CN102929148B - Multiple product production mode statistical process control method based on T-K control chart - Google Patents

Abstract

The invention discloses a multiple product production mode statistical process control method based on a T-K control chart. The multiple product production mode statistical process control method includes the following steps: (1) building a T control chart for monitoring process parameter mean value; (2) building a K control chart for monitoring process parameter standard deviation; and (3) under a multiple product production mode, the T-K control chart is used for monitoring a device operation state, as long as each type of product sample data reaches more than 2 batches, if distribution parameters are known, one batch of data is enough, and sample capacity of each batch of products is guaranteed to be identical and larger than 1. Control limits are determined according to whether the mean value of the process parameter matrix or standard deviation is known, and the T-K control chart is built. Instance analysis and simulation verification prove that the process control method can detect abnormal factors causing an incontrollable phenomenon in a production process under the multiple product production mode timely and effectively, prompts operation staff to make response timely, and enables the production process to remain in a statistical controlled state so as to guarantee product quality.

Description

Based on the multi-item production mode statistical course control method for use of T-K control chart

Technical field

The invention belongs to commercial production and manufacturing industry technical field, relate to a kind of statistical process control method, specifically, relate to a kind of multi-item production mode statistical course control method for use based on T-K control chart.

Background technology

Statistical Process Control (Statistical Process Control, SPC) technology is the Main Means evaluated production run statistics slave mode and then ensure product quality.Many scholars propose numerous dissimilar control chart technology, and these Traditional control diagram technologies are used widely in volume industrial is produced, and create positive effect to improvement productivity effect, aspect of improving the quality of products.But production run meets some requirements to use Charts to require.First, control limit to calculate, require the average of process and standard deviation known, or can be calculated by the data gathered.But calculate based on the data gathered and control in limited time, in order to ensure confidence level, at least to need 20 to 25 lot sample notebook datas, often criticizing 5 sample points, that is: at least needing 100 to 125 data from the sample survey.In addition, the prerequisite of application Charts is that each batch of sample data gathering in requirement production run is separate and obey same normal distribution, namely usually said independent normal is with distribution (Independent and IdenticallyNormally Distributed, IIND) condition.

But, in actual production, there is the feature of obvious multi items, short run in some production run, same procedure processes several product that even tens kinds of technological specifications are different possibly, and this makes Traditional control diagram technology be difficult to the quality control of this kind of production run.The production run of first this multi items, short run can not know average and the standard deviation of procedure parameter usually in advance, and due to product category various, the product of single variety batch is less, is difficult to meet the data volume requirement of setting up control chart.As adopted less data construct control chart, reduce making the monitoring capacity of control chart.In addition, dissimilar product is often different owing to producing starting material, working condition or processing request, and cause technological parameter parent to disobey same distribution, this has obviously run counter to IIND condition.These problems all propose challenge to implementing SPC in multiple variety and small batch production.

For solving the problem that in small serial production pattern, data volume is very few, some scholars propose self-starting (self-starting) control chart technology.The advantage of Self-starting control chart is sample data amount less demanding, can set up control chart without the need to undergoing analysis control chart, and along with the constant renewal estimator of parent distribution parameter of monitor procedure.Propose a series of self-starrting control chart based on Q statistical magnitude in prior art, be called as Xiu Hate Q control chart, for the fluctuation of testing process technological parameter average and standard deviation.Be discussed in detail average run-length (Average Run Length, the ARL) characteristic of Q control chart and Q control chart is optimized.Propose the CUSUM control chart and MEWMA control chart with self-starting feature.Recently, the people such as Zhang propose Xiu Hate t control chart, and compared with traditional Xiu Hate mean chart, t control chart is without the need to the undergoing analysis control chart stage and have more stable monitoring capacity.Control choosing to have made and revising and the t control chart proposed for small serial production pattern of limit to t control chart, this technology possesses the advantage of Xiu Hate t control chart and is more suitable for the quality monitoring of small batch production process.

