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# Process Capibility

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Submitted By nelson11
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* Identify the reasons for using process capability studies and the limitations of these studies * Compare the applications of the three types of process capability studies (potential, short term and long term) * Determine whether a process is capable of meeting specified tolerances by using Cp and Cpk indexes * Estimate inherent variability in a process * Use calculations to determine whether a process is centered * Evaluate the potential and short term capability of a process

Welcome to Process Capability Studies. In this lesson, we will cover the following topics: * What is Process Capability? * Pittfalls of Process Capability Studies.
After completing this lesson, you should be able to: * Identify examples of real world situations in which a process capability study could be used * Identify the equations associated with process capability studies * Select the times during the life of a process where a process capability study can be run * Identify the appropriate equation for long term studies vs. single time studies * Select the common pitfalls or limitations associated with conducting a process capability study * Identify the factors that contribute to the limitations of process capability studies * Analyze a scenario that describes a process capability study.
"It is good management to reduce variation of any quality characteristic, whether this characteristic be in a state of control or not, and even when few or no defectives are being produced."
---- Dr. W. Edwards Deming

The intent of this lesson is to prepare an individual for developing a process capability study, analyzing the results from a process capability study and interpreting and using the results from a process capability study.

Welcome to What is Process Capability?

Process capability is generally thought of in terms of long term variation. That is, the total inherent variation that can be expected from a process over a long period of time, such as days, weeks or months.

In this topic, we will look at process capability studies, the preferred method for studying variation in any process

What is Process Capability?
The total variability of a particular characteristic of the product is the net result of the variations of all the factors that influence the process. When the process is operating at an acceptable level, the effects due to these factors are small, random and indistinguishable from one another. When the effects of one or more of these factors are large, they tend to dominate the total variability and, if severe enough, causes out of specification product to be produced. In order to understand these factors, process capability studies are conducted

Process Capability Studies
A process capability study is an analytical method, which can be used to: * Measure the amount of variation in the process over time * Determine if the process is stable with time * Determine if the process is inherently capable of meeting the tolerances * Determine if the process performance is on target * Identify causes of assignable variation

Common Process Situations
Process capability can be better understood by taking a brief look at some common process situations:

We've already talked about what process capability is, now let's look at how process capability is expressed.
The most widely adopted expression for process capability is:
Process capability = ±3Sp (LONG TERM)
This equation is appropriate when the study includes many days. If the study is conducted on only one day or on one shift then the variations due to day o day tolerance will not be included in the estimate of capability.
If the equation Process Capability = ±3Sp is appropriate for multi-day studies, what equation will you use if you have a short and finite amount of time to evaluate the process?
If the study must be concluded in one day or one shift, this equation provides a better estimate:
Process capability = ±4Sp (short term)
Circumstances and time constraints will be the deciding factors when it comes to choosing the best equation for expressing process capability. Take a look at this example:
Bob and Steve are mechanical engineers. They need to conduct two separate process capability studies, but under very different sets of circumstances.
Process capability studies should be run under normal operating conditions with a single set of factors making up the manufacturing process.
Calibration of equipment nt during study should be avoided
Operator should avoid adjusting or changing the process or equipment during the study

Capability studies can be run at various times during the life of the process, including: * Prior to taking delivery of new equipment * After the equipment has been delivered and setup * Just after production begins on new equipment * Just before modifying a process * Just after modifying a process * On an ongoing basis to monitor the performance of the equipment or process * When an out of specification situation is identified and the reasons are unknown
There are several factors, which affect the quality of process capability studies, including: * Sample size * Data collection * Statistical control * Sensitivity to measuring equipment

Process Capability Studies on the Job * Now that you know about when to run process capability studies, let's take a closer look at specific situations you're likely to run into on the job where process capability studies could come in handy.
To design a product, purchase new equipment, judging acceptability ogf equipment
Evaluating a new process
Knowing how and when to run process capability studies in your work environment will go a long way in terms of helping you eliminate variation.

