CN101770233A - Statistical control method based on measurement assurance plan - Google Patents

Abstract

The invention discloses a statistical control method based on a measurement assurance plan, which comprises the following steps: firstly, calculating the average value x of each sub group and the average value of the average values of m sub groups, which is the same as a Shewhart control chart; and then, calculating the intergroup standard difference sb according to the average values of m sub groups, and setting a control boundary according to sb, which is different from the Shewhart control chart. The corresponding center line CL, the upper control limitation UCL and the lower control imitation LCL are respectively shown as the accompanying drawing. Thereby, the control boundary does not represent the short-period mobility of the measurement, but also can reflect the long-term mobility of the measurement, so the plan can carry out the statistical control on the influence of the measurement process by the effect of an uncontrolled system and the influence of the measurement process by the uncontrolled random effect.

Description

Statistical control method based on measurement assurance plan

Technical field

The present invention relates to a kind of statistical control method of measuring process, particularly relate to a kind of statistics control, also can be adapted to statistics control production run to measuring equipment and measurement standard based on measurement assurance plan.

Background technology

Control chart is a kind of graphic recording that whether measuring process is in the statistics state of a control.It can judge and provide the information that whether has abnormal factors in the measuring process, so that find out the reason that generation is unusual, and take measures to make measuring process to be in the statistics state of a control again.

Control chart is divided into X-control chart and standard deviation control chart or range chart, and is unusual if X-control chart occurs, and shows that then measuring process is subjected to the influence of not controlled systemic effect; And unusual if standard deviation control chart or range chart occur, show that then measuring process is subjected to the influence of not controlled stochastic effects.Standard deviation control chart and range chart can be chosen any one kind of them, and generally speaking, measure selection of times and can adopt range chart more after a little while in group, otherwise can adopt the standard deviation control chart.

The at present domestic foundation that measuring process is added up control is GB/T 4091-2001 " shewhart control chart ", its adopting by equation international standard ISO8258:1991 " Shewhart control chart " (Shewhartcontrol charts) and revise for 1993 No. 1 single.In JJF1033-2008 " measurement standard examination standard ", whether the method that has also proposed the employing control chart is in the statistics state of a control to measuring process is controlled, and in appendix C, describe Shewhart control chart in detail, illustrate simultaneously that for the higher and important measurement standard of accuracy suggestion adopts control chart that its measuring process is carried out continuous and long-term statistics control as far as possible.

The foundation of Shewhart control chart at first is that obtaining of its preliminary date is under repeated condition, and the check standard that chooses is done n independent duplicate measurements, and this n time measurement result is called a son group.Under the measuring condition of measurement verification regulations or technical manual regulation, repeat top measuring process by certain time interval, measure m son group altogether.The measurements of adjacent two the son groups time enough of should being separated by.

Then, the counting statistics controlled quentity controlled variable: when adopting mean value-standard deviation control chart (x-s figure), the statistics controlled quentity controlled variable that should calculate is: the mean value x of each son group, the standard deviation s of each son group, the mean value of each sub-cell mean

Mean value s with each son group standard deviation.

When adopting mean value-range chart (x-R figure), the statistics controlled quentity controlled variable that should calculate is: the mean value x of each son group, the extreme difference R of each son group, the mean value of each sub-cell mean

Mean value R with each son group extreme difference.

Calculation control boundary again: calculate the center line (CL) of each control chart, upper control limit (UCL) and lower control limit (LCL).For different control charts, the computing formula of its control limit is different.

Wherein as follows for mean value-standard deviation control chart (x-s figure) computation process:

X-control chart, x figure.Its centre line C L, upper control limit UCL and lower control limit LCL are respectively:

$\mathrm{CL}=\stackrel{\‾}{\stackrel{\‾}{x}}$

$\mathrm{UCL}=\stackrel{\‾}{\stackrel{\‾}{x}}+A_3\stackrel{\‾}{s}$

$\mathrm{LCL}=\stackrel{\‾}{\stackrel{\‾}{x}}-A_3\stackrel{\‾}{s}$

And as follows for mean value-range chart (x-R figure) computation process:

X-control chart, x figure.Its centre line C L, upper control limit UCL and lower control limit LCL are respectively:

$\mathrm{CL}=\stackrel{\‾}{\stackrel{\‾}{x}}$

$\mathrm{UCL}=\stackrel{\‾}{\stackrel{\‾}{x}}+A_2\stackrel{\‾}{R}$

$\mathrm{LCL}=\stackrel{\‾}{\stackrel{\‾}{x}}-A_2\stackrel{\‾}{R}$

Each coefficient A in the calculating ₂And A ₃Value and sample size n (the measurement number of times that each son group is comprised) relevant, its value sees the table 15-1 of the practical evaluation of uncertainty in measurement (third edition) [M] that China Measuring Press published in 2009 or the table C-1 of JJF1033-2008 measurement standard examination standard [S].

The inventor thinks that X-control chart upper control limit UCL in the peaceful mean-range chart of mean value-standard deviation control chart (x-s figure) (x-R figure) and the regulation of lower control limit LCL are problematic, is that example illustrates with mean value-standard deviation control chart here.

