Some standard content:
1 Scope of application
National Standard of the People's Republic of China
Control chartsforarithmetic
mean with warning limits
This standard applies to the control of process mean under the condition that the process standard deviation is known. 2 Symbols and physical meaning
UDC 519.26
(083,5)
GB 4888-85
1 Non-uniform chain length, that is, when the mean of the production process is kept at a certain value, when the out-of-control signal is obtained on the control chart, the average number of sample points drawn.
Half-mean chain length of a controlled process
.1Average chain length of an out-of-control process
CL Centerline
Upper action limit
Lower action limit
UWL Upper warning limit
Lower alert limit
Maximum allowable value of the process mean.
Minimum allowable value of the process mean.
Upper specification limit
TLLower specification limit
. Process mean
Process standard deviation
Sample size
KThe number of consecutive sample points that fall between the action limit and the warning limit (including the upper warning limit) on the same side, and the process is judged to be out of control. 8 Standard deviation
μo -
P1 Maximum allowable value of defective rate
B, coefficient used to calculate action limit
B3: Coefficient used to calculate warning limit Www.bzxZ.net
3 Preparation
(When the mean is biased upward)
(When the mean is biased downward)
3.1 After the standard deviation control chart has been in the required statistical control state for a long time, the mean control chart with warning limits can be used to control the process mean.
National Bureau of Standards 1985-01-28 Issued
19B5-10-01 Implementation
GB 488685
3.2 Specified the initial values of the statistical control plan for the production process uo, T, T, P1, Ln minimum value, L maximum value, sample size n. The standard deviation is known.
a.3 Calculate u, and according to,, T, n, μ, and,. H = Tu- OZ (1- Pi)
μl = T + ozc1 - p)
where Z (I-) is the (1-P,) quantile of the standard normal distribution. , V (upward skew)
μe - HL
n (lower skew)
3.4 According to the given L, and La and the calculated Vn, find the optional combination of B,, B2 and K in Tables 1 to 3 or Tables 4 to 6.
Use Tables 1 to 3 for one-sided control charts. Use Tables 4 to 6 for two-sided control charts. a. In each table, the value of the row with zero value corresponds to ten, and the value of the row with non-zero V value corresponds to 1. b. Find the columns in the table that meet the requirements of L. . Find the row with the value of 8, and the values not in the table should be linearly interpolated. d. Find the value that meets the L requirement among the intersections of the columns and the row that have been found (usually there are multiple). e: Find the corresponding B1, B2, K values in the column where the above value is located. This is the available solution. 8.5 If several different solutions meet the requirements, the one with the larger Lo/L should be selected. When L./L is large (>40), it is recommended to use the solution with the smaller L.
3.8 If the sample size is not determined in advance, find the possible solution through Tables 1 to 6. Find the column that meets the given conditions with L in Tables 1 to 3 or Tables 4 to 6. The first number that just meets L. is the value of 8, and n is calculated from the known. If n is not an integer, it shall be modified to the nearest integer according to the digital rounding rules in Appendix C of GB1.1 "Guidelines for the Preparation of Standards for Standardization Work: - Stock Provisions". 3.7 Calculate CL, UAL, LAL, UWL, LWL CL=
UAL=p+
LAL =Ho
LWL=μo
3.8 Draw a mean control chart on grid paper
The vertical axis is the sample mean, the horizontal axis is the sample number or sampling time, the center line is represented by a solid line, and the action limit and warning limit are represented by a dotted line.
4 Use of mean control chart
GB 4886—85
4.1 Take samples according to the specified interval and sample size, measure their quality characteristic values, and fill in the special data table. , 2 Calculate the sample mean and point it on the control chartri
4.8 Principles for judging process out of control
As long as one of the following is met, the process is judged to be out of control: rent. The point falls on or outside the action limit! b. The number of consecutive points between the warning limit (including the warning limit) and the action limit on the same side is equal to K. 4.Process out of control
Find out the abnormal reasons that reduce quality and take measures to eliminate them so that they will not occur again. Correction of warning limits and action limits
After using for a period of time, the warning limits and action limits should be corrected according to the actual quality level. (12)
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A,1 one-sided control chart
GB 48B68 6
Appendix A
Estimate the maximum or minimum allowable value of the process mean based on the maximum allowable defective rate
(reference)
At1 Control the upper deviation of the mean of the production process The defective rate P of the controlled production process is determined by the following formula: P,= 1 -
The defective rate of the out-of-control production process is determined by the following formula: P,= 1 —
The formula is the distribution function of the standard normal distribution (,). If Tu and are known, u can be determined by the following formula: G.
μ= T-αZ ip
Formula: Z(>N(,1)'s (1-) quantile. A.1.2 Controlled production process mean deviation
The qualified product rate of a controlled production process is determined by the following formula: =1d
The unqualified product rate of an out-of-control production process is determined by the following formula:,=1
If and are known, then it is determined by the following formula:
M= T.+ o, Zr-pri
A.2 Two-sided control chart
The unqualified product rate of a controlled production process is determined by the following formula: P.- 1- 0
The unqualified product rate of an out-of-control production process is determined by the following formula: Tu—fta
P=1 -0(T=u) + 1 -0(==T
（upward offset）,
GB 4886
6—85
p, 1 (
(-u)（downward offset）
+1-Φ
can be ignored, (A8)Wu changes to (A2), Hu is determined by (A3). can be ignored,
（A9） changes to (A5), μL is determined by (A6). (A)
GB 4886--85
Appendix B
(reference)
A factory uses a conventional mean-standard deviation control chart to analyze the process quality of small carbon film resistors. Long-term experience shows that the standard deviation has been under control, and the change in process quality is caused by the change in the mean. Therefore, it is decided not to control the standard deviation in the future, and to use a mean control chart with warning limits to control the mean.
B. Preparation
B-1.t Given T =86.1k2,7= 77.9k,p =0.01%,F. 500,L,< 8,0 =0.860,n= 4 B.1.2 Calculate μ, M and 8vn
r = TL— a Z $1 = 86.1 - 0.860x 3,72 = 82.899Ht=Ti+ , Z:-d: = 77.9 +0.860 ×3.72 = 81.101adn=
82.899 82.0
=1.045×2=2.09
= 1.045x2 = 2.09
B.1.3 Look up the table to find the combination of B, B and K
This example is a two-sided control chart, so look up Tables 4 to 6. 82.0-8t.101
Tables 4 to 5 are all less than 500, so look up Table 6
The columns that meet the L requirement in Table 6 are the 8th, 9th, 10th, 12th, 13th, 14th, and 15th columns. b. 8, =2.09, there is no such value in the numerical table, so linear interpolation is used. At the intersection of the row with v㎡=2.09 and the column found in a, find the values that meet the L requirement: 4.3, 5.0, 6.0, 4.8, 5.5, 6.4, 7.2.
Available solutions
Determine the control solution
All available solutions
Bz=1.50,K=3.
>40, so the smaller Z should be selected. The final control solution is B,=3.25,
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