CN105676817B - The statistical process control method of different size sample average-standard deviation control figure - Google Patents
The statistical process control method of different size sample average-standard deviation control figure Download PDFInfo
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- CN105676817B CN105676817B CN201610023611.7A CN201610023611A CN105676817B CN 105676817 B CN105676817 B CN 105676817B CN 201610023611 A CN201610023611 A CN 201610023611A CN 105676817 B CN105676817 B CN 105676817B
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- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
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- Y02P—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN THE PRODUCTION OR PROCESSING OF GOODS
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- Y02P90/02—Total factory control, e.g. smart factories, flexible manufacturing systems [FMS] or integrated manufacturing systems [IMS]
Abstract
The invention discloses a kind of statistical process control method of different size sample average standard deviation control figure, mainly solve the problems, such as to implement statistical Process Control when existing control figure can not be to sample size difference.Implementation step is：1, product sample is obtained；2, the mean value and standard deviation of every group of sample is calculated；3, Parent Mean and standard deviation are obtained；4, two respective characteristic values of control figure in mean value standard deviation control figure are calculated, two respective control lines of control figure in mean value standard deviation control figure are obtained；5, according to the method for drafting of Shewhart control chart, characteristic value and control line are depicted as corresponding control figure；6 judge the control figure of step 5 using deterministic process exception criterion, show whether production process is in the result of slave mode.The present invention is applied widely, and the mean value and standard deviation calculation precision of parent are high, can be used for the identical or different statistical Process Control of sample size.
Description
Technical field
The invention belongs to quality of production control field, more particularly to it is big to can be used for sample for a kind of statistical process control method
Whether monitoring production status is in the statistical Process Control of slave mode when small different.
Background technology
" statistical Process Control " is a kind of current most popular and most effective quality improvement method.Statistical process control technology
It refers mainly to monitor each stage of product in process of production, i.e. process with the Process Control Theory i.e. control figure of Xiu Hate
Mass property analyze the trend of mass property according to the point distribution situation in control figure, take preventive measures, it is ensured that production
Process is in state in cont rol, to achieve the purpose that improvement and ensure quality.But it is using the premise of Charts
It is required that each batch sample data acquired in production process obeys independent and obeys the same normal distribution, i.e., usually said is only
It is vertical to divide with normal state, IIND conditions.In order to calculate control limit, it is desirable that mean value and the standard deviation of process are it is known that or can be by acquiring
Data be calculated.But the data based on acquisition calculate control and prescribe a time limit, and in order to ensure confidence level, at least need 20 to 25 batches
Sample data, and it is identical to require every batch of sample data size to need.
However, in producing in practice, there are following two situations：1. batch products amount difference is larger；2. batch products
Measure the product volume very little of of different sizes and each batch.It is for the traditional way of the first situation：Fixed sampling sample is big
It is small, but it the shortcomings that be actual conditions that sampling samples cannot really reflect each batch of product.For the second situation tradition
Way be：It is sampled by product volume minimum in all batches, but due to product volume very little, the difference of sample drawn can cause
As a result have big difference, and when the batch products amount smaller of subsequent production, the product volume of most emerging minimum need to be pressed again
It is sampled.It is etc. to be done than sampling for the second situation is most ideal to be directed to the optimal methods of sampling of the first situation in fact
Method is all products as sample.But the situation different there have been sample size in this way.When sample size difference, tradition control
The method of drawing is no longer applicable in, and can not be established control figure and be carried out statistical Process Control.
Invention content
It is an object of the invention to the deficiencies for existing Charts, propose a kind of based on different size sample standard deviation
The statistical process control method of value-standard deviation control figure, to realize, every batch of product sample drawn is of different sizes in actual production
When statistical Process Control.
The technical proposal of the invention is realized in this way：
One, technical principles
The realization of statistical Process Control SPC refer to after often having produced a batch to identical product will to this batch of product into
Row sampling, obtains sample data；Mathematical Statistics Analysis is carried out to sample data again, finds the sign that system sexual factor occurs in time
Million, and take measures to eliminate its influence, so that process is maintained the slave mode only influenced by random factor, reaches quality improvement
Purpose.