Although above-mentioned technology solves the very few problem of sample size that small batch production process brings well, still multi items problem can not be solved.For multi items problem, conventional settling mode first changes raw data, result data is made to obey same normal distribution, again result data implementation process is controlled, as: with desired value deviation control chart (Deviations from Nominal, DNOM) and standardization DNOM control chart (Standardized DNOM).But, utilize these control charts, need to estimate dissimilar Product Process parameter and standard deviation, need all will gather abundant data to the product of each kind for this reason, otherwise standard deviation estimated value error is larger, control chart hydraulic performance decline will be caused, show as False Rate lifting or insensitive to abnormal cause.For multi-varieties and small-batch situation, be usually difficult to the requirement meeting this data acquisition amount.

Summary of the invention

In order to solve the problems of the technologies described above, overcome the defect existed in prior art, the invention provides a kind of multi-item production mode statistical course control method for use based on T-K control chart, this method propose the T-K control chart under multi-item production pattern, for the fluctuation of characterization processes parameter Parent Mean and standard deviation.Its basic thought adopts a kind of method not high to sample size requirements, based on the every lot sample notebook data gathered, calculates T, K statistic, makes T, K statistic separate separately and obey same distribution.According to actual conditions, propose the method for two kinds of compute statistics.A kind of known for technological parameter average, the another kind of situation being used for average the unknown.

Its technical scheme is as follows:

Based on a multi-item production mode statistical course control method for use for T-K control chart, comprise the following steps:

1) the T control chart for monitoring technological parameter average is set up

Suppose that a production process planning is according to the different code requirement converted products of P kind, that is: produce P kind product.If X is key process parameter, randomly draw n observation sample, { X to often criticizing product ^(r)i, j, l ..., X ^(r)i, j, n} are i-th group of sample, i=1,2 ...; J represents the product type sequence number that this batch of sample is corresponding, j=1,2 ... P; N is sample size, and subscript r represents the sequence number of this lot sample originally in same type product.If no special instructions, aiming symbol under having involved in literary composition, the first subscript represents sample batch serial number, and the second subscript represents kind sequence number corresponding to this sample, and the 3rd subscript shows the sequence number of these data in affiliated batch; Subscript in bracket represents the sequence number of this group sample in respective type product sample.Statistics slave mode under, in same batch and batch between technological parameter data separate, the sample data of same kind obeys same normal distribution, and the sample data of different cultivars obeys different normal distributions, that is: X _{i, j, k}~ N (μ _j, σ _j), i=1,2 ..., j=1,2 ... P, k=1,2 ... n, wherein μ _jand σ _jobey by jth kind Product Process parameter parent under slave mode average and the standard deviation of distribution.The sample average of i-th group of sample and sample standard deviation S _{i, j}be respectively:

${\stackrel{\‾}{X}}_{i,j}=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{X}_{i,j,k}$ $S_{i,j}=\sqrt{\frac{1}{n-1}\underset{k=1}{\overset{n}{\mathrm{\Σ}}}{(X_{i,j,k}-{\stackrel{\‾}{X}}_{i,j})}^2}---\left(1\right)$

1.1) definition of T statistic

In actual production, the average μ of technological parameter estimator of parent distribution is generally unknown parameter.If Product processing desired value and technological parameter actual distribution mean bias are not quite, μ as estimator of parent distribution average, or when can determine the value of μ according to practical production experience, can be considered as known parameters by available targets value.When building T statistic, whether known according to all types of Product Process parameter Parent Mean, there are two kinds of modes to set up statistic.

Situation one: technological parameter Parent Mean is known

For each lot sample originally, i=1,2 ..., statistic T _{i, j}expression formula as follows:

$T_{i,j}=\frac{{\stackrel{\‾}{X}}_{i,j}-{\mathrm{\μ}}_j}{S_{i,j}/\sqrt{n}},$ j＝1，2，..P (2)

Wherein n is every lot sample capacity originally, μ _jfor jth kind Product Process parameter Parent Mean during controlled process.When production run is in statistics slave mode, T _{i, j}separate and obedience degree of freedom is the t distribution of n-1.

