In this paper, the principle of mathematical statistics is used to explain the error distribution rule of the length of the packaging bag produced by the ZXJ-1000C automatic printing and bag making unit, and the use of histogram, process capability index, average-range control chart to control the production process, and ensure packaging Bag bag length quality method.
Bags occupy a very important position in the packaging products, such as cement, flour, starch, feed, fertilizers, chemical raw materials, agricultural and sideline products and mineral products such as powder and granular materials are mostly bag packaging. The length of the bag determines the volume of the bag, and ultimately determines the amount of goods. The length of the packaging bag is insufficient, which can easily lead to breaking of the package or insufficient amount of goods during potting and damage the interests of the customer. The length of the packaging bag is too long, resulting in waste of packaging materials and detrimental to the interests of the production enterprise. To increase the accuracy of the package quantification, we must first control the length of the package.
ZXJ-1000C Automatic Printing Bag Making Machine (hereinafter referred to as the unit) is a professional equipment for producing packaging bags. It is equipped with an online measuring device that can automatically measure the length of the bag during the production process and print the sampling data. According to the above, the stability of the production process can be determined by using the X-average control chart and the R-range control chart, and the unstable factors in the production process can be found and eliminated in time to ensure the accuracy of the bag barrel length.
Bag barrel length error and distribution pattern The unit adopts changing the gear ratio between the cutter and the traction to achieve different bag length adjustments. When the cutting speed is fixed and the pulling speed is slow, the cut bag is short. When the pulling speed is fast, the cut bag is long. Once the transmission ratio is fixed, the length of the cut bag is fixed. It is equal to the length of the reciprocating bag barrel, which is the nominal bag length. However, testing the length of a batch of bags will reveal that, except for a portion that is just equal to the length of the nominal bag, some are shorter than the nominal length of the bag, and some are longer than the nominal length of the bag, and the number of excesses and shortfalls is approximately equal. According to the principle of mathematical statistics, this phenomenon is normal. For example, the nominal bag length of a production cement packaging bag is 800mm, and 100 inspections are randomly selected in a batch of bag cylinders. The maximum length is 805mm, and the shortest is 796mm. The distribution range is 805-796=9mm.
Take each length of bag tube as a group, a total of K groups, calculate the frequency of each group. If the length of each group of bags is the abscissa and the frequency is the ordinate, the frequency distribution histogram can be drawn. The top edge of each column of the histogram is connected with a smooth curve. This curve reflects the frequency distribution rule of bag barrel length, which is the actual distribution curve. If there are many pieces detected and the group distance is very small, the smooth curve can be described by the theoretical curve—normal distribution curve. According to the normal distribution theory, an important parameter standard deviation σ in the normal distribution curve can be calculated.
The allowable error of the length of a given bag is generally given in the production. The error of the length of the produced bag should be within this range. This depends on the quality of work of the production process, ie, the cut used in the bag cutting process of the unit. Bag machine performance is closely related. The degree of assurance of the production process to the work quality is called the process capability. The common process capability index, CPK, is used to represent the formula: CPK=(T-2XO+2X mean)6σ. Where T is the allowable tolerance range for the bag length, XO is the standard bag length value, and X mean is the average value of the actual bag length. Process capability is divided into five grades: special grade, grade one, grade two, grade three, and grade four. If the grade is too high, the process capability is too full and not economical; if it is too low, the process capability is insufficient, and unqualified products will appear. If the process capability index CPK belongs to the second level, indicating that the process capability is acceptable, monitoring should be closely watched.
The quality control method of the bag barrel production process To verify the stability of the bag cutting process and understand the dynamic situation of the quality parameter change over time, the quality control of the production process can be performed by using the mean control chart and the extreme difference control chart in combination. The specific method is to divide the bag length data detected by the unit into K groups in the order of m. Find the average X-average value of each group and the range R of each group. Draw the mean and range control charts respectively. . The average control chart mainly observes and analyzes the changing trend of the average value; the extreme difference control chart mainly observes and analyzes the dispersion of accidental errors. Determine whether the process is stable based on the points on the control chart, the center line, and the upper and lower control limits.
The center line of the mean chart: X 0 = the number of sets of mean values ​​for each group. The center line of the control chart: R 0 = the upper line of each group and the average value of the control chart: UCLX=X 0+A ·R 0
The lower control line of the mean chart: LUCX=X 0-A·R 0
Upper Control Line of Range Control Chart: UCLR=D 1·R 0
The lower control line of the range control chart: LCLR=D 2·R 0
Among them, the values ​​of A 1, D 1, D 2 can be determined from the control chart by the coefficient table to find the number of components per module m AD 1 D 2
4 0.73 2.28
5 0.58 2.11
6 0.48 2.00
7 0.42 1.92 0.08
8 0.37 1.86 0.14
9 0.34 1.82 0.18
10 0.31 1.78 0.22
An example is given to illustrate the use of the mean and range controls. The production bag barrel with a bag length of 800mm requires a tolerance range of ±5mm. The unit automatically measures the bag length and prints, the value is accurate to 1mm, the number of detected pieces is 100, and the production order is divided into 25 groups, and the number of each component is 4. The above calculation method obtains mean and range control chart data.