What the mean value s of each son group standard deviation characterized is under repeated condition, and the check standard that chooses is done n independent duplicate measurements, the compromise of gained result's dispersiveness, and it has reflected the measurement short-period fluctuation, is the result that influences of stochastic effects, coefficient A ₃Value be approximately

So A ₃S also is approximately the standard deviation s of mean value x of 3 times child group _xIt is a standard deviation under the repeated condition, this standard deviation do not comprise check standard and by check standard in time (longer) change and this undulatory property of drift of producing, and environmental baseline also may be different and the undulatory property that produces in the long period.And X-control chart is controlled is the undulatory property of value under the repdocutbility condition (the mean value x of son group), so its control limit should be determined by the dispersiveness of the mean value x of son group under the repdocutbility condition, just standard deviation s between the group of being organized by m son _oDetermine that it has reflected the long-term mobility of value.In a word, we can not control the influence of a systemic effect with the dispersiveness of a stochastic effects influence.For example its short-period fluctuation of certain controlling object is fine, and promptly repeated standard deviation is very little, and the control limit of She Zhiing will be very narrow in view of the above, if the long-term undulatory property big (but still belonging to normal) of its value, then measurement point will be easy to exceed the control limit.Moreover for same controlling object, when the group group was measured frequency n and trended towards enough greatly, s trended towards a reliable constant, and A ₃Trend towards zero, thereby make A ₃S also trends towards zero, narrow down (trending towards zero) limit in this control that X-control chart just occurs, and each sub-cell mean is the measurement result under the repdocutbility condition, its dispersiveness is an outwardness, also be conspicuous, its value can not diminish because the child group measures the increase of frequency n, and this just may make one a little group mean value x exceed the control limit.

Summary of the invention

Therefore, the present invention is in order to overcome the defective that existing statistical control method control limit can not reflect the long-term mobility of value, a kind of statistical control method based on measurement assurance plan has been proposed, so that measuring process is subjected to the influence of not controlled systemic effect, and control is added up in the influence that is subjected to not controlled stochastic effects.

The present invention is by the following technical solutions:

This invention is based on the measurement assurance plan statistical control method, and it may further comprise the steps:

A) under repeated condition, the check standard that chooses is done n independent duplicate measurements;

B) under the measuring condition of regulation, press preset time repeating step measuring process a) at interval, obtain m son group altogether;

C) m son group data that obtain according to step b), statistics controlled quentity controlled variable in obtaining organizing according to following formula respectively: mean value x, group internal standard deviation s or extreme difference R;

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i---\left(1\right)$

$s=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2}---\left(2\right)$

R＝x _max-x _min (3)

In the formula: n---measure number of times;

x _i---the i time measured value;

x _Max---greatest measurement;

x _Min---minimum measured value;

D) mean value x, group internal standard deviation s or extreme difference R in the group that obtains according to step c) obtain the statistics controlled quentity controlled variable of m group data: mean value between group according to following formula And standard error of the mean s between group _B, the standard deviation s of standard deviation between the mean value s of standard deviation and group between group _b, the standard deviation s of extreme difference between the mean value R of extreme difference and group between group _R

$\stackrel{\‾}{\stackrel{\‾}{x}}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\‾}{x}}_j---\left(4\right)$

$s_B=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{({\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}})}^2}---\left(5\right)$

$\stackrel{\‾}{s}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{s}_j---\left(6\right)$

$s_b=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(s_j-\stackrel{\‾}{s})}^2}---\left(7\right)$

$\stackrel{\‾}{R}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{R}_j---\left(8\right)$

$s_R=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(R_j-\stackrel{\‾}{R})}^2}---\left(9\right)$

In the formula: m---measurement group number;

x _j---mean value in the group of j group;

s _j---the group internal standard deviation of j group;

R _j---the extreme difference of j group;

E) data detection is to dispose abnormal data;

F) final data through the step e) check is recomputated according to step d), get statistics controlled quentity controlled variable finally;

G) set up control chart according to the resulting statistics controlled quentity controlled variable of step f):

1) X-control chart in the group: with mean value between group

Be center line (CL), with

Be upper control limit (UCL), with

Be lower control limit (LCL), mean value in organizing is added up control; The statistics controlled quentity controlled variable that calculates is marked on figure, connect adjacent 2 points with straight line successively;

2) group internal standard deviation control figure: the mean value s with standard deviation between group is center line (CL), with s+3s _bFor upper control limit (UCL), with s-3s _bBe lower control limit (LCL), group internal standard deviation is added up control;

3) range chart in the group: the mean value R with extreme difference between group is center line (CL), with R+3s _RFor upper control limit (UCL), with R-3s _RBe lower control limit (LCL), extreme difference in organizing is added up control.

Statistical control method according to technical solution of the present invention at first calculates the mean value x of each son group and the mean value of m sub-cell mean

This is identical with Shewhart control chart; Next according to standard deviation s between the mean value calculation group of m son group _b, according to s _bControl limit is set, and these are different with Shewhart control chart.Its pairing centre line C L, upper control limit UCL and lower control limit LCL are respectively: $\mathrm{CL}=\stackrel{\‾}{\stackrel{\‾}{x}},$ $\mathrm{UCL}=\stackrel{\‾}{\stackrel{\‾}{x}}+3s_b,$ $\mathrm{LCL}=\stackrel{\‾}{\stackrel{\‾}{x}}-3s_b,$ $s_b=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{({\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}})}^2},$ Thereby, said control limit has not only been represented the short-period fluctuation of measuring, long-term mobility that also can reflected measurement makes this scheme can be subjected to the influence of not controlled systemic effect to measuring process, and control is added up in the influence that is subjected to not controlled stochastic effects.

