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**VIII Measure - Capability and Measurement**

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Initial Thoughts Success depends upon the ability to measure performance. Rule #1: A process is only as good as the ability to reliably measure. Rule #2: A process is only as good as the ability to repeat. Gordy Skattum, CQE VIII-2

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Initial Thoughts It is impossible for us to improve our processes if our gaging system cannot discriminate between parts or if we cannot repeat our measurement values. Every day we ask “Show me the data” - yet we rarely ask is the data accurate and how do you know? VIII-2

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**Purpose of Measurement**

Product Control Detection, conformance to a design specification Process Control Prevention, real-time control, assessing a feature to its natural process variation What is a measurement system used for? VIII-2

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**AIAG/MSA/Gage R&R AIAG – Automotive Industry Action Group**

Collaboration between “Big 3” to create one set of guidelines for all suppliers MSA Reference Manual – Measurement System Analysis Introduction to MSA Covers normally occurring measurement situations Developed to meet specific needs of the automotive industry Gage Repeatability and Reproducibility A study to understand the within-system and between-system variation in a measurement system A comparison of standard deviation VIII-2

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**Measurement Terms Discrimination**

In selecting or analyzing a measurement system, we are concerned about the system’s discrimination, or the capability of the system to detect and faithfully indicate even small changes of the measured characteristic - also known as resolution. The smallest readable unit 100ths graduation decimal rule VIII-4

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**Accuracy vs. Precision Precise (low variation) Yes No No**

Accurate (on target) Yes VIII-4

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**MSA Terms Bias Choices for addressing bias error**

The difference between the observed average of measurements and the reference value. The reference value, also known as the accepted reference value or master value, is a value that serves as an agreed-upon reference for the measured values. Bias is measured as “accuracy” or as “accuracy shift.” Choices for addressing bias error Calibrate the gage; adjust, correct, or apply an offset Change the system (instrument, condition, masters, …) VIII-4

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**MSA Terms Stability Time 2 Time 1**

Stability (or drift) is the total variation in the measurements obtained with a measurement system on the same master or parts when measuring a single characteristic over an extended time period. The change in bias over time. Stability Time 2 Time 1 VIII-4

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**MSA Terms Linearity Choices for addressing linearity**

Linearity is the bias over the operating range of a measurement system. This, along with bias, is checked as part of the calibration procedure. Choices for addressing linearity Calibrate, adjust the gage or build offset table Change the system (condition, masters, …) VIII-4

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**MSA Terms Repeatability (EV)**

Repeatability is the variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristics on the same part. Includes all within-system variation. Repeatability VIII-4

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**MSA Terms Reproducibility (AV)**

Reproducibility is the variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristics on the same part. Includes all between-system variation. Operator A Operator B Operator C Repeatability VIII-4

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Effective Resolution The sensitivity of a measurement system to detect process variation Rules for determining effective resolution Count the number of “0” plot points on the process range control chart. If >25%, then the gage lacks effective resolution Count the gage discrimination levels between the UCL and the LCL of the process average control chart. If <5 levels, gage lacks effective resolution VIII-4

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**Effective Resolution Levels between UCL-LCL? Number of zeros?**

Individuals Chart UCL=5.2633 LCL= CEN=2.16 -2 2 4 6 1 3 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Moving R Chart UCL=3.8115 LCL=0.0 CEN=1.1667 -1 Levels between UCL-LCL? Number of zeros? VIII-4

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**Gage R&R Levels A capability measure Typically we compare**

Gage R&R to tolerance Gage R&R to process variation Three levels of results 0-10% 10-30% +30% VIII-5

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**Impact on SPC and 6s If you have a poor measurement system…**

Difficult/impossible to make process improvements Causes quality / cost / delivery / responsiveness problems False alarm signals, increases process variation, loss of process stability Improperly calculated control limits Can make your processes worse! VIII-5

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**Guidelines for Determining a Gage R&R**

Since the purpose of the analysis of a measurement system is to understand the systems variation, the use of graphical tools is very important. Personal investigations have unveiled many powerful gage analysis software packages. SPCXL (Sigma Zone) Minitab All will deliver identical results* SPCXL is easy to use and inexpensive. Minitab is a complete statistical analysis package which requires a lot of training. VIII-7

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Guidelines (cont.) The four standard methods for analyzing measurement systems are: Range method (short form) Average and Range (long form) ANOVA (Analysis of Variance) Attribute gage study (both short and long form methods) Each method has its advantages and disadvantages as well as limitations. Refer to the AIAG MSA Reference Manual (Measurement Systems Analysis) for additional information. VIII-7

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**Initial Control Chart Analysis**

Our first concerns are about the measurements systems discrimination (meet 10:1 rule?) We can determine if the measurement system has adequate discrimination by reviewing the process control charts for the process ahead of time. (effective resolution? stable?) We need to make sure we study parts over the total range for the process or tolerance, whichever is greater VIII-8

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**Preparation for Conducting a GR&R Study**

