The purpose of the measure phase is to collect and validate measures that represent the improvement area. This includes a data collection plan, selection of measures, validation of the measurement system, and the establishment of a baseline. Data collection is discussed in the PDCA cycle; therefore, only three of these deliverables are discussed in this section for successful completion of this phase: (1) cause and effect matrix, (2) measurement system analysis, and (3) performance baseline. [83]
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5.2.1 Cause and effect matrix
The cause and effect matrix uses the CTQ characteristics, which was identified in the previous step, to determine the key input measures that influence the process. This information is crucial to ensure that the team focus on the significant improvement opportunities that affect the process as a whole. Once these are identified the team can establish a performance baseline to track and control improvement activities. [12]
The cause and effect matrix is often required when the process has multiple CTQ characteristics. All the significant input characteristics can then be identified though their correlation with weighted CTQ characteristics. This process is discusses below.
Step 1: List the CTQ characteristics at the top of the matrix. Use a scale from 1 to 10 to assign a weight for each characteristic in terms of their relative importance to the final customer. Let 1 indicates the least critical and 10 the most critical characteristics.
Chapter 5 Six sigma thinking Industrial Engineering Page 107
Process Name: Bread production line
CTQ characteristics
Cycle Time Cost Sigma Level
Weight 8 10 6
Input
characteristics Correlation of input to CTQ characteristics Total
Vendor 3 3 1 60
Flour Grade 0 9 9 144
Oven Temperature 9 3 9 156
SCALE: 0 = None 1 = Weak 3 = Moderate 9 Strong Figure 5.7: Cause and effect matrix
Step 2: List in the first column all input characteristics that may affect any of the CTQ characteristics. Rate the degree to which the input characteristics are correlated to each CTQ characteristic. Use a scale where 0 indicates no correlation, 3 indicates weak correlation, 6 indicates moderate correlation, and 9 indicates strong correlation.
Step 3: Multiply each correlation value with the weight and sum across each row to determine the relative importance of each input characteristic. The inputs with the highest total scores must be measured together with the CTQ characteristics. These significant inputs and CTQ characteristics are the critical process characteristics.
5.2.2 Measurement system analysis
Measurement system analysis (MSA) is crucial to ensure that data driven decisions are based on valid data, even though this is often neglected by inexperienced six sigma practitioners because they do not realise that the measurement system is also subjected to variation as any other process; MSA also requires statistical knowledge that can discourage novice practitioners. However, it is important to understand the philosophy behind MSA because of its relevance to various project applications. [88]
The measurement system is a process with specific inputs that are transformed to produce an output in the form of a measurement. It is therefore normal to assume that the measurement system can produce some variation that influences the validity of measurements. The source of this variation can be traced back to various system factors; these can include stability, bias, linearity, discrimination, and precision. [89]
Chapter 5 Six sigma thinking Industrial Engineering Page 108 Stability is the capability of a measure to maintain a constant distribution over time with a given measurement approach. Measurement data can be plotted on a time based chart to visually represent any deviation. The difference between the mean values of the measurement series are used to calculate the stability. Deviation can result from various environmental effects and changes in the measurement system. .
Bias is the difference between the average of the measurement data and the actual reference value. The reference value is an industry based standard that provides an undisputed target for a specific measure. Several measurements must be made to make a valid conclusion about the bias. The objective is to reach the reference value.
Linearity describes how reliable the measurement approach is over a diverse range of measurement types. A particular approach may not be suitable for measures with different characteristics because tool calibration is based on the assumption that the same conditions prevail. The change in deviation from the mean values calculated from the actual measures of the measurement range is used to determine linearity.
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Discrimination is the capability of the measurement system to adapt to small changes in a measurement characteristic. The problem is that even these small changes can affect the credibility of the measurement system. Therefore, if the system is not able to adapt appropriately to these changes, errors in the process will be difficult to find.
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Precision is crucial to MSA because of its high contribution to the standard deviation of the measurement system. It is therefore common to assign considerable statistical effort to determine its significance in terms of system repeatability and reproducibility.