Whether you have an extended amount of time or just one shift, process capability studies can help you deal with variation when it occurs.

Welcome to Pitfalls of Process Capability Studies.

In this topic, you will take a closer look at the pitfalls and limitations inherent to process capability studies. Knowing about the limitations and pitfalls will help you avoid unsuspected trouble.
Common Pitfalls
In the course of conducting a process capability study, there are pitfalls and limitations that must be recognized in order to avoid unsuspected trouble. Process capability study pitfalls and limitations may involve: * Sample size * Time frame * Data collection * Statistical control * Sensitivity of measuring equipment
Sample Size and Time Frame * Let's take a closer look at two common pitfalls of process capability studies: sample size and time frame. How do these two elements impact process capability studies?

Time Frame: It is possible to have a process capability study where insufficient time was allowed for long term variable s or factors to surface. Long term factors include things like tool change, tool or machine wear, machine settings, machine maintenance, raw materials, etc
Sample Size: It is possible to have a process capability study where the sampling is way too narrow and the data does not represent the total process variability. Information factors such as machine number, operator, inspector, and tool number are frequently overlooked.
In addition to time frame and sample size, process capability studies can also be affected by data collection, statistical control and the sensitivity of the measuring equipment.
Measuring Equipment: It is important to be sure that the equipment is sensitive or accurate enough to measure the true performance of the process. It is important to determine, before the study, the sensitivity and accuracy of the intended measuring device.
Data Collection: Data collected by different people who did not record the same kind of information could have a negative effect on a study. The end result is that the data cannot be combined together into a large analysis with any reasonable degree of confidence.
Statistical Control: If the process was not under a state of statistical control, studies on the process will only reveal what has happened today, when the study may be different tomorrow.

You have just learned: * To select the common pitfalls or limitations associated with conducting a process capability study * To identify factors that contribute to the limitations of process capability studies

Lesson Introduction
Welcome to Types of Process Capability Studies. In this lesson, we will cover the following topics: * Process Capability Study Types * Basic Design Layout
After completing this lesson, you should be able to: * Identify the three types of process capability studies * Match the three types of process capability studies to their respective characteristics * Associate basic design layouts with their respective process capability study type * Analyze a scenario about a process capability study and determine its type based on its characteristics and design layout

You're buying a new piece of equipment. Your team will depend on this machine to work efficiently and produce products without down time or costly variation. Though the equipment seems to be what you're looking for, isn't there something you can do to test it?

How do you know the machines on your shop floor are performing up to standard? Is there room to increase efficiency? What about when machines start having trouble and producing variation?

Process capability studies are the answer to all three of these dilemmas. Do you know the various types of process capability studies and when to use each respective type? Do you know how to design and layout a process capability study? This lesson will teach you about the various types of process capability studies and provide a high-level understanding of design layout.

Welcome to Process Capability Types.
There are three types of process capability studies: * Potential studies * Short term studies * Long term studies

Take a look at the three types of process capability studies and how they differ from one another. Click on each study type to learn more about where it can be conducted. * Potential studies * Potential studies are used when there is a very short time frame to assess whether the process or equipment has the inherent capability to meet the tolerances and hit the target. * Can be conducted at either vendor’s site or users site * Short term studies * Short term studies are used to determine whether the process or equipment has the inherent capability to meet the tolerances or hit the target over a period of several shifts or days. * Performed at the users site under normal operating conditions * Long term studies * Long term studies are used to determine whether the process or equipment has the inherent capability to meet the tolerances, hit the target, and to be stable over a period of many days. * Performed at the users site under normal operating conditions

Potential Studies
Let's take a closer look at potential studies. The purpose of a potential study is to determine if the process or equipment has the inherent capability to meet the tolerances and to hit the target during a very short time period, generally, less than a day.
Potential studies are useful for assessing equipment or a process quickly. Potential studies are valuable when you're considering the purchase of a new piece of equipment, or when you've only got a few hours to assess capability.
These engineers are visiting a vendor today to assess a new drill press they're thinking of buying. They are planning on conducting a potential study while they are there. Let's take a look at what they'll do to conduct this potential study. * One run (a batch, a coil, a lot of materials, etc.) is processed. * During the run, at least ten samples or specimens are taken from the beginning, middle, and end of the run.