According to the unbiasedness, validity and congruence of estimator, calculate in the case of different sample sizes mean value and
Then the estimator of standard deviation converts the mean value of every batch of sample and standard deviation to the number of results for obeying standardized normal distribution
According to." mean value-standard deviation " control figure finally is drawn according to the method for drafting of Shewhart control chart, to complete to sample size
Asynchronous statistical Process Control
Two, implementations
According to principles above, realization step of the invention includes as follows：
(1) collecting sample：
After identical product is in the completion processing of corresponding process, according to enterprise's standard for manual sampling, k lot sample sheets are acquired；Note i-th batch
Size is ni, i-th batch of j-th of sample is xij, wherein i=1,2 ..., k, j=1,2 ... ni, k >=25, ni≥2；
(2) according to the sample of every batch of, the mean value and standard deviation of every batch of sample are obtained, wherein i-th batch of mean valueAnd mark
Quasi- deviation siFor:
(3) it according to every batch of size, mean value and standard deviation, obtains Parent Mean estimator μ and standard deviation is estimated
Evaluation σ：
(4) two respective characteristic values of control figure in " mean value-standard deviation " control figure are obtained：
4b) according to i-th crowd of standard deviation si, Parent Mean estimator μ and standard deviation estimation values sigma, obtain standard deviation
The characteristic value of poor control figure：
(5) two respective control lines of control figure in " mean value-standard deviation " control figure are obtained：
5a) according to the characteristic value μ of mean chartdiThe characteristic of standardized normal distribution is obeyed, ' 3sigma ' principle is utilized, obtains
To the center line CL of mean chart1, upper control line UCL1With lower control line LCL1：
CL1=0
UCL1=3；
LCL1=-3
5b) according to the characteristic value s of standard deviation control figurediApproximation obeys the characteristic of standardized normal distribution, utilizes
‘3sigma’
Principle obtains the center line CL of standard deviation control figure2, upper control line UCL2With lower control line LCL2：
CL2=0
UCL2=3；
LCL2=-3
(6) according to the method for drafting of Shewhart control chart, the result that step (4a) and step (5a) obtain is plotted to
It is worth in control figure, the result that step (4b) and step (5b) obtain is plotted in standard deviation control figure；
(7) two control figures that step (6) obtains are judged using deterministic process exception criterion：If two controls
Figure does not occur exception, then illustrates that production process is controlled, continue to produce；There are one such as two control figures or two controls
There is exception in drawing, then illustrates that production process is out of control, then needs to stop producing, search reason out of control and take appropriate measures.
The invention has the advantages that：
1. applied widely
The present invention is applicable not only to the different statistical Process Control of sample size, and is suitable for the identical mistake of sample size
Process control；Suitable for the various methods of samplings, it might even be possible to using entire block as sample.
2. the calculating of Parent Mean and standard deviation is very accurate
Estimation of Mean value and standard deviation estimated value in the present invention, meet the unbiasedness, validity and Strong consistent of estimator
Property, thus Estimation of Mean value and standard deviation estimated value are very accurate.
Description of the drawings
The implementation flow chart of Fig. 1 present invention；
Fig. 2 is the standard-standard deviation control figure obtained in different sample sizes in the present invention.
Specific implementation mode
Below in conjunction with the accompanying drawings, by taking certain company produces 5 Ohmic resistances as an example, the present invention will be further described.
Referring to Fig.1, steps are as follows for realization of the invention：
Step 1：Collecting sample.
A collection of product 1a) is often machined, carries out etc., than sampling, carrying out the sample of extraction using 1% sampling proportion
Sample data is obtained after measurement；
25 lot sample notebook datas 1b) are obtained after continuous acquisition 25 times, as shown in table 1, remember that i-th batch of size is ni, i-th
J-th of the sample criticized is xij, wherein i=1,2 ..., 25, j=1,2 ... ni。
1 resistance sample data of table
Step 2：The mean value X that following formula calculates i-th crowd is utilized according to the data of table 1iWith standard deviation si:
Result of calculation is as shown in table 2：
The mean value and standard deviation of 2 sample of table
Step 3：According to the data of table 2, the mean μ and standard deviation of parent are calculated using following formula.
Parent Mean μ=4.9936 and standard deviation=0.0952 is calculated.
Step 4：Obtain two respective characteristic values of control figure in mean value-standard deviation control figure.