Situation two: technological parameter Parent Mean is unknown

Definition:

${\stackrel{\‾}{\stackrel{\‾}{X}}}_j^{(r-1)}=\frac{1}{r-1}\underset{h=1}{\overset{r-1}{\mathrm{\Σ}}}{\stackrel{\‾}{X}}_j^{\left(h\right)},$ j＝1，2，..P，r＝2，3... (3)

represent that product type is the average of the front r-1 lot sample notebook data of j, the expression formula of T statistic is:

$\begin{array}{c}{T}_{i,j}^{\left(1\right)}=0\\ T_{i,j}^{\left(r\right)}=\frac{{\stackrel{\‾}{X}}_{i,j}^{\left(r\right)}-{\stackrel{\‾}{\stackrel{\‾}{X}}}_j^{(r-1)}}{S_{i,j}^{\left(r\right)}}\sqrt{\frac{n(r-1)}{r}}\end{array}$ j＝1，2，..P，r＞1 (4)

In visible T control chart, first statistic of all types of product is constant 0, and follow-up statistic by its appearance position in respective type product and in the past data determine.

1.2) T control chart controls the determination of limit

T control chart controls to be limited to:

$\mathrm{UCL}=G_t^{-1}(1-\frac{\mathrm{\α}}{2}|n-1)$

CL＝0 (5)

LCL＝-UCL

Wherein the t of to be degree of freedom be n-1 distributes the inverse function of Cumulative Distribution Function, and α is level of significance, and according to statistical process control, upper lower control limit corresponds to ± 3 σ positions, and namely α value is 0.0027.For same production run, if process is in slave mode, technological parameter average offsets, so variety classes product, as long as the sample size of each subgroup is identical, then separate by each subgroup process parameter measurement value calculated T statistic and obey same t and distribute, and there is identical control limit.These T statistics are painted in same control chart, just can carry out quality monitoring to production run.Can be found by above-mentioned analytic process, even if at the initial period that SPC analyzes, the level of significance of T control chart is still identical with traditional Shewhart control chart remains on fixed value 0.0027, even if this shows that T control chart still normally can implement quality monitoring to production run under small serial production pattern.

Choosing that the level of significance of T control chart, control are limit is all consistent with Shewhart control chart, and T statistic is separate, and therefore the judgment rule of Charts is still applicable to T control chart.In the monitoring of technological process, except whether detection has the point exceeding and control limit, any point showing nonrandom phenomenon in control chart is also considered as point out of control, in these criterions out of control also need by control chart ± position of σ (probable value 0.3173) and ± 2 σ (probable value 0.0455).T control chart is determined to control limit according to the fractile that t distributes, and it is relevant to the sample size of every batch data that it controls limit, for convenience of practical application, lists under Different Sample T control chart center line in table 1, controls to limit and the value of ± σ and ± 2 σ positions.

The control limit of table 1.T control chart and ± σ and ± 2 σ values

Sample size	CL	±σ	±2σ	UCL/LCL
					n＝2	0	±1.8373	±13.9677	+/-235.7837
n＝3	0	±1.3213	±4.5265	+/-19.2060
					n＝4	0	±1.1969	±3.3068	+/-9.2187
n＝5	0	±1.1416	±2.8693	+/-6.6201
					n＝6	0	±1.1105	±2.6486	+/-5.5070
n＝7	0	±1.0906	±2.5165	+/-4.9040
					n＝8	0	±1.0767	±2.4288	+/-4.5299
n＝9	0	±1.0665	±2.3664	+/-4.2766
					n＝10	0	±1.0587	±2.3198	+/-4.0942

2) for monitoring the K control chart of technological parameter standard deviation

Similar with the definition of T control chart statistic, whether known according to technological parameter standard deviation, the foundation of K control chart in two kinds of situation.