The approach to be used should be well planned out. Determine the number of appraisers, sample parts, and trials in advance. The appraisers chosen should be selected from those who normally operate the instrument. The sample parts selected must represent at least the entire range of the process. Each part will be marked for identification. VIII-8

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**Preparation (cont.) Verify use of the 10:1 rule.**

Assure that the appraisers method of measuring the characteristics feature is following the defined measurement procedure. Each should use the same technique.* VIII-8

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Preparation (cont.) To minimize the likelihood of misleading results, the following steps should be taken: The measurements should be made in a random order. The appraisers should be unaware of which numbered part is being checked in order to avoid any possible knowledge bias. In reading the equipment, the readings should be estimated to the nearest resolution that can be obtained. If possible, readings should be made to one-half of the smallest resolution. YOU must oversee the entire study so that bias’ does not occur. VIII-8

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**Gage R&R Sheet Available on Website**

Quality Tools.xlsx VIII-8

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Analysis of Results Following are examples of gage analysis charts one would find using SPCXL. VIII-8

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Results (cont) VIII-8

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Total Variance The total amount of variance in the gage and in the process VIII-14

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**What Happens When “Shift Happens”?**

Most processes are designed to meet the customer specification Because we are using all of our tolerance, we’re forced to keep the process exactly centered. If the process shifts at all, nonconforming parts will be produced Target Lower Limit Upper Limit VIII-19

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Getting Started Using 75% or less of a tolerance will allow processes to shift slightly without producing any defects. The goal is to improve your process in order to use the least amount of tolerance possible Reduce the opportunity to produce defects Reduce the cost of the process VIII-19

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**Potential Process Capability Index (Cp)**

Defines the width of the process distribution Cp is calculated by dividing the tolerance zone width by the width of the +/- 3 sigma distribution This Cp number (or index) tells how many times the distribution will fit into the tolerance zone A Cp of at least 1.33 is desired * * Which standard deviation do I use? VIII-25

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What it Looks Like… If a process uses 50% of a tolerance zone, the Cp value would be 2.0 If a process uses 100% of the tolerance zone, the Cp value would be 1.0 If a process uses 200% of the tolerance zone, the Cp value would be 0.5 The higher the number, the more precise the process distribution and the more potentially capable the process is of meeting the specification. VIII-25

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**Capability Ratio (CR) Process capability as a percentage of tolerance**

The inverse of the calculations for Cp Divide the width of the +/- 3 sigma distribution by the width of the tolerance zone A CR of no more than .75 is desired * * Which standard deviation do I use? VIII-25

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**Calculating CR If a processes Cp = 1.0 the CR = 100%**

neat VIII-25

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**Actual Process Capability (Cpk)**

Takes into account not only the spread of the distribution, but also the location of it as well A Cpk of at least 1.33 is desired Calculating Cpk: * * * Which standard deviation do I use? Cpk = Cp - a “Penalty” for off-center distributions! VIII-26

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What it Looks Like... If a process uses 100% of a tolerance zone, Cp = 1.0 If the distribution is not centered, the Cpk <1.0 Cpk = Cpk <1.0 VIII-26

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**What it Looks Like (cont.)**

If a process uses 1/2 of the tolerance zone, the Cpk = 2.0 If the process is not centered, the Cpk value would be <2.0 Cpk = Cpk <2.0 LSL USL Target LSL USL this stuff is so awesome VIII-26

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**PROCESS CAPABILITY “Cp”, “CR” & “Cpk”**

Low Speed Limit High Speed Limit MEAN 1s 65 70 75 * Cp = USL - LSL 6s * Cpk = MEAN - LSL 3s * 6 s Min CR = USL - LSL Cpk = USL - MEAN 3s VIII-26

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**Where Do I Improve? Control then capability 1st Shape – control chart**

Stabilize process Am I in control? 2nd Spread – Cp Reduce variation Cp>1.33? 3rd Location – Cpk Center process Cpk>1.33? Control then capability VIII-26

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**What Cp and Cpk Can Tell Us**

We can determine next steps to improve the process by comparing the Cp and Cpk numbers. For example: High Cp, high Cpk… Process is centered (accurate) and capable (precise). No improvements are needed. High Cp, low Cpk… Process is capable (precise) but not centered (accurate). Improvements should shift the process mean to match the target. Low Cp, low Cpk… Process is not centered (accurate), and variation must be reduced to be precise. <Write some Cp and Cpk numbers on a flip chart or on a white board to illustrate these three concepts> Remember, shifting the mean of a capable process to make a process more accurate is relatively cheap. Improving a process by identifying and removing variation is more expensive – it’s usually a Green Belt or Black Belt project. VIII-26

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**Capability Indices Exercise**

USL = 1.505 LSL = s = CR = Cp = USL = .507 LSL = .506 s = USL = 2800 PPH LSL = PPH Xbar = 2750 PPH s = 12.5PPH Cpk = USL = 750 Mhz LSL = 735 Mhz Xbar = 740 Mhz s = 1.333Mhz USL = 1.503 Xbar = 1.501 USL = .251 LSL = .250 Xbar = .250 s = VIII-26

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