According to the data of table 2, Parent Mean μ and standard deviation, the characteristic value μ of mean chart is calculated using following formuladiWith
The characteristic value s of standard deviation control figuredi：
Result of calculation is as shown in table 3：
3 mean values of the table-corresponding characteristic value of standard deviation control figure
| Batch | The characteristic value μ of mean chartdi | The characteristic value s of standard deviation control figuredi |
| 1 | -0.7114 | 1.6771 |
| 2 | -1.2111 | 0.5927 |
| 3 | -0.2317 | -0.7180 |
| 4 | -0.9121 | 0.0399 |
| 5 | 0.3880 | -1.1752 |
| 6 | 1.0656 | -0.8881 |
| 7 | 1.1377 | -0.3502 |
| 8 | -0.4273 | 1.9672 |
| 9 | 1.3038 | -0.4499 |
| 10 | -1.8064 | -0.5895 |
| 11 | -0.8895 | 0.6280 |
| 12 | -0.7646 | -0.7585 |
| 13 | 1.0497 | 0.9396 |
| 14 | 0.9416 | 0.1769 |
| 15 | -0.7207 | -0.6359 |
| 16 | -0.1863 | 0.8807 |
| 17 | 1.4223 | -0.6064 |
| 18 | -0.0265 | 0.9976 |
| 19 | 0.4748 | 0.3241 |
| 20 | -0.4939 | 0.0286 |
| 21 | -0.8171 | 0.7040 |
| 22 | 0.6588 | -0.7315 |
| 23 | 0.1991 | -1.0380 |
| 24 | 0.5948 | -0.1632 |
| 25 | -1.2138 | -0.8722 |
(5) two respective control lines of control figure in mean value-standard deviation control figure are obtained：
5a) according to the characteristic value μ of mean chartdiThe characteristic of standardized normal distribution is obeyed, ' 3sigma ' principle is utilized, obtains
To the center line CL of mean chart1, upper control line UCL1With lower control line LCL1：
CL1=0
UCL1=3；
LCL1=-3
5b) according to the characteristic value s of standard deviation control figurediApproximation obeys the characteristic of standardized normal distribution, utilizes
' 3sigma ' principle obtains the center line CL of standard deviation control figure2, upper control line UCL2With lower control line LCL2：
CL2=0
UCL2=3；
LCL2=-3
' 3sigma ' principle is a Statistics, for the control line in counting statistics control figure.Upper control line
Be characterized value mean value add 3 times characteristic value standard deviation, the mean value that lower control limit is characterized value subtracts 3 times of characteristic value
Standard deviation.
Step 6：According to the method for drafting of Shewhart control chart, the quasi- deviation control figure of mean value-is drawn.
6a) create plane right-angle coordinate A, step 5a drawn out in A) in obtained center line CL1, upper control line
UCL1With lower control line LCL1, then in upper control line UCL1With center line CL1Between draw two dotted lines, and by upper control line UCL1
With center line CL1Between apart from trisection；Then in lower control line LCL1With center line CL1Between, two solid lines are drawn, and
By lower control line LCL1With middle control line CL1The distance between trisection；
6b) by step 4a) obtained characteristic value is indicated in plane right-angle coordinate A, lot sequence is then pressed by data
Point is connected with broken line, has thus obtained mean chart；
6c) create plane right-angle coordinate B, step 5b drawn out in B) in obtained center line CL2, upper control line
UCL2With lower control line LCL2, then in upper control line UCL2With center line CL2Between, two dotted lines are drawn, and by upper control line
UCL2With center line CL2The distance between trisection；In lower control line LCL2With center line CL2Between, two solid lines are drawn, it will
Lower control line LCL2With middle control line CL2The distance between trisection；
6d) by step 4b) obtained characteristic value is indicated in plane right-angle coordinate B, lot sequence is then pressed by data
Point is connected with broken line, has thus obtained standard deviation control figure；
Finally obtained mean value-standard deviation control figure is as shown in Fig. 2, wherein figure (2a) is mean chart, figure
(2b) is standard deviation control figure.
Step 7：The mean value obtained to step (6) using deterministic process exception criterion-standard deviation control figure judges.
Whether deterministic process exception criterion is to be fallen in upper and lower control line according to data point and random alignment is judged：
If data point is fallen in upper and lower control line, and data point is random alignment, then control figure is normal；
If data point falls outside upper and lower control line or falls on upper and lower control line just or data point non-random array,
Then control figure is abnormal；
If two control figures do not occur exception, illustrates that production process is controlled, continue to produce；
If there are one two control figures or exception occur in two control figures, illustrate that production process is out of control, then needs to stop giving birth to
Production, searches reason out of control and takes appropriate measures.
From figure 2 it can be seen that the data point of mean chart and standard deviation control figure all falls within upper and lower control line
It is interior, and data point is random alignment, so control figure is normal, illustrates that production process is controlled, can proceed with production.