Above-mentioned statistical control method after described step g) control chart is set up, tries again at interval to verify every preset time and measures, and obtain the statistics controlled quentity controlled variable according to formula (1), (2), (3), marks in corresponding control chart, connects consecutive point with straight line successively.

Above-mentioned statistical control method, the range of control of the control chart that described step g) is obtained is divided into 6 districts, is labeled as A, B, C, C, B, A from top to bottom respectively, and judges the unusual of statistics controlled quentity controlled variable based on this:

Pattern one: if measurement point appears at outside the A district, then measuring process is unusual, and if measurement point exceeds the upper bound, shows that the average of adding up controlled quentity controlled variable increases; And if measurement point exceeds lower bound, then its average reduces;

Pattern two: if continuous 9 measurement points appear at the same side of center line and form 9 chains, then measuring process occurs unusual;

Pattern three: if the trend of monotone increasing or monotone decreasing appears in continuous 6 measurement points, then measuring process is unusual;

Pattern four: arrange if alternatively up and down appears in continuous 14 measurement points, then measuring process is unusual;

Pattern five: if having appear at A district, the same side at 2 in continuous 3 measurement points, then measuring process occurs unusual;

Pattern six: if having 4 points to appear in the side B district or A district of center line in continuous 5 measurement points, then the selected statistics controlled quentity controlled variable of control chart is moved to this lateral deviation;

Pattern seven: if continuous 15 measurement points appear in the C district of center line both sides, then measuring process is unusual;

Pattern eight: if continuous 8 measurement points appear at the center line both sides and all not in C district, then measuring process occurs unusually.

Above-mentioned statistical control method, unusual if measuring process occurs, the data that inspection immediately is associated are also handled, and perhaps remeasure; If occur continuously then stopping to measure unusually, check associated data, unusual until getting rid of; If can't get rid of unusually, then the described step a) of foundation is to g) the reconstruction control chart.

Above-mentioned statistical control method, to not comprising that initial statistics control quantitative statistics controlled quentity controlled variable measuring process is got rid of the formed many group statistics controlled quentity controlled variables in back unusually and initial statistics controlled quentity controlled variable gathers, according to described step b) to d) calculate new statistics controlled quentity controlled variable, and rebulid control chart according to described step g).

Above-mentioned statistical control method, preferably, in the described step a) as when adopting the standard deviation control chart, n 〉=12 then; If when adopting range chart, n 〉=5 then.

Preferably, m 〉=20 in the described step b).

More preferably, m 〉=25 in the described step b).

Preferably, data detection comprises in the described step e):

The check of one, measured value: to the i time measured value x of every group of data _iTest, during as if employing standard deviation control chart, and satisfy n 〉=12, then adopt the Rye to reach criterion, if measured value x _jResidual error satisfy | x _i-x|＞3s then thinks x _iFor exceptional value is rejected, then do for supplement a secondary data, recomputate mean value x and group internal standard deviation s in the group, test again, exist until no abnormal value; If when adopting range chart, and satisfy n 〉=5, then adopt the Grubbs criterion, as measured value x _iResidual error satisfy | x _i(n p) * s, then thinks x to-x|＞λ _iShould reject for exceptional value, then do for supplement a secondary data, test again, exist until no abnormal value; Wherein, (n p) is and measures the frequency n function relevant with fiducial probability p λ;

Two, the check of mean value in the group: if satisfy $|{\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}}|>3s_B,$ Then should the interior mean value x of group _jOut of control, ascertain the reason, one group of data out of control weed out; Recomputate mean value between the group of remaining m-1 group data

And standard error of the mean s between group _B, test mean value x in N/R group again _jExist;

Its three, the check of group internal standard deviation: if satisfy | s _j-s|＞3s _b, then should group internal standard deviation s _jOut of control, ascertain the reason, one group of data out of control weed out, and recomputate the standard deviation s of standard deviation between the mean value s of standard deviation between the group of remaining m-1 group data and group _b, test again, until N/R group of internal standard deviation s _jExist;

Four, the check of extreme difference in the group: if satisfy | R _j-R|＞3s _R, then should the interior extreme difference R of group _jOut of control, should ascertain the reason, one group of data out of control can weed out, and recomputate the standard deviation s of extreme difference between the mean value R of extreme difference between the group of remaining m-1 group data and group _R, test extreme difference R in N/R group again _jExist.

Description of drawings

Below in conjunction with Figure of description technical scheme of the present invention is further elaborated, makes those skilled in the art better understand the present invention, wherein:

Fig. 1 is the control chart style based on the embodiment of technical solution of the present invention.

Fig. 2 is the subsequent control figure style based on the embodiment of technical solution of the present invention.

Fig. 3 appears at outside the A district for measurement point.

Fig. 4 appears at center line the same side for continuous 9 points.

Fig. 5 presents monotone increasing for continuous 6 measurement points or successively decreases.