Repeatability variation is a result of the gauge itself. The problem occurs when an operator measures a characteristic multiple times with the same gauge and obtains different results in fixed conditions. This variation can be reduced or eliminated with gauge modifications; otherwise a new gauge must be used for future measurements.
Reproducibility variation is a result of differences between operators and inconsistent measurement procedures. The problem occurs when multiple operators measure a characteristic multiple times with the same gauge and obtain different results. One solution is to train operators to use operational definitions and standardised methods.
Chapter 5 Six sigma thinking Industrial Engineering Page 109 Repeatability and reproducibility studies are most reliable when conducted as blind studies where a sample of representative characteristics is measured two or three times by two or three independent operators; then analyse the data to validate the consistency and accuracy of the measured outcomes. Computer software is often used to deal with this complicated statistical analysis and quantify the variation. [12]
5.2.3 Performance baseline
The final deliverable for the measure phase is to create a performance baseline for the critical process characteristics as soon as the measurement system is verified as consistent and accurate; a baseline represents the initial performance of a process characteristic and also serves as a reference point to track improvement efforts. [90] .
There are several measures that can be used as a baseline for the critical process characteristics. These measures include defect rate, process yield, and capability indices. Capability indices use relatively complex measures based on the assumption of normality and is limited to stable processes. It is therefore not discussed in this report because it may lead to a great deal of confusion for novice practitioners. [15]
Measure 1: Process defect rate
A unit (product or service) that does not perform within specification is considered a defective. This means that it produced a nonconformance, known as a defect, on one of its fundamental characteristics; each of these characteristics provides a defect opportunity. Defect rate is most often measured in terms of defects per unit (DPU), defects per opportunity (DPO), and defects per million opportunities (DPMO). [12]
Defects per unit: Defects per million opportunities:
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Total number of defects = Defects per opportunity x 1 000 000 Number of units Sigma Level DPMO (shift = 1.5)
6.0 3.40
5.0 233
Defects per opportunity: 4.0 6 210
=
Total number of defects 3.0 66 807
Total number of defect opportunities 2.0 308 538
1.0 691 462
Chapter 5 Six sigma thinking Industrial Engineering Page 110 DPU refers to the average number of defects per unit. However, this value does not provide a fair comparison between units with different levels of complexity because the opportunity for defects is larger in complex units. It is therefore recommended to determine the defects per opportunity to create a comparable performance baseline.
DPO refers to the total number of defects in proportion to the total number of defect opportunities. This allows the measure to consider the complexity of a unit. However, the value of DPO can become very small when calculations are done on complex units with thousands of defect opportunities. Therefore, rather multiply this value with one million and use DPMO as the baseline. Notice that DPMO is also the benchmark rate that is used to describe the sigma level of a process as shown in Figure 5.8. [15]
Measure 2: Process yield
The complementary measure of defect rate is process yield, which is defined as the proportion of units that perform within specification. Measures derived from yield are also appropriate to describe process capability. Three types of yield can be used to create a baseline: (1) final yield, (2) first pass yield, and (3) rolled throughput yield. [91]
Final yield is the ratio of the total number of defect free units that a process delivers over the number of units that entered the system. The problem is that this traditional method to calculate yield does not consider the resources used for rework, which cause hidden factories to originate. A hidden factory is an extension of the process that is caused when the process does not run within specification limits the first time.
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Chapter 5 Six sigma thinking Industrial Engineering Page 111 First pass yield (FPY) is a unit based measure that indicates the percentage of defect free units that passed through a process the first time without rework. The problem with FPY is its complete dependence on the distribution of defects. For example, suppose 100 units enter a process and 10 defects are produced. Now consider a scenario where all 10 defects occurred in one unit and another scenario where the 10 defects occurred in 10 different units, which give a respective FPY of 99% and 90%. .
Throughput yield is a defect based measure that differs from FPY in two fundamental criteria. First, it refers to the number of defects produced, rather than the number of defective units. Second, it is used to predict future yield based on the assumption that defects are produced according to a Poisson distribution. These criteria ensure that throughput yield gives the same value regardless of where the defects occurred; so it is a more consistent measure, than unit based yield, of the process as a whole.