2.1) technological parameter parent standard deviation is known

Now, the K of each batch of sample _{i, j}statistic is:

$K_{i,j}=\frac{(n-1)S_{i,j}^2}{{\mathrm{\σ}}_j^2},$ j＝1，2，..P (6)

Wherein n is subgroup sample size, σ _jfor jth series products technological parameter parent standard deviation during controlled process.When production run is in statistics slave mode, K _{i, j}obey card side's distribution that degree of freedom is n-1, the control of K control chart is limited to:

$\mathrm{LCL}=H_{\mathrm{\χ}}^{-1}\left(\frac{\mathrm{\α}}{2}\right|n-1)$

$\mathrm{CL}=H_{\mathrm{\χ}}^{-1}\left(0.5\right|n-1)---\left(7\right)$

$\mathrm{UCL}=H_{\mathrm{\χ}}^{-1}(1-\frac{\mathrm{\α}}{2}|n-1)$

Wherein the inverse function of card side's distribution Cumulative Distribution Function of to be degree of freedom be n-1, α is level of significance, value is 0.0027, similar with T control chart, the value of the control line up and down of K control chart when can obtain Different Sample equally, center line and ± σ and ± 2 σ positions.For same production run, as long as process is in slave mode, technological parameter standard deviation offsets, the sample size of each batch of measurement data is identical, then separate by every batch data process parameter measurement value calculated K statistic and obey the distribution of same card side, and there is identical control limit.Therefore the K statistic from dissimilar product can carry out quality monitoring by same control chart.

2.2) technological parameter parent standard deviation is unknown

Definition:

${\stackrel{\‾}{S_j^2}}^{(r-1)}=\frac{1}{r-1}\underset{h=1}{\overset{r-1}{\mathrm{\Σ}}}{S}_j^{2\left(h\right)},$ j＝1，2，..P，r＝2，3... (8)

represent that product type is the average that the front r-1 of j criticizes sample variance.

Definition intermediate variable:

${\mathrm{\λ}}_{i,j}^{\left(r\right)}=\frac{S_{i,j}^{2\left(r\right)}}{{\stackrel{\‾}{S_j^2}}^{(r-1)}},$ j＝1，2，..P，r＝2，3，... (9)

Statistic K _{i, j}expression formula be:

$\begin{array}{c}{K}_{i,j}^{\left(1\right)}=1\\ K_{i,j}^{\left(r\right)}={\mathrm{\Φ}}^{-1}\left[F_{n-1,(n-1)(r-1)}\left({\mathrm{\λ}}_{i,j}^{\left(r\right)}\right)\right]\end{array}$ j＝1，2，..P，r＞1 (10)

Wherein be first be freely v ₁second degree of freedom is v ₂f distribution Cumulative Distribution Function.Suppose 0 < s < t, then press the statistic of above formula definition with separate, because as j ≠ k, the sample from dissimilar product is separate, therefore both must be independent; If j=k, be defined as follows variable:

$W_1=(n-1)\underset{h=1}{\overset{r_s-1}{\mathrm{\&Sigma;}}}{S}_{\&CenterDot;,j}^{2\left(h\right)},$ $W_2=(n-1)\underset{h=r_s}{\overset{r_i-r_s}{\mathrm{\&Sigma;}}}{S}_{\&CenterDot;,j}^{2\left(h\right)},$ $W_3=(n-1)S_{i,j}^{2\left(r_i\right)}$

Obvious W ₁: w ₂: w ₃: wherein: v ₁=(n-1) (r _s-1), v ₂=(n-1) (r _t-r _s), v ₃=n-1, due to W ₁, W ₂with W ₃par wise irrelevance, so W ₂/ W ₁with W ₃/ (W ₁+ W ₂) separate.Can be obtained by conversion:

${\mathrm{\&lambda;}}_{s,j}^{\left(r_s\right)}=\frac{(n-1)(r_s-1)S_{s,j}^{2\left(r_s\right)}}{W_1},$ ${\mathrm{\&lambda;}}_{i,j}^{\left(r_i\right)}=\frac{v_1+v_2}{v_3}\frac{W_3}{W_1+W_2}$