Fig. 6 is that continuous 14 measurement point alternatively up and down are arranged.

Fig. 7 has appear in the A district, center line the same side at 2 in continuous 3 measurement points.

Fig. 8 is for having in continuous 5 measurement points in 4 B districts or A district that appear at center line the same side.

Fig. 9 appears in the C district of center line both sides for continuous 15 measurement points.

Figure 10 appears at the center line both sides and all not in the C district for continuous 8 measurement points.

Figure 11 is the X-control chart under two kinds of control limits of 0.01 Ω, two constant resistances.

Figure 12 is the standard deviation control chart under two kinds of control limits of 0.01 Ω, two constant resistances.

Figure 13 is 0.01 Ω, two constant resistance X-control charts.

Figure 14 is the second-class resistance standard deviation control of 0.01 Ω figure

Embodiment

According to technical scheme of the present invention, this embodiment is based on the measurement assurance plan statistical control method, and it may further comprise the steps:

A) under repeated condition, the check standard that chooses is done n independent duplicate measurements;

B) under the measuring condition of regulation, press preset time repeating step measuring process a) at interval, obtain m son group altogether;

Step a) and step b) are used to obtain preliminary date, and this is to set up the needed basic sampled data of control chart, requires sampling process to be in the STOCHASTIC CONTROL state.Carry out the calculating of initial data statistics amount then, just step c) and step d).

C) m son group data that obtain according to step b), statistics controlled quentity controlled variable in obtaining organizing according to following formula respectively: mean value x, group internal standard deviation s or extreme difference R;

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i---\left(1\right)$

$s=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2}---\left(2\right)$

R＝x _max-x _min (3)

In the formula: n---measure number of times;

x _i---the i time measured value;

x _Max---greatest measurement;

x _Min---minimum measured value;

D) mean value x, group internal standard deviation s or extreme difference R in the group that obtains according to step c) obtain the statistics controlled quentity controlled variable of m group data: mean value between group according to following formula

And standard error of the mean s between group _B, the standard deviation s of standard deviation between the mean value s of standard deviation and group between group _b, the standard deviation s of extreme difference between the mean value R of extreme difference and group between group _R

$\stackrel{\‾}{\stackrel{\‾}{x}}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\‾}{x}}_j---\left(4\right)$

$s_B=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{({\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}})}^2}---\left(5\right)$

$\stackrel{\‾}{s}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{s}_j---\left(6\right)$

$s_b=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(s_j-\stackrel{\‾}{s})}^2}---\left(7\right)$

$\stackrel{\‾}{R}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{R}_j---\left(8\right)$

$s_R=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(R_j-\stackrel{\‾}{R})}^2}---\left(9\right)$

In the formula: m---measurement group number;

x _j---mean value in the group of j group;

s _j---the group internal standard deviation of j group;

R _j---the extreme difference of j group;

E) data detection is to dispose abnormal data;

F) to through the final data of step e) check according to step d), recomputate the m group preliminary date that to obtain, through weeding out all unusual data of respectively organizing, to remaining data again respectively by mean value between the new group of formula (4) and (5), (6) and (7), (8) and (9) calculating

And standard error of the mean s between group _B, the standard deviation s of standard deviation between the mean value s of standard deviation and group between group _b, the standard deviation s of extreme difference between the mean value R of extreme difference and group between group _RThereby, obtain final statistics controlled quentity controlled variable, and enter next step in view of the above;

G) set up control chart according to the resulting statistics controlled quentity controlled variable of step f):

1) X-control chart in the group: with mean value between group

Be center line (CL), with

Be upper control limit (UCL), with

Be lower control limit (LCL), mean value in organizing is added up control; The statistics controlled quentity controlled variable that calculates is marked on figure, connect adjacent 2 points with straight line successively, shown in Figure of description 1;

2) group internal standard deviation control figure: the mean value s with standard deviation between group is center line (CL), with s+3s _bFor upper control limit (UCL), with s-3s _bBe lower control limit (LCL) that group internal standard deviation is added up control, and style is shown in Figure of description 1;

3) range chart in the group: the mean value R with extreme difference between group is center line (CL), with R+3s _RFor upper control limit (UCL), with R-3s _RBe lower control limit (LCL) that extreme difference in organizing is added up control, and style is shown in Figure of description 1.

After described step g) control chart is set up, try again at interval every preset time and verify to measure, and obtain the statistics controlled quentity controlled variable according to formula (1), (2), (3), in corresponding control chart, mark, connect consecutive point with straight line successively, the broken line that connects measurement point is prolonged (dotted line in the Figure of description 2) one by one, just become the control chart that can carry out daily monitoring, shown in Figure of description 2 measuring process.

Can suitably shorten or prolong the verification measuring intervals of TIME according to verify measuring the control result, for example extending to 3 months by 1 month, or by foreshortening to a week etc. in 1 month.