X 0=800.44
UCLX=803.62
LCLX=797.26
R 0=4.36
UCLR=9.95
Based on the group number as the abscissa, the mean value and the range difference control chart can be drawn for each set of average values, each group's range is the ordinate, and the standard deviation σ=2.086mm, the standard bag length XO=800mm, and the actual bag are calculated. The average value of the long-term average X is 800.44 mm, and the process capability index CPK is 0.74, which is a level 3, indicating that the process capability is insufficient and a small number of defective products may appear. The root cause of the search error is mainly due to the fact that the traction tension of the bag-cutting machine is too large, resulting in slippage after being pulled tight, and the traction speed is not uniform. After adjusting the pulling tension, the pulling speed is uniform, and 100 bags are measured again to measure the length of the bag. The drawing data is calculated according to the same method as described above. X 0 = 800.36, R 0 = 2.84, U-CLX = 802 .43, LCLX = 798.31, UCLR = 6.48, also with the group number as the abscissa, each group of average, each set of range for the ordinate to draw the mean, range control chart.
All points did not exceed the control limits, indicating that the process of this process is stable. Divide the data into 6 groups, and make the frequency distribution table and histogram and calculate the standard deviation of the normal distribution curve and the dispersion range σ=1.38. Calculate the process capability index CPK = 1.12, indicating that the process capability is acceptable, but it must be strictly controlled and carefully tested, otherwise unqualified products will be easily produced.
When using the average control chart and the range control chart, it should be noted that the point on the control chart first does not exceed the control limit. In order to avoid erroneous judgment due to small amount of data, it is stipulated that there should be at least 25 consecutive points within the control limits to determine; secondly, whether there is an abnormality in the distribution pattern of points should be paid special attention to: (1) Continuous More than 7 points appear on one side of the centerline; (2) More points appear intermittently on one side of the centerline; (3) More than 7 points rise or fall continuously; (4) Points rise or fall There are obvious periodic intervals; (5) More points are close to upper and lower control limits. If the above situation occurs, the cause should be promptly identified and the necessary measures taken.
The above method of controlling the length of the bag barrel has been successfully applied in the production process of the unit. Firstly, the bag length data is automatically measured by the detection device, and then the data is processed by the microcomputer. The standard deviation, average value, range, and process capability index values ​​can be calculated, and the histogram, mean value control chart and range control chart can be drawn. , It can also complete the alarm function of control maps and distribution defects. Yao Jiansong; Che Shiming; Yang Hao; Li Yuejin; Liang Guohe
Bags occupy a very important position in the packaging products, such as cement, flour, starch, feed, fertilizers, chemical raw materials, agricultural and sideline products and mineral products such as powder and granular materials are mostly bag packaging. The length of the bag determines the volume of the bag, and ultimately determines the amount of goods. The length of the packaging bag is insufficient, which can easily lead to breaking of the package or insufficient amount of goods during potting and damage the interests of the customer. The length of the packaging bag is too long, resulting in waste of packaging materials and detrimental to the interests of the production enterprise. To increase the accuracy of the package quantification, we must first control the length of the package.
ZXJ-1000C Automatic Printing Bag Making Machine (hereinafter referred to as the unit) is a professional equipment for producing packaging bags. It is equipped with an online measuring device that can automatically measure the length of the bag during the production process and print the sampling data. According to the above, the stability of the production process can be determined by using the X-average control chart and the R-range control chart, and the unstable factors in the production process can be found and eliminated in time to ensure the accuracy of the bag barrel length.
Bag barrel length error and distribution pattern The unit adopts changing the gear ratio between the cutter and the traction to achieve different bag length adjustments. When the cutting speed is fixed and the pulling speed is slow, the cut bag is short. When the pulling speed is fast, the cut bag is long. Once the transmission ratio is fixed, the length of the cut bag is fixed. It is equal to the length of the reciprocating bag barrel, which is the nominal bag length. However, testing the length of a batch of bags will reveal that, except for a portion that is just equal to the length of the nominal bag, some are shorter than the nominal length of the bag, and some are longer than the nominal length of the bag, and the number of excesses and shortfalls is approximately equal. According to the principle of mathematical statistics, this phenomenon is normal. For example, the nominal bag length of a production cement packaging bag is 800mm, and 100 inspections are randomly selected in a batch of bag cylinders. The maximum length is 805mm, and the shortest is 796mm. The distribution range is 805-796=9mm.