So with separate.Because (9) formula obeys the F distribution that the first degree of freedom is (n-1), the second degree of freedom is (n-1) (r-1), therefore K statistic separate and obey N (0,1), that is: all statistics points are separate and obey standardized normal distribution in K control chart.Control the selection mode of limit with reference to traditional Shewhart control chart, when standard deviation is unknown, the control of K control chart is limited to:

LCL＝-3

CL＝0 (11)

UCL＝3

In sum, under multi-item production pattern, T-K control chart is adopted to monitor equipment running status, as long as every type product sample data reach more than 2 batches (if distribution parameter is known, 1 batch data) and to ensure often to criticize the sample size of product identical and be greater than 1, according to the average of technological parameter estimator of parent distribution or standard deviation whether known, by (2) formula or (4) formula, (6) formula or (10) formula compute statistics, determine to control limit according to (5) formula, (7) formula or (11) formula, and set up T-K control chart.

Beneficial effect of the present invention:

The T-K control chart that technical scheme of the present invention is applicable to Multi-varieties and Small-batch Production environment has two aspect advantages.It, to the monitoring of average and standard deviation, only need a control chart can make correct evaluation to the running status of multi-item production process respectively, and this control chart algorithm is simple, is convenient to practical application.Its two, T-K control chart has self-starting feature, estimates the distribution parameter of parent without the need to undergoing analysis with the control chart stage, and especially the process of establishing of T control chart is irrelevant with parent standard deviation.Even if when estimator of parent distribution unknown parameters, as long as the data of each kind reach 2 batches, T-K control chart can control multiple variety and small batch production implementation quality.

Accompanying drawing explanation

Fig. 1 be average out of control time T-K control chart analysis result;

Fig. 2 be standard deviation out of control time T-K control chart analysis result;

Fig. 3 is bonding technology T-K control chart.

Embodiment

Below in conjunction with accompanying drawing embodiment, method of the present invention is described in more detail.

Embodiment 1. verifies by emulation mode the ability that T-K control chart testing process average is out of control.Randomizer is utilized to produce 25 batch datas, often criticize 5 samples, suppose the product A of this 25 batch data by two types, B is formed, Normal Distribution N (10 respectively, 0.1) and N (20, 0.5), during generation random number, every lot sample product type is originally determined at random with equiprobability, suppose that the 1 to 15 batch data is in slave mode, from the 16th batch data, there is the skew of 3 times of standard deviations in the average of two kinds of products, and standard deviation does not change, that is: category-A type product parameters obeys N (10.3, 0.1), category-B type product parameters obeys N (21.5, 0.5).Adopt T-K control chart to analyze this 25 batch data, result is as Fig. 1.

1st to the 15th batch data is in slave mode in theory, and no matter be category-A type product or category-B type product, average and standard deviation all fluctuate, and therefore in T-K control chart, point out of control should not appear in front 15 batch datas.From the 16th batch data, due to " appearance of abnormal factors ", cause mean parameter generation skew and standard deviation remains unchanged.Therefore, there is the point out of control exceeding upper control line in T control chart from the 16th batch data, and all statistics points of K control chart are in slave mode always.

Embodiment 2. utilizes emulation mode to verify the ability that T-K control chart testing process standard deviation is out of control.Proof procedure and example 2 similar.Randomizer is utilized to produce 25 batch datas, often criticize 5 samples, this 25 batch data is made up of the product A of two types, B, Normal Distribution N (10 respectively, 0.1) and N (20,0.5), suppose that the 1 to 15 batch data is in slave mode, from the 16th batch data, the standard deviation of two kinds of products occurs extremely expanding as original 3 times, and average does not change, that is: category-A type product parameters obeys N (10,0.3), category-B type product parameters obeys N (20,1.5).Adopt T-K control chart to analyze this 25 batch data, result is as Fig. 2.This 25 batch data average offsets in theory, therefore on T control chart, should not occur point out of control; And from the 16th batch, " abnormal cause appears in production run " causes technological parameter standard deviation to offset, therefore K control chart there is point out of control.