Short Term Studies
The purpose of a short term study is to determine if the process or equipment has the inherent capability to meet the tolerances and to hit the target over a period of several shifts or days.

Let's take a closer look at how a short term study is conducted.

When a short term study is conducted, several runs (batches, coils, lots of material. Etc) are processed. At least 10 samples are taken from beginning, the middle, and the end of each run. Also the process is studied on at least 3 different days over a 10 day period.

Remember, in a short term study: * Several batches (coils, lots, etc.) are run over three days. * At least ten samples are taken from the beginning, middle, and end of each run. * The process is studied on at least three different days over a ten day period.
What does the design layout for a short term study look like?
Long Term Studies

What is the purpose of a long term process capability study? The purpose of a long term process capability study is to determine if the process or equipment has the inherent capability to meet the tolerances, to hit the target, and to be stable over a period of many days.

A long term study several runs, batches, or coils are processed over at least 30 days. At least 10 samples are taken from the beginning, middle and the end of each run.
Actually, the design layout is similar to that of a short term study, except that the number of days is increased to at least ten days spanning at least thirty working days

Whether you're faced with the need to evaluate the capability of a process in hours, days, or weeks, there is a process capability study type designed to meet your needs.

If you need to determine if the process or equipment has the inherent capability to meet the tolerances and to hit the target during a very short period of time, a potential study will give you the information you need.

If you need to know whether the equipment or process can hit the target over a period of several shifts or days, a short term study may be the study type you choose.

Finally, if you need to know whether a process or equipment can meet the tolerances and hit the targets over a period of many days, a long term study is the optimal choice for you.

Topic Introduction

Welcome to Basic Design Layout.

Each of the three types of process capability studies is associated with a basic design layout. The design layout illustrates the way the study is set up and how and when samples were taken for study.

Whether you're conducting a potential process capability study, a short term study, or a long term study, it is essential that you follow the basic design layout.

Potential Studies

potential process capability study is conducted on one day or one shift. Its basic design layout is quite simplistic.

Based on a minimum of thirty samples (ten from the beginning, ten from the middle, and ten from the end of the batch, coil, or run), the potential study is the fastest type of process capability study to perform

Matt and his lead engineer are preparing to conduct a potential process capability study on a drill press they are thinking of buying for their plant.

When you look at the basic design layout, each X represents the result of a particular quality measure on a single item or specimen.

The basic design layout for potential studies is simple because it is based on one run on one day. In the image on the right, ten samples were taken at the beginning, middle, and end of the run. Keep in mind, however, that it is possible to take more than ten samples when conducting a potential process capability study. If fifteen samples were taken, 15 X's would appear in the basic design layout.
Short Term Studies
In a short term study, the process is studied on at least three different days over a ten day period. On each day, several runs, batches, or coils are studied.

This graphic shows the design layout for a short term study where three runs were studied on three different days.

Note that for this short term study, a total of 270 samples were taken.

Because a short term study involves multiple runs, over multiple days, and significantly more samples than a potential study, the design layout is more complex.

The example on the right shows ten samples or specimens taken at the beginning, middle and end of each run. Keep in mind, however, that ten is the minimum number of samples that can be taken from each respective section of the run. If the person performing the study feels it is warranted, more than ten samples may be taken.

Long Term Studies
The design layout for long term process capability studies is the most complex. Because long term studies look at a minimum of ten samples from the beginning, middle, and end of several runs on at least ten days, spread over a thirty-day time period, the basic design layout is quite long.

