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: اقتباس از Introduction to Statistical Quality Control, 5th edition
Douglas C. Montgomery
دکتر محمد صالح اولیاء دانشکده مهندسی صنایع دانشگاه یزد
کنترل کیفیت آماری
تحلیل قابلیت فرایند و ابزار 7
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 3
فهرست مطالب: تحلیل قابلیت فرایند با استفاده از
هیستوگرام و ترسیم نرمال نمودارهای کتنرل طراحی آزمایشها
نسبتهای قابلیت فرایند تحلیل قابلیت فرایند ابزارهای اندازه گیری
تعیین حدود فنی
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 4
Process Capability
Natural tolerance limits are defined as follows:
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 5
Uses of process capability data:
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 6
Process may have good potential capability
Reasons for Poor Process Capability
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Data collection steps:
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 8
Example 7-1, Glass Container Data
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 9
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 10
Probability PlottingMean and standard deviation could be estimated from the
plot
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 11
• The distribution may not be normal; other types of probability plots can be useful in determining the appropriate distribution. See Chapter 2, also Figure 7-6.
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Practical interpretation – relationship of PCR to the proportion of the tolerance interval used by the process:
For the hard bake process:
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 15
One-Sided PCR
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 16
Interpretation of the PCR
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 17
• Violation of these assumptions can lead to big trouble in using the data in Table 7-2.
Assumptions for Interpretation of Numbers in Table 7-2
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• Cp does not take process centering into account
• It is a measure of potential capability, not actual capability
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 20
A Measure of ActualCapability
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 21
Normality and Process Capability Ratios
The assumption of normality is critical to the usual interpretation of these ratios (such as Table 7-2) For non-normal data, options are
1. Transform non-normal data to normal2. Extend the usual definitions of PCRs to handle non-
normal data3. Modify the definitions of PCRs for general families of
distributions
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Other Types of Process Capability Ratios (Section 7-3.5)
First generationSecond generationThird generation Lots of research has been done to develop ratios that overcome some of the problems with the basic onesNot much evidence that these ratios are used to any significant extent in practice
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 23
• Confidence intervals are an important way to express the information in a PCR
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 24
CI is wide because the
sample size is small
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 25
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 26
CI is wide because the
sample size is small
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 27
Recommended for use when the process is not in control.
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• Specifications not needed to estimate parameters and establish stability
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 30
• Since LSL = 200
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 31
• Use DOX to isolate sources of variability
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Estimating the Variance Components
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 38
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 39
The gauge is not capable by this criterion
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 40
Discrimination Ratio
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 41
We have focused only on precision
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 42
Gauge R&R Studies
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 43
• Gauge R&R studies are usually conducted with a factorial experiment
Variance Components
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 44
• This is a two-factor factorial experiment
• ANOVA methods are used to conduct the R&R analysis
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• Negative estimates of a variance component would lead to filling a reduced model, such as, for example:
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For this Example
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Other Topics in Gauge R&R Studies
Section 7-6.3 provides a description of methods to obtain confidence intervals on the variance components and measures of gauge R&R
Section 7-6.4 presents a new measure of gauge capability, the probabilities of misclassification of parts
Rejecting good units (producer’s risk)Passing bad units (consumer’s risk)Methods for calculating these two probabilities are given
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Linear Combinations
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Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 61
For the normal distribution with unknown mean and variance:
• Difference between tolerance limits and confidence limits
• Nonparametric tolerance limits can also be calculated
Introduction to Statistical Quality Control, 5th Edition by Douglas C. Montgomery. 2005, WileyDr. Owlia- Yazd University 62
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