Because control chart adopts 3 σ principles design control limit, for simplicity, the range of control of the control chart that described step g) is obtained is divided into 6 districts, is labeled as A, B, C, C, B, A from top to bottom respectively, and judges the unusual of statistics controlled quentity controlled variable based on this:

Pattern one: with reference to Figure of description 3, among the figure " X " point show occurred unusual.Therefore the probability that measurement point appears at outside the A district only is 0.27%, and any measurement point appears at that all can be judged to measuring process outside the A district immediately unusual.And, show that the average of adding up controlled quentity controlled variable increases if measurement point exceeds the upper bound; And, show that its average reduces if measurement point exceeds lower bound;

Pattern two: shown in Figure of description 4, the phenomenon that measurement point appears at the same side of control chart center line continuously is called " chain ", calculating shows, the probability of 9 chain appearance is 0.38%, the level of significance 0.27% that most approaches to stipulate, therefore, if continuous 9 measurement points appear at the same side of center line and form 9 chains, just can declare measuring process and occur unusual; The appearance of chain shows that the average that the statistics controlled quentity controlled variable distributes moves to a lateral deviation that chain occurs;

Pattern three: shown in Figure of description 5, the arrangement of measurement point monotone increasing occurs or the state that successively decreases is called " trend " in the control chart.Calculating shows that the probability of 6 trend appearance is 0.27%, and is consistent with the level of significance of regulation.Therefore, measurement point in control chart is if the trend of monotone increasing or monotone decreasing appears in continuous 6 measurement points, and then measuring process is unusual;

Pattern four: with reference to Figure of description 6, calculating shows that the probability that continuous 14 measurement points present the alternatively up and down arrangement is 0.37%, therefore, arrange if alternatively up and down appears in continuous 14 measurement points, it is unusual then to be judged as measuring process, and this shows that measuring process is subjected to certain periodically influence of effect;

Pattern five: with reference to Figure of description 7, though the A district is also within range of control, if measurement point frequently is still unallowed among the A district.And calculating shows that it is 0.27% that two probability that appear in the center line one side A district are arranged in continuous 3 measurement points, and is consistent with the level of significance of regulation.Therefore, three kinds of situations as shown in Figure of description 7 when measurement point " X " when occurring, if having appear at A district, the same side at 2 in continuous 3 measurement points, then are judged as measuring process and occur unusually;

Pattern six: calculate and to show, have 4 to appear at the A district of center line one side or the probability in B district is 0.51% in continuous 5 measurement points, relatively approach the level of significance of stipulating.Shown in Figure of description 8, if having 4 points to appear in the side B district or A district of center line in continuous 5 measurement points, then the selected statistics controlled quentity controlled variable of control chart is moved to this lateral deviation, shows that at this moment the selected statistics controlled quentity controlled variable of this control chart moves to this lateral deviation;

Pattern seven: calculate and to show, the probability that continuous 15 measurement points appear in the C district of center line both sides is 0.33%, relatively approaches the level of significance of stipulating.Therefore, with reference to Figure of description 9, when measurement point " X " when occurring, if continuous 15 measurement points appear in the C district of center line both sides, then measuring process is unusual;

Unusual for this distribution, do not think that this is the result that measuring process is improved.The appearance of this situation often shows that control limit is wide to be caused owing to mistake in the control chart design causes.The control chart of this moment has lost the control action to measuring process, and image data is made new control chart again.

Pattern eight: shown in Figure of description 10, if continuous 8 measurement points appear at the center line both sides and all not in C district, then measuring process occurs unusually.

The situation of appearance pattern 8, the distribution that often shows this statistics controlled quentity controlled variable are the mixing of two kinds of different distributions, and the average of the average of one of them distribution and another distribution has evident difference, and two kinds of distributions alternately occur in measuring process simultaneously.

Check by above-mentioned eight kinds of patterns is decision statistic controlled quentity controlled variable unusual clearly, is convenient in time take appropriate measures.

If measuring process occurs unusual, the data that inspection immediately is associated are also handled, and perhaps remeasure; If occur continuously then stopping to measure unusually, check associated data, unusual until getting rid of; If can't get rid of unusually, then the described step a) of foundation is to g) rebuild control chart, the abnormal conditions that occur are made timely processing.

To not comprising that initial statistics control quantitative statistics controlled quentity controlled variable measuring process is got rid of the formed many group statistics controlled quentity controlled variables in back unusually and initial statistics controlled quentity controlled variable gathers, according to described step b) to d) calculate new statistics controlled quentity controlled variable, and rebulid control chart according to described step g).Thereby can obtain to have more the control chart of long-term directiveness.Here need explanation, said initial statistics controlled quentity controlled variable refers to the statistics controlled quentity controlled variable of acquisition for the first time.

The control limit of above-mentioned control chart is based on that a large amount of measurement statistics comes, and for given application purpose, can do suitable adjustment to this control limit, promptly amplifies or dwindles, thereby obtain a kind of control chart of given control limit.

Each son group should reflect statistics control law of short-term at least, therefore, in the described step a) as when adopting the standard deviation control chart, n 〉=12 then; If when adopting range chart, n 〉=5 then.

M in the described step b) 〉=20 are preferably got 25 groups in real work, though when small pin for the case group data occur ascertaining the reason unusual and disallowable the time, still can keep data more than 20 groups.In addition, the group number is many more, and the time of experience is also long more, can display with check standard with by the value undulatory property of appraisal standards fully.Certainly,, can't finish the measurement of 20 groups of above preliminary dates for the moment, also can be no less than 12 groups and just begin to set up preliminary control chart after measuring finishing if the workload of measuring is bigger.