Actually, the basic design layout for a long term process capability study is fundamentally the same as that of a short term study. The primary difference is the extended number of days.

Lesson Introduction
Welcome to Process Capability Indexes. In this lesson, we will cover the following topics: * Performance Measures * Cp Index * Cpk Index * Using Cp and Cpk Indexes
After completing this lesson, you should be able to: * Match the three performance measures with their respective uses * Determine whether a process is capable of meeting specified tolerances by using Cp * Determine whether a process is capable of meeting specified tolerances by using Cpk * Apply the Cp and Cpk indexes to determine whether a process is capable when presented with a real-life scenario

Welcome to Performance Measures.
In this topic you will: * Identify the three performance measures or acceptance criteria associated with process capability studies * Match the three performance measures with their respective uses

Capability Indexes * Generally, there are three performance measures or acceptance criteria associated with process capability studies. The three are:
Capability
* is the ability of the process to meet customer specifications consistently. It is measured by estimating process capability indexes (i.e., Cp and Cpk).
Centering
* is a measure of the average performance of the process. It represents the ability of the process to hit the target or the nominal value specification range.
Stability
* is a measure of the consistency of the process with time. That is, is the process in a state of statistical control through time? Stability is estimated by comparing the total process variability and the inherent process variability.

Process Capability
The best way to judge the ability of a process to meet the tolerances is to compare ±3Sp to the product tolerances.
If ±3Sp is less than the product tolerances, then the process is capable of meeting the tolerances. If ±3Sp is greater than the product tolerance, than the process is not capable of meeting the tolerances.
Welcome to Cp Index.
In this topic you will:
Recognize the equation for Cp
Determine whether a process is capable of meeting specified tolerances by using Cp
Capability Indexes
To better understand this relationship between process capability and the product tolerance, several capability indexes have been developed. Two common capability indexes are: * Cp * Cpk * Cp is a ratio between the product tolerance range and the process capability. * Cpk is a ratio between the estimated process spread and the tolerance range. Cpk has an added feature of taking into consideration how close the process mean is to the nominal value.

Cp * The first capability index used is Cp. Cp is simply a ratio between the product tolerance range and the process variation. This ratio can be expressed as follows:

Cp= Tolerance Range/6Sp

To demonstrate the expression, consider the following example:
Dale conducted a process capability study on a cutting process. The product specification is 5.285 ± 0.005 inches. The estimated process variation of the process is Sp = 0.001. Therefore, given the equation:
Cp = Tolerance range / 6Sp
Cp = 0.010 / 6(0.001) = 1.67
Capability Guidelines
The following guidelines can be used to determine whether or not a process is capable of meeting tolerances when Cp is used. * If Cp is equal to or greater than 1.33, then the process is more than capable. * If Cp is less than 1.33, but equal to or greater than 1.0, then the process is capable, but must be closely controlled. * If Cp is less than 1.0, then the process is not capable.

Topic Introduction
Welcome to Cpk Index.
In this topic you will: * Recognize the equation for Cpk. * Determine whether a process is capable of meeting specified tolerances by using Cpk.
The Cpk Index * The Cpk Index is sometimes referred to as the Ford method because it is used extensively by the Ford Motor Company. * The Cpk index is similar to the Cp index because it is also a ratio between the estimated process spread and the tolerance range. However, it has the added feature of taking into consideration how close the process mean is to the nominal value. The general formula for the Cpk index is:
CPK=(z min)
Z1= (USL –X)/3s - USL – Upper Spec Limit, X – The process mean, S – standard deviation when in a state of control
Z2- (x-LSL) /3s - LSL – lower spec limit
Determining Capability
When using the Cpk index, the capability of the process is determined by the following guidelines: * If Cpk is equal to or greater than 1.3 than the process is considered very capable. * If Cpk is equal to or greater than 1.0 and less than 1.3, then the process is considered capable if it is closely monitored. * If Cpk is less than 1.0, then the process is considered not capable.