Take each length of bag tube as a group, a total of K groups, calculate the frequency of each group. If the length of each group of bags is the abscissa and the frequency is the ordinate, the frequency distribution histogram can be drawn. The top edge of each column of the histogram is connected with a smooth curve. This curve reflects the frequency distribution rule of bag barrel length, which is the actual distribution curve. If there are many pieces detected and the group distance is very small, the smooth curve can be described by the theoretical curve—normal distribution curve. According to the normal distribution theory, an important parameter standard deviation σ in the normal distribution curve can be calculated.
The allowable error of the length of a given bag is generally given in the production. The error of the length of the produced bag should be within this range. This depends on the quality of work of the production process, ie, the cut used in the bag cutting process of the unit. Bag machine performance is closely related. The degree of assurance of the production process to the work quality is called the process capability. The common process capability index, CPK, is used to represent the formula: CPK=(T-2XO+2X mean)6σ. Where T is the allowable tolerance range for the bag length, XO is the standard bag length value, and X mean is the average value of the actual bag length. Process capability is divided into five grades: special grade, grade one, grade two, grade three, and grade four. If the grade is too high, the process capability is too full and not economical; if it is too low, the process capability is insufficient, and unqualified products will appear. If the process capability index CPK belongs to the second level, indicating that the process capability is acceptable, monitoring should be closely watched.
The quality control method of the bag barrel production process To verify the stability of the bag cutting process and understand the dynamic situation of the quality parameter change over time, the quality control of the production process can be performed by using the mean control chart and the extreme difference control chart in combination. The specific method is to divide the bag length data detected by the unit into K groups in the order of m. Find the average X-average value of each group and the range R of each group. Draw the mean and range control charts respectively. . The average control chart mainly observes and analyzes the changing trend of the average value; the extreme difference control chart mainly observes and analyzes the dispersion of accidental errors. Determine whether the process is stable based on the points on the control chart, the center line, and the upper and lower control limits.
The center line of the mean chart: X 0 = the number of sets of mean values ​​for each group. The center line of the control chart: R 0 = the upper line of each group and the average value of the control chart: UCLX=X 0+A ·R 0
The lower control line of the mean chart: LUCX=X 0-A·R 0
Upper Control Line of Range Control Chart: UCLR=D 1·R 0
The lower control line of the range control chart: LCLR=D 2·R 0
Among them, the values ​​of A 1, D 1, D 2 can be determined from the control chart by the coefficient table to find the number of components per module m AD 1 D 2
4 0.73 2.28
5 0.58 2.11
6 0.48 2.00
7 0.42 1.92 0.08
8 0.37 1.86 0.14
9 0.34 1.82 0.18
10 0.31 1.78 0.22
An example is given to illustrate the use of the mean and range controls. The production bag barrel with a bag length of 800mm requires a tolerance range of ±5mm. The unit automatically measures the bag length and prints, the value is accurate to 1mm, the number of detected pieces is 100, and the production order is divided into 25 groups, and the number of each component is 4. The above calculation method obtains mean and range control chart data.
X 0=800.44
UCLX=803.62
LCLX=797.26
R 0=4.36
UCLR=9.95
Based on the group number as the abscissa, the mean value and the range difference control chart can be drawn for each set of average values, each group's range is the ordinate, and the standard deviation σ=2.086mm, the standard bag length XO=800mm, and the actual bag are calculated. The average value of the long-term average X is 800.44 mm, and the process capability index CPK is 0.74, which is a level 3, indicating that the process capability is insufficient and a small number of defective products may appear. The root cause of the search error is mainly due to the fact that the traction tension of the bag-cutting machine is too large, resulting in slippage after being pulled tight, and the traction speed is not uniform. After adjusting the pulling tension, the pulling speed is uniform, and 100 bags are measured again to measure the length of the bag. The drawing data is calculated according to the same method as described above. X 0 = 800.36, R 0 = 2.84, U-CLX = 802 .43, LCLX = 798.31, UCLR = 6.48, also with the group number as the abscissa, each group of average, each set of range for the ordinate to draw the mean, range control chart.
All points did not exceed the control limits, indicating that the process of this process is stable. Divide the data into 6 groups, and make the frequency distribution table and histogram and calculate the standard deviation of the normal distribution curve and the dispersion range σ=1.38. Calculate the process capability index CPK = 1.12, indicating that the process capability is acceptable, but it must be strictly controlled and carefully tested, otherwise unqualified products will be easily produced.
When using the average control chart and the range control chart, it should be noted that the point on the control chart first does not exceed the control limit. In order to avoid erroneous judgment due to small amount of data, it is stipulated that there should be at least 25 consecutive points within the control limits to determine; secondly, whether there is an abnormality in the distribution pattern of points should be paid special attention to: (1) Continuous More than 7 points appear on one side of the centerline; (2) More points appear intermittently on one side of the