Data detection comprises in the described step e):

The check of one, measured value: surveyed one group of data, should press the i time measured value x of following formula immediately to every group of data _iTest, during as if employing standard deviation control chart, and satisfy n 〉=12, then adopt the Rye to reach criterion (claiming the 3s criterion again), if measured value x _jResidual error satisfy | x _i-x|＞3s then thinks x _iFor exceptional value is rejected, then do for supplement a secondary data, recomputate mean value x and group internal standard deviation s in the group, test again, exist until no abnormal value.

If when adopting range chart, and satisfy n 〉=5, then adopt the Grubbs criterion, the factor of fiducial probability (getting 99% usually) has also been considered in the influence that it has not only considered to measure number of times.As measured value x _iResidual error satisfy | x _i(n p) * s, then thinks x to-x|＞λ _iShould reject for exceptional value, then do for supplement a secondary data, test again, exist until no abnormal value; Wherein, (n p) is and measures the frequency n function relevant with fiducial probability p that its value sees Table 1 to λ.

Table 1 λ (n, P) value table

Two, the check of mean value in the group: to the m group preliminary date that obtains, calculating between final group between mean value and group before the standard error of the mean, should be earlier to mean value x in the group of each group _jTest.If satisfy $|{\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}}|>{3s}_B,$ Then should the interior mean value x of group _jOut of control, ascertain the reason, one group of data out of control weed out; Recomputate mean value between the group of remaining m-1 group data

And standard error of the mean s between group _B, test mean value x in N/R group again _jExist;

Its three, the check of group internal standard deviation: to the m group preliminary date that obtains, between mean value that calculates standard deviation between final group and group before the standard deviation of standard deviation, also group internal standard deviation s of each group of reply _jTest.If satisfy | s _j-s|＞3s _b, then should group internal standard deviation s _jOut of control, ascertain the reason, one group of data out of control weed out, and recomputate the standard deviation s of standard deviation between the mean value s of standard deviation between the group of remaining m-1 group data and group _b, test again, until N/R group of internal standard deviation s _jExist;

Four, the check of the interior extreme difference of group: the m that obtains is organized preliminary date, between mean value that calculates extreme difference between final group and group, before the standard deviation of extreme difference, also tackle extreme difference R in each group of organizing _jTest.If satisfy | R _j-R|＞3sR then should the interior extreme difference R of group _jOut of control, should ascertain the reason, one group of data out of control can weed out, and recomputate the standard deviation s of extreme difference between the mean value R of extreme difference between the group of remaining m-1 group data and group _R, test extreme difference R in N/R group again _jExist.

By check, guarantee that the final statistics controlled quentity controlled variable of gained does not exist unusually, to be used for long-term statistics control to data.

Come the comparative illustration beneficial effect of this programme once below in conjunction with an example:

The foundation of control chart and with the comparison (not relating to concrete processing procedure) of Shewhart control chart:

Verifying with second-class resistance standard device is the making that example is introduced X-control chart and standard deviation control chart, and with the comparison of Hart control chart.Table 2 is that second-class resistance standard device 0.01 Ω verifies mean value and group internal standard deviation data in the group that obtains when initial parameter is set up in measurement, these 22 groups of data are all checked on request, N/R data exist, and can calculate the control limit of two kinds of control charts in view of the above.

Mean value and group internal standard are poor in the group of table 2 0.01 Ω observed reading

2. the making of X-control chart

The mean value that at first calculates sub-cell mean is promptly organized a mean value $\stackrel{\‾}{\stackrel{\‾}{x}}=0.0100000878\mathrm{\Ω},$ Standard deviation s between group _R=6.4 * 10 ^-9Ω, mean value s=2.3 * 10 of each son group standard deviation ^-9Ω, measurement number of times of organizing owing to each son all is 12 times, then A ₃=0.886.So the center line that can obtain X-control chart is 0.010 000 087 8 Ω; The upper control limit of determining according to this method 1 is $\stackrel{\‾}{\stackrel{\‾}{x}}+3s_B=0.0100001069\mathrm{\Ω}$ With lower control limit 1 be $\stackrel{\‾}{\stackrel{\‾}{x}}-3s_B=0.0100000688\mathrm{\Ω};$ Upper control limit 2 according to the Shewhart control chart viewpoint is $\stackrel{\‾}{\stackrel{\‾}{x}}+A_3\stackrel{\‾}{s}=0.0100000898\mathrm{\Ω}$ With lower control limit 2 be $\stackrel{\‾}{\stackrel{\‾}{x}}-A_3\stackrel{\‾}{s}=0.0100000858\mathrm{\Ω}.$

According to mean value in the group in above-mentioned two kinds of control limits and the table 2, utilize the control chart of excel spreadsheet lattice under the two kinds of control limits of drawing under the same coordinate system, and the range of control of the control chart that will draw according to this method is divided into 6 districts, the width in each district all is equivalent to the standard deviation of the statistics controlled quentity controlled variable that adopts, be labeled as A, B, C, C, B and A from top to bottom respectively, as Figure of description Figure 11.Can find out significantly that from Figure 11 22 groups of data all do not exceed the control limit that is provided with according to this method, maximum fluctuation occurs between the 1st group and the 3rd group of data, and maximal phase is 2.4 * 10 to fluctuation ^-6, it is 20 * 10 that the year of 0.01 Ω, two constant resistances allows relative stability ^-6, therefore, the undulatory property of being verified out is rational.But 22 groups of data of same this but have exceeded the control limit that is provided with according to the Shewhart control chart viewpoint at 20, and this control limit setting is too narrow, unreasonable in other words.