Topic Introduction\
Welcome to Using the Cp and Cpk Indexes. In this topic you will: * Recognize rules and standards for using Cp and Cpk * Apply the Cp and Cpk indexes to determine whether a process is capable when presented with a real-life scenario Using the Capability Indexes * The Cpk index should be used with the Cp index. The Cp index only takes into account the amount of variation in the process, while the Cpk takes into account where the process mean is located with respect to the target and the process variability.
Remember the following key points when using the Cp and the Cpk indexes: * Cp and Cpk can only be calculated for processes that are in control. * Cpk is always less than or equal to Cp. Capability: Cp and Cpk in Action
Cp and Cpk used together reveal important insights regarding the capability of the process.
Click on each of the items below to learn what each situation reveals about the capability of a process.
Cp = Cpk = 1.0 - Cp = Cpk = 1.0 indicates that the process is just able to meet the specifications (the process is producing 0.27% non-conforming components on the average)
Cpk > 1.0 - Cpk > 1.0 indicates that the process is capable of meeting the specifications.
Cpk < 1.0- Cpk < 1.0 indicates that the process is not capable of meeting specifications.
Cp and Cpk in Action (cont.)
Cp and Cpk values reveal important information about where a process is centered
Cp = Cpk only when the process mean is centered at the center of the specifications.
Cpk = 0 whenever the process mean is centered at either the upper specification limit or the lower specification limit.
Cpk < 0.0 indicates that the process mean is centered either below the lower specification limit or above the upper specification limit.

Testing for Normality * Testing for normality is the second step when assessing process capability. This step is very important. If the process does not follow a normal distribution, then other statistical techniques must be used to evaluate the process. * To determine if the process follows a normal distribution, formal or informal statistical techniques can be used. The informal techniques are: * Drawing histograms * Probability plots

Formal Techniques
When testing for normality, it is necessary to use statistical software. There are many programs available. The formal techniques for testing for normality include:
An Anderson-Darling Test is used to confirm that a data set comes from a specified distribution.The Anderson-Darling test makes use of the specific distribution in calculating critical values. It has the advantage of allowing a more sensitive test and the disadvantage that critical values must be calculated for each distribution

The Lin-Mudholkar test is a statistical test used to test for normal distribution in a process

The Shapiro-Wilk Test tests whether a random sample comes from (specifically) a normal distribution

The Chi Square test is used to test if a sample of data came from a population with a specific distribution.

Detecting Normality
If sufficient data has been collected (over fifty data points), the informal techniques are very effective for detecting lack of normality. Some of the SPC software packages on the market have routines for testing for normality, which can be very helpful.
Topic Introduction

Welcome to Inherent Variability. In this topic you will: * Estimate inherent variability by calculating the standard deviation * Identify alternative ways for estimating inherent variability

Estimating Inherent Variability for Normal, Stable Distributions
If the underlying distribution of a process is normal and the process is stable, (that is, in a state of statistical control) with time, then the inherent variability (Sp) can be estimated by calculating the standard deviation of all the data problems with Estimating Inherent Variability
If the underlying distribution of the process is not normal or if the process is not stable with time, then the inherent variability (Sp) cannot be estimated by calculating the standard deviation of all data.
Estimating Inherent Variability in Non-normal & Unstable Distributions
How do you estimate inherent variability when the underlying distribution of a process is not normal or when the process is not stable with time? Since you cannot rely on calculating the standard deviation, a more flexible method is needed.

Control charts for the range or control charts for standard deviation can be used.

