard axles. The production of skateboard Axles at Smartboard Company is currently carried out using the die-casting process. In order to achieve the strength values required by the customer in the skateboard axles, they are subjected to a heat treatment process at the end of the die-casting process. For this purpose, the skateboard axles are brought to heat treatment temperature in a continuous furnace, and then cooled to room temperature in a water bath. During the rapid cooling process, undesirable changes in the shape of the skateboard Axles can occur, which are still accepted by the customer to a certain extent and must therefore not exceed a certain value in accordance with customer requirements. The core of this Minitab tutorial unit is to find out whether the heat transformation process has a required process performance PPk of at least 1.33, in relation to the maximum permissible shape change. However, we will find out right at the beginning of the training unit, that our data in this sample data set does not follow the laws of normal distribution. A central topic in this training unit will therefore be, to first work out which distribution laws our non-normally distributed data set most closely follows. In this context, we will get to know the very helpful function “ Individual Distribution Identification“, in order to be able to assess an existing non-normally distributed data landscape by means of a corresponding so-called mathematical data transformation, by using the already known performance indicators. We will get to know all the transformation functions that are relevant in practice, and understand the system and criteria that can be used to determine the appropriate transformation function, for the respective practical scenario. As part of our process capability analysis of non-normally distributed process data, we will see how the quality team uses the useful and efficient „Capability Six Pack“ option, to efficiently evaluate the test for normal distribution according to Anderson Darling, and the stability analysis using the corresponding control charts in a single step, in addition to the actual capability analysis. This means that we can use the available results based on the necessary data transformation of the non-normally distributed data set, to assess whether the process performance required by the customer is achieved, and how high the error or process yield is based on the available process performance.

MAIN TOPICS MINITAB TUTORIAL 28

- Non-normally distributed process data, fundamentals
- Analysis of process data using descriptive statistics
- Boxplot Analysis
- Test for normal distribution according to Anderson Darling
- Identification of the distribution type by using data transformation
- Checking the process stability of non-normally distributed data
- Use of the „Capability Six Pack“ option
- Analysis of the process capability based on capability plot and process yield

**29 PROCESS CAPABILITY, BINOMIALLY DISTRIBUTED
**In the 29th Minitab tutorial, we take a closer look at the assembly process in the final assembly department at Smartboard Company. As we already know all the individual skateboard components are assembled into a finished skateboard in this department, and then subjected to an automatic surface inspection before being shipped to the customer. Skateboards without surface damage are classified in the attributive category „good“, and can be sold to the customers. Skateboards with surface damage are classified in the attributive category „bad“, and must either be reworked at great expense or, in the worst case scrapped. The special feature of this process capability analysis is that we are no longer dealing with normally distributed data, as our quality attribute is present in the two categories good and bad, and therefore the statistical laws of the so-called binomial distribution must also be taken into account. In this Minitab tutorial, we will therefore use tools for our process capability analysis that take the laws of binomial distribution into account. We will learn how to carry out the necessary tests with our data set in advance of the actual process capability analysis of binomially distributed data, in order to check whether the laws of binomial distribution are actually observed by our data set. With these findings, we can then carry out the necessary process stability analysis as a preliminary stage to the actual process capability analysis, in order to ensure that the necessary process stability is actually guaranteed. For this purpose, we will use the corresponding control charts, such as the p-chart, and the np-chart, which take into account the laws of binomial distribution. Finally, we can also assess the process performance of binomially distributed process data. The parameters such as the so-called cumulative proportions of defective units, and the so-called rate of defective units, will play an important role here. And we will be able to use a graphical derivation, to understand the sigma level in our binomially distributed process data landscape.

MAIN TOPICS MINITAB TUTORIAL 29

- Scale levels, fundamentals
- Process stability analysis of binomially distributed data
- Report on the process capability of binomially distributed data
- p- chart and np- chart in the context of binomially distributed process data
- Cumulative proportions of defective
- Rate of defective units
- Graphical derivation of the sigma level of binomially distributed process data

**30 PROCESS CAPABILITY, POISSON DISTRIBUTED
**In the 30th Minitab tutorial, we are still in the final assembly department of Smartboard Company. Here, all individual skateboard components are assembled into a finished skateboard and finally subjected to an automatic surface inspection before shipping to the customer to ensure that no undesirable surface damage e.g. in the form of scratches, has occurred during final assembly, which could lead to unwanted customer complaints. In the past skateboards without surface scratches were classified in the attributive quality category „good part“, and could be delivered to customers. Skateboards with surface damage, on the other hand were classified in the attributive quality category „bad part“, and either reworked at great expense or even scrapped. In order to record the severity of the surface damage on the skateboards in even greater detail, the number of scratches per skateboard has also been recorded by the automatic surface inspection system. The focus of this training unit is now to analyze whether the assembly process can be classified as a capable process in terms of the number of scratches. In a previous Minitab tutorial, in which the surface inspection system had only classified the skateboards into two categories good and bad, we were able to carry out all the necessary analysis steps based on the binomial distribution in order to evaluate the process capability. In this practical scenario, the focus is no longer on the number of defects parts per subgroup, but on the number of defects per skateboard and subgroup. We will therefore learn that in this case the statistical laws of the Poisson distribution, rather than the binomial distribution, apply. The focus of this tutorial is therefore on process capability analysis, based on the laws of Poisson distribution.

We will learn that process stability is also an important prerequisite for a capability analysis based on Poisson distributed characteristics, in order to be able to correctly evaluate the process capability. In this context, we will learn how to perform the Poisson distribution test to ensure that our data actually follows the laws of Poisson distribution. We will use the so-called quality control chart u-chart, and the corresponding control tests to quickly work out whether Smartboard Company’s assembly process also has the required process stability as a preliminary stage to process capability, under these conditions. In addition to the important „Poisson plot“, we will also get to know the informative “ Cumulative DPU plot“ diagram, and interpret both. We will then move into the actual process capability analysis of our Poisson distributed data, to obtain the required capability metrics to assess process capability. In this context, we will get to know a number of important parameters, such as the lower and upper confidence interval limit, or the key figure DPU, in order to ultimately be able to assess the process performance in the necessary depth. As part of our analysis, we will also get to know a very efficient option for generating all the necessary analysis steps and information for assessing the quality of the Poisson distribution, process stability and process capability in one step, in the form of a process capability report. With all the necessary information from this process capability report, we can reliably derive whether the process capability of our Poisson distributed data can be classified as a capable, or non-capable process in relation to the customer’s target specification.

MAIN TOPICS MINITAB TUTORIAL 30

- Process stability tests in the run-up to capability analysis
- u- chart, principle
- Accumulated DPU
- Poisson plot for analyzing Poisson distribution
- Cumulative DPU plot
- Statistical analysis of the process capability of poisson distributed data
- Lower and upper CI-limit
- DPU: mean, min/max and target