3. the making of standard deviation control chart

Calculate mean value s=2.32 * 10 of standard deviation between the son group equally ^-9Ω, the standard deviation s of standard deviation between group _b=0.69 * 10 ^-9Ω, measurement number of times of organizing owing to each son all is 12 times, then B ₄=1.646B ₃=0.354.So the center line that can obtain X-control chart is 2.32 * 10 ^-9Ω; The upper control limit of determining according to this method 1 is s+3s _b=4.40 * 10 ^-9Ω and lower control limit 1 are s-3s _b=0.24 * 10 ^-9Ω; Upper control limit 2 according to the Shewhart control chart viewpoint is s+B ₄S=6.14 * 10 ^-9Ω and lower control limit 2 are s-B ₃S=1.50 * 10 ^-9Ω.

Poor according to the group internal standard in above-mentioned two kinds of control limits and the table 2, utilize the control chart of excel spreadsheet lattice under the two kinds of control limits of drawing under the same coordinate system, and the range of control of the control chart that will draw according to this method is divided into 6 districts, be labeled as A, B, C, C, B and A from top to bottom respectively, as Figure 12.Can find out significantly that from Figure of description 12 22 groups of data all do not exceed the control limit that is provided with according to this method, maximum standard deviation is 3.2 * 10 ^-9Ω, its relative value is 0.32 * 10 ^-6, this also is rational concerning two constant resistances of 0.01 Ω.But 22 groups of data of same this but have exceeded the control limit that is provided with according to the Shewhart control chart viewpoint at 4, and are to have exceeded lower control limit.In addition, it can also be seen that from figure the upper control limit of Shewhart control chart is too wide, the setting of last lower control limit is all unreasonable.

4. the use of control chart

After control chart is set up,, remake one group and verify measurement,, and carry out the check of measured value by formula (1), (2) counting statistics controlled quentity controlled variable every certain time interval.Mean value x and group internal standard deviation s mark in X-control chart and standard deviation control chart in will organizing respectively, and be linked to be broken line with adjacent 2, the broken line that connects measurement point is prolonged the (dotted line among the figure one by one, utilize the excel spreadsheet lattice to make equally), just become the control chart (four groups of data) that can carry out daily monitoring to measuring process.Shown in Figure of description 13 and 14.

Mean value and group internal standard are poor in the group of the daily control observation value of table 3 0.01 Ω

Claims (9)

1. one kind based on the measurement assurance plan statistical control method, and it may further comprise the steps:

A) under repeated condition, the check standard that chooses is done n independent duplicate measurements;

B) under the measuring condition of regulation, press preset time repeating step measuring process a) at interval, obtain m son group altogether;

It is characterized in that it is further comprising the steps of:

C) m son group data that obtain according to step b), statistics controlled quentity controlled variable in obtaining organizing according to following formula respectively: mean value x, group internal standard deviation s or extreme difference R;

$\stackrel{\‾}{x}=\frac{1}{n}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{x}_i---\left(1\right)$

$s=\sqrt{\frac{1}{n-1}\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(x_i-\stackrel{\‾}{x})}^2}---\left(2\right)$

R＝x _max-x _min (3)

In the formula: n---measure number of times;

x _i---the i time measured value;

x _Max---greatest measurement;

x _Min---minimum measured value;

D) mean value x, group internal standard deviation s or extreme difference R in the group that obtains according to step c) obtain the statistics controlled quentity controlled variable of m group data: mean value between group according to following formula

And standard error of the mean s between group _B, the standard deviation s of standard deviation between the mean value s of standard deviation and group between group _b, the standard deviation s of extreme difference between the mean value R of extreme difference and group between group _R

$\stackrel{\‾}{\stackrel{\‾}{x}}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{\stackrel{\‾}{x}}_j---\left(4\right)$

$s_B=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{({\stackrel{\‾}{x}}_j-\stackrel{\‾}{\stackrel{\‾}{x}})}^2}---\left(5\right)$

$\stackrel{\‾}{s}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{s}_j---\left(6\right)$

$s_b=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(s_j-\stackrel{\‾}{s})}^2}---\left(7\right)$

$\stackrel{\‾}{R}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{R}_j---\left(8\right)$

$s_R=\sqrt{\frac{1}{m-1}\underset{j=1}{\overset{m}{\mathrm{\Σ}}}{(R_j-\stackrel{\‾}{R})}^2}---\left(9\right)$

In the formula: m---measurement group number;

x _j---mean value in the group of j group;

s _jThe group internal standard deviation of-the j group;

R _j---the extreme difference of j group;

E) data detection is to dispose abnormal data;

F) final data through the step e) check is recomputated according to step d), get statistics controlled quentity controlled variable finally;

G) set up control chart according to the resulting statistics controlled quentity controlled variable of step f):

L) X-control chart in the group: with mean value between group

Be center line (CL), with

Be upper control limit (UCL), with

Be lower control limit (LCL), mean value in organizing is added up control; The statistics controlled quentity controlled variable that calculates is marked on figure, connect adjacent 2 points with straight line successively;

2) group internal standard deviation control figure: the mean value s with standard deviation between group is center line (CL), with s+3s _bFor upper control limit (UCL), with s-3s _bBe lower control limit (LCL), group internal standard deviation is added up control;

3) range chart in the group: the mean value R with extreme difference between group is center line (CL), with R+3s _RFor upper control limit (UCL), with R-3s _RBe lower control limit (LCL), extreme difference in organizing is added up control.