Using Control Charts
Control charts for the range can be used to estimate the inherent variability since subgroup ranges reflect the process variability. The following steps are used when using the control chart for ranges method:
Step 1 – Select the appropriate subgroup size (generally 4-5)
Step 2 – Maintaining the time order of the data, divide the data into subgroups
Step 3 – Calculate the range (r) for each subgroup
Step 4- Plot the range in time sequence
Step 5 – Calculate the average range

Potential studies are usually performed on a single shift using one production run. They do not evaluate: * Long term capability of the process * Long term stability of the process Samples * Achieving the objectives of a potential process capability study requires that at least thirty measurements be taken from the run for the characteristic of interest. * This means that samples should be taken from the entire run (beginning, middle, and end) in order to obtain a representative picture of the performance of the process.
Design Layout * Here's a quick review on the design layout of a potential process capability study: * * If a potential process capability study requires at least thirty samples taken from the beginning, middle, and end of the run, what does the design layout look like?

Evaluating Potential Studies
To evaluate the potential process capability, follow these steps: * STEP 1: Plot the data in time sequence * STEP 2: Evaluate the data for normality * STEP 3: Determine if the process is in control * STEP 4: Estimate the inherent variability * STEP 5: Determine capability and ability to hit the target by calculating a capability index

Topic Introduction

Welcome to Using Potential Process Capability Studies.
In this topic you will: * Evaluate the potential capability of a process when presented with an example. * Apply the five steps to evaluate the capability of a potential process described in a case study

Evaluating Potential Capability
How do you evaluate the potential capability of a process? Take a look at the following example:

Ken, a process engineer, wanted to determine the potential capability of a waxing process. He decided to evaluate several coils produced by the process over a short period of time. The four coils were sampled in ten different locations along the length of each coil.

At each location, a full width specimen was taken and sent to the laboratory for testing. All the specimens were taken from the center of the sheet. The process specification is 15±3 mg/foot. The results of the study were as follows:

Step One
Follow along as Ken applies the five steps for evaluating the potential capability of a process.
The first step, when evaluating the potential capability of a process, is to plot the data in a time sequence.
The image below is the time sequence plot Ken created from his test results.
A time sequence plot represents a record of the process over time and can give a clear picture of the performance of the process with time. It can indicate if the process is stable. It can also show when trends or sudden shifts in the average performance occurred and what direction the trends or sudden shifts took. In addition, time sequence plots permit the engineer or production supervisor to determine sources of variations affecting the process.

Step Five
The final step is to determine capability and ability to hit the target by calculating a capability index.
Since the distribution is normal in Ken's waxing process, the process capability is:
±3Sp= ±3(1.21) =±3.66

Lesson Introduction

Welcome to Analyzing Process Capability.
In this lesson, we will cover the following topic: * Short Term Study Analysis

Welcome to Short Term Study Analysis.
In this topic you will: * Evaluate the short term capability of a process when presented with a case study

Short Term Studies * How do you go about conducting a short-term process capability study? Take a look at the following example: * Ed wants to determine the process capability of a cutter. The product characteristic is width and the product specification is 16 ± 2.00 inches. The process was evaluated on five different days. On each day, at least two runs were looked at and five consecutive items were measured from each run.
Conducting the Study
The steps used when conducting a short-term process capability study are the same as the steps used when conducting a potential process capability study. In a short-term study, there is more data to collect and interpret. The steps are: * Plot the data in time sequence * Evaluate the data for normality * Determine if the process is in control * Estimate the inherent variability * Determine capability and the ability to hit the target by calculating a capability index

For the Range control chart, all points are within the control limits.

For the X-Bar control chart, all points are within the control limits.

Therefore, it can be concluded that during the study, the process was in statistical control.
Step Four
The fourth step is to estimate the inherent variability for the cutting process.
The inherent variability can be estimated from the range control chart since the process is in a state of statistical contro

With a Cpk index of 0.69, it can be concluded that the cutting process Ed set out to study is not capable of meeting the product tolerances. The problem appears to be a variability issue rather than a location issue.

Remember, process capability is a measure of the ability of a process to produce to the requirements. Process capability indexes measure the relationship between actual process performance and the expectations of the process.

Remember too that regardless of the type of study you are planning on conducting, prior planning is needed in order to minimize the influence of any extraneous variables and to maximize the obtainable information.