Embodiment 3. utilizes T-K control chart to evaluate the running status of actual process process.In the bond sequence that microcircuit is produced, the bonding wire of employing has 2 kinds, and model is F30 and F50 respectively.In normal productive process, monitored 25 batch datas altogether, often criticized 5 samples, adopt T-K control chart to carry out SPC analysis, result as shown in Figure 3.Analysis result shows, bonding process is in statistics slave mode.

Conclusion

When carrying out quality control to multi-item production process, often because data volume is not enough and dissimilar Product Process parameter disobey same normal distribution, make Traditional control diagram technology cannot be directly used in multi-item production environment.Propose the T-K control chart technology being applicable to multi-item production pattern herein, comprise the determination that the definition of T, K statistic and account form and T-K control chart control to limit, the method only needs a control chart just can monitor technological parameter average and standard deviation respectively, carries out quality control to multi-item production pattern.Meanwhile, T-K control chart possesses self-starting feature.Theoretical analysis shows that the monitoring capacity of T-K control chart is consistent with traditional Shewhart control chart, even if T-K control chart still can keep stable monitoring performance when sample size is less.Instance analysis and simulating, verifying show, T-K control chart effectively for the quality monitoring of multi-item production process, can make correct judgement to the running status of production run.

The above; be only the better embodiment of the present invention; protection scope of the present invention is not limited thereto; anyly be familiar with those skilled in the art in the technical scope that the present invention discloses, the simple change of the technical scheme that can obtain apparently or equivalence are replaced and are all fallen within the scope of protection of the present invention.

Claims (4)

1., based on a multi-item production mode statistical course control method for use for T-K control chart, it is characterized in that, comprise the following steps:

1) the T control chart for monitoring technological parameter average is set up

Suppose that a production process planning is according to the different code requirement converted products of P kind, that is: producing P kind product, if X is key process parameter, randomly drawing n observation sample, { X to often criticizing product ^(r) _{i, j, 1}..., X ^(r) _{i, j, n}be i-th group of sample, and i=1,2 ...; J represents the product type sequence number that this batch of sample is corresponding, j=1,2 ... P; N is sample size, subscript r represents the sequence number of this lot sample originally in same type product, if no special instructions, aiming symbol under having involved in literary composition, first subscript represents sample batch serial number, second subscript represents kind sequence number corresponding to this sample, and the 3rd subscript shows the sequence number of these data in affiliated batch; Subscript in bracket represents the sequence number of this group sample in respective type product sample, under statistics slave mode, in same batch and batch between technological parameter data separate, the sample data of same kind obeys same normal distribution, and the sample data of different cultivars obeys different normal distributions, that is: X _{i, j, k}~ N (μ _j, σ _j), i=1,2 ..., j=1,2 ... P, k=1,2 ... n, wherein μ _jand σ _jobey by jth kind Product Process parameter parent under slave mode average and the standard deviation of distribution, the sample average of i-th group of sample and sample standard deviation S _{i, j}be respectively:

$\begin{array}{cc}{\stackrel{\&OverBar;}{X}}_{i,j}=\frac{1}{n}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{X}_{i,j,k}& S_{i,j}=\sqrt{\frac{1}{n-1}\underset{k=1}{\overset{n}{\mathrm{\&Sigma;}}}{(X_{i,j,k}-{\stackrel{\&OverBar;}{X}}_{i,j})}^2}---\left(1\right)\end{array}$

1.1) definition of T statistic

When building T statistic, whether known according to all types of Product Process parameter Parent Mean, have two kinds of modes to set up statistic:

Situation one: technological parameter Parent Mean is known

For each lot sample originally, i=1,2 ..., statistic T _{i, j}expression formula as follows:

$T_{i,j}=\frac{{\stackrel{\&OverBar;}{X}}_{i,j}-{\mathrm{\&mu;}}_j}{S_{i,j}/\sqrt{n}},j=\mathrm{1,2},..P$

Wherein n is every lot sample capacity originally, μ _jfor jth kind Product Process parameter Parent Mean during controlled process, when production run is in statistics slave mode, T _{i, j}separate and obedience degree of freedom is the t distribution of n-1;

Situation two: technological parameter Parent Mean is unknown

${\stackrel{\stackrel{\&OverBar;}{\&OverBar;}}{X}}_j^{(r-1)}=\frac{1}{r-1}\underset{h=1}{\overset{r-1}{\mathrm{\&Sigma;}}}{\stackrel{\&OverBar;}{X}}_j^{\left(h\right)},j=\mathrm{1,2},..P,r=\mathrm{2,3}...$

represent that product type is the average of the front r-1 lot sample notebook data of j, the expression formula of T statistic is:

$\begin{array}{c}{T}_{i,j}^{\left(1\right)}=0\\ T_{i,j}^{\left(r\right)}=\frac{{\stackrel{\&OverBar;}{X}}_{i,j}^{\left(r\right)}-{\stackrel{\stackrel{\&OverBar;}{\&OverBar;}}{X}}_j^{(r-1)}}{S_{i,j}^{\left(r\right)}}\sqrt{\frac{n(r-1)}{r}}\end{array},j=\mathrm{1,2},..P,r>1$

In T control chart, first statistic of all types of product is constant 0, and follow-up statistic by its appearance position in respective type product and in the past data determine, the statistic set up by above formula is separate and obey same t and distribute;

1.2) T control chart controls the determination of limit

T control chart controls to be limited to:

$\mathrm{UCL}=G_t^{-1}(1-\frac{\mathrm{\&alpha;}}{2}|n-1)$

CL＝0

LCL＝-UCL

Wherein the t of to be degree of freedom be n-1 distributes the inverse function of Cumulative Distribution Function, and α is level of significance, and according to statistical process control, upper lower control limit corresponds to ± 3 σ positions, and namely α value is 0.0027;

2) the K control chart for monitoring technological parameter standard deviation is set up

Whether known according to technological parameter standard deviation, the foundation of K control chart in two kinds of situation:

2.1) technological parameter parent standard deviation is known

Now, the K of each batch of sample _{i, j}statistic is:

$K_{i,j}=\frac{(n-1)S_{i,j}^2}{{\mathrm{\&sigma;}}_j^2},j=\mathrm{1,2},..P$

Wherein n is subgroup sample size, σ _jfor jth series products technological parameter parent standard deviation during controlled process, when production run is in statistics slave mode, K _{i, j}obey card side's distribution that degree of freedom is n-1, the control of K control chart is limited to:

$\mathrm{LCL}=H_{\mathrm{\&chi;}}^{-1}\left(\frac{\mathrm{\&alpha;}}{2}\right|n-1)$

$\mathrm{CL}=H_{\mathrm{\&chi;}}^{-1}\left(0.5\right|n-1)$

$\mathrm{UCL}=H_{\mathrm{\&chi;}}^{-1}(1-\frac{\mathrm{\&alpha;}}{2}|n-1)$

Wherein the inverse function of card side's distribution Cumulative Distribution Function of to be degree of freedom be n-1, α is level of significance, value is 0.0027, the control line up and down of K control chart when obtaining Different Sample, the value of center line and ± σ and ± 2 σ positions, for same production run, as long as process is in slave mode, technological parameter standard deviation offsets, the sample size of each batch of measurement data is identical, then separate by every batch data process parameter measurement value calculated K statistic and obey same card side distribution, and there is identical control limit, K statistic from dissimilar product can carry out quality monitoring by same control chart,

2.2) technological parameter parent standard deviation is unknown

Definition:

${\stackrel{\&OverBar;}{S_j^2}}^{(r-1)}=\frac{1}{r-1}\underset{h=1}{\overset{r-1}{\mathrm{\&Sigma;}}}{S}_j^{2\left(h\right)},j=\mathrm{1,2},..P,r=\mathrm{2,3}...$

represent that product type is the average that the front r-1 of j criticizes sample variance,

Definition intermediate variable:

${\mathrm{\&lambda;}}_{i,j}^{\left(r\right)}=\frac{S_{i,j}^{2\left(r\right)}}{{\stackrel{\&OverBar;}{S_j^2}}^{(r-1)}},j=\mathrm{1,2},..P,r=\mathrm{2,3},...$

Statistic K _{i, j}expression formula be:

$\begin{array}{c}{K}_{i,j}^{\left(1\right)}=1\\ K_{i,j}^{\left(r\right)}={\mathrm{\&Phi;}}^{-1}\left[F_{n-1,(n-1)(r-1)}\left({\mathrm{\&lambda;}}_{i,j}^{\left(r\right)}\right)\right]\end{array},j=\mathrm{1,2},..P,r>1$

Wherein be first be freely v ₁second degree of freedom is v ₂f distribution Cumulative Distribution Function, suppose 0 < s < t, then press above formula define statistic with separate, because as j ≠ k, the sample from dissimilar product is separate, therefore both must be independent; If j=k, be defined as follows variable:

$W_1=(n-1)\underset{h=1}{\overset{r_s-1}{\mathrm{\&Sigma;}}}{S}_{\&bull;,j}^{2\left(h\right)},W_2=(n-1)\underset{h=r_s}{\overset{r_t-r_s}{\mathrm{\&Sigma;}}}{S}_{\&bull;,j}^{2\left(h\right)},W_3=(n-1)S_{t,j}^{2\left(r_t\right)}$

Obviously wherein: v ₁=(n-1) (r _s-1), v ₂=(n-1) (r _t-r _s), v ₃=n-1, due to W ₁, W ₂with W ₃par wise irrelevance, so W ₂/ W ₁with W ₃/ (W ₁+ W ₂) separate, can be obtained by conversion:

${\mathrm{\&lambda;}}_{s,j}^{\left(r_s\right)}=\frac{(n-1)(r_s-1)S_{s,j}^{2\left(r_s\right)}}{W_1},{\mathrm{\&lambda;}}_{t,j}^{\left(r_t\right)}=\frac{v_1+v_2}{v_3}\frac{W_3}{W_1+W_2}$

So with separate, because (9) formula obeys the F distribution that the first degree of freedom is (n-1), the second degree of freedom is (n-1) (r-1), therefore K statistic separate and obey N (0,1), that is: in K control chart all statistics points separate and obey standardized normal distribution, control the selection mode of limit with reference to traditional Shewhart control chart, when standard deviation is unknown, the control of K control chart is limited to:

LCL＝-3

CL＝0

UCL＝3

3) under multi-item production pattern, T-K control chart is adopted to monitor equipment running status, as long as every type product sample data reach more than 2 batches, if distribution parameter is known, 1 batch data, and it is identical and be greater than 1 to ensure often to criticize the sample size of product, according to the average of technological parameter estimator of parent distribution or standard deviation whether known, determine to control limit, and set up T-K control chart.

2. the multi-item production mode statistical course control method for use based on T-K control chart according to claim 1, it is characterized in that, step 1) described in T control chart level of significance, to control choosing of limit all consistent with Shewhart control chart, and T statistic is separate.

3. the multi-item production mode statistical course control method for use based on T-K control chart according to claim 1, it is characterized in that, step 1) in the monitoring of technological process, except whether detection has the point exceeding and control limit, any point showing nonrandom phenomenon in control chart is also considered as point out of control, in these criterions out of control also need by control chart ± position of σ and ± 2 σ.

4. the multi-item production mode statistical course control method for use based on T-K control chart according to claim 1, is characterized in that, step 1) in T control chart according to the fractile that t distribute determine control limit, its control limit relevant to the sample size of every batch data.