2. statistical control method according to claim 1, it is characterized in that: after described step g) control chart is set up, try again at interval every preset time and verify to measure, and obtain the statistics controlled quentity controlled variable according to formula (1), (2), (3), in corresponding control chart, mark, connect consecutive point with straight line successively.

3. statistical control method according to claim 1 and 2, it is characterized in that: the range of control of the control chart that described step g) is obtained is divided into 6 districts, be labeled as A, B, C, C, B, A from top to bottom respectively, and judge the unusual of statistics controlled quentity controlled variable based on this:

Pattern one: if measurement point appears at outside the A district, then measuring process is unusual, and if measurement point exceeds the upper bound, shows that the average of adding up controlled quentity controlled variable increases; And if measurement point exceeds lower bound, then its average reduces;

Pattern two: if continuous 9 measurement points appear at the same side of center line and form 9 chains, then measuring process occurs unusual;

Pattern three: if the trend of monotone increasing or monotone decreasing appears in continuous 6 measurement points, then measuring process is unusual;

Pattern four: arrange if alternatively up and down appears in continuous 14 measurement points, then measuring process is unusual;

Pattern five: if having appear at A district, the same side at 2 in continuous 3 measurement points, then measuring process occurs unusual;

Pattern six: if having 4 points to appear in the side B district or A district of center line in continuous 5 measurement points, then the selected statistics controlled quentity controlled variable of control chart is moved to this lateral deviation;

Pattern seven: if continuous 15 measurement points appear in the C district of center line both sides, then measuring process is unusual;

Pattern eight: if continuous 8 measurement points appear at the center line both sides and all not in C district, then measuring process occurs unusually.

4. statistical control method according to claim 3 is characterized in that: unusual if measuring process occurs, the data that inspection immediately is associated are also handled, and perhaps remeasure; If occur continuously then stopping to measure unusually, check associated data, unusual until getting rid of; If can't get rid of unusually, then the described step a) of foundation is to g) the reconstruction control chart.

5. statistical control method according to claim 4, it is characterized in that: to not comprising that initial statistics control quantitative statistics controlled quentity controlled variable measuring process is got rid of the formed many group statistics controlled quentity controlled variables in back unusually and initial statistics controlled quentity controlled variable gathers, according to described step b) to d) calculate new statistics controlled quentity controlled variable, and rebulid control chart according to described step g).

6. statistical control method according to claim 5 is characterized in that: in the described step a) as when adopting the standard deviation control chart, and n 〉=12 then; If when adopting range chart, n 〉=5 then.

7. statistical control method according to claim 5 is characterized in that: m in the described step b) 〉=20.

8. statistical control method according to claim 7 is characterized in that: m in the described step b) 〉=25.

9. statistical control method according to claim 5 is characterized in that: data detection comprises in the described step e):

The check of one, measured value: to the i time measured value x of every group of data _iTest, during as if employing standard deviation control chart, and satisfy n 〉=12, then adopt the Rye to reach criterion, if measured value x _jResidual error satisfy | x _i-x|＞3s then thinks x _iFor exceptional value is rejected, then do for supplement a secondary data, recomputate mean value x and group internal standard deviation s in the group, test again, exist until no abnormal value; If when adopting range chart, and satisfy n 〉=5, then adopt the Grubbs criterion, as measured value x _iResidual error satisfy | x _i(n p) * s, then thinks x to-x|＞λ _iShould reject for exceptional value, then do for supplement a secondary data, test again, exist until no abnormal value; Wherein, (n p) is and measures the frequency n function relevant with fiducial probability p λ;

Two, the check of mean value in the group: if satisfy

Then should the interior mean value x of group _jOut of control, ascertain the reason, one group of data out of control weed out; Recomputate mean value between the group of remaining m-1 group data

And standard error of the mean s between group _B, test mean value x in N/R group again _jExist;

Three, the check of group internal standard deviation: if satisfy | s _j-s|＞3s _b, then should group internal standard deviation s _jOut of control, ascertain the reason, one group of data out of control weed out, and recomputate the standard deviation s of standard deviation between the mean value s of standard deviation between the group of remaining m-1 group data and group _b, test again, until N/R group of internal standard deviation s _jExist;

Four, the check of extreme difference in the group: if satisfy | R _j-R|＞3s _R, then should the interior extreme difference R of group _jOut of control, should ascertain the reason, one group of data out of control can weed out, and recomputate the standard deviation s of extreme difference between the mean value R of extreme difference between the group of remaining m-1 group data and group _R, test extreme difference R in N/R group again _jExist.

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