Claims (3)
1. a kind of statistical process control method of different size sample average-standard deviation control figure, which is characterized in that including with
Lower step：
(1) collecting sample：
After identical product is in the completion processing of corresponding process, according to enterprise's standard for manual sampling, k lot sample sheets are acquired；Remember the i-th lot sample sheet
Size be ni, i-th batch of j-th of sample is xij, wherein i=1,2 ..., k, j=1,2 ... ni, k >=25, ni≥2；
(2) according to the sample of every batch of, the mean value and standard deviation of every batch of sample are obtained, wherein i-th batch of mean valueAnd standard deviation
Poor siFor:
(3) according to every batch of size, mean value and standard deviation, Parent Mean estimator μ and standard deviation estimation values sigma are obtained：
Wherein C2(ni)、C3(ni) it is intermediate variable, it is about sample size niFunction, calculation formula is：Γ(ni/ 2) and Γ ((ni- 1) it is/2) about sample
Size niGamma function；
(4) two respective characteristic values of control figure in mean value-standard deviation control figure are obtained：
4a) according to i-th batch of mean valueParent Mean estimator μ and standard deviation estimation values sigma, obtain the spy of mean chart
Value indicative：
4b) according to i-th crowd of standard deviation si, Parent Mean estimator μ and standard deviation estimation values sigma, obtain standard deviation control
The characteristic value of figure：
(5) two respective control lines of control figure in mean value-standard deviation control figure are obtained：
5a) according to the characteristic value μ of mean chartdiThe characteristic of standardized normal distribution is obeyed, ' 3sigma ' principle is utilized, is obtained
It is worth the center line CL of control figure1, upper control line UCL1With lower control line LCL1：
5b) according to the characteristic value s of standard deviation control figurediApproximation obeys the characteristic of standardized normal distribution, utilizes ' 3sigma ' former
Reason, obtains the center line CL of standard deviation control figure2, upper control line UCL2With lower control line LCL2：
(6) according to the method for drafting of Shewhart control chart, the result that step (4a) and step (5a) obtain is plotted to mean value control
In drawing, the result that step (4b) and step (5b) obtain is plotted in standard deviation control figure；
(7) two control figures that step (6) obtains are judged using deterministic process exception criterion：If two control figures are equal
Do not occur exception, then illustrates that production process is controlled, continue to produce；There are one such as two control figures or two control figures
There is exception, then illustrate that production process is out of control, then needs to stop producing, search reason out of control and take appropriate measures.
2. a kind of statistical Process Control side of different size sample average-standard deviation control figure according to claim 1
Method, according to the method for drafting for stopping what special control figure in the step (6), result drafting that step (4a) and step (5a) are obtained
Into mean chart, the result that step (4b) and step (5b) obtain is plotted in standard deviation control figure, by following step
It is rapid to carry out：
Step 5a 6a) is drawn out on mean chart) in obtained center line CL1, upper control line UCL1With lower control line
LCL1, then in upper control line UCL1With center line CL1Between, two dotted lines are drawn, and by upper control line UCL1With center line CL1's
Between apart from trisection；Then in lower control line LCL1With center line CL1Between, two solid lines are drawn, and by lower control line LCL1
With middle control line CL1The distance between trisection；
6b) by step 4a) obtained characteristic value is indicated on mean chart, then connects data point broken line by lot sequence
It connects；
6c) draw out step 5b in standard deviation control figure) in obtained center line CL2, upper control line UCL2With lower control line
LCL2, then in upper control line UCL2With center line CL2Between, two dotted lines are drawn, and by upper control line UCL2With center line CL2It
Between apart from trisection；In lower control line LCL2With center line CL2Between, two solid lines are drawn, by lower control line LCL2With middle control
Line CL processed2The distance between trisection；
6d) by step 4b) obtained characteristic value is indicated in standard deviation control figure, lot sequence is then pressed by data point folding
Line connects.
3. a kind of statistical Process Control side of different size sample average-standard deviation control figure according to claim 1
Method, the step (7) is middle to judge two control figures that step (6) obtains using deterministic process exception criterion, is basis
Whether data point data point is fallen falls in upper and lower control line and random alignment is judged：
If data point is fallen in upper and lower control line, and data point is random alignment, then control figure is normal；
If data point falls outside upper and lower control line or falls on upper and lower control line just or data point non-random array, control
Drawing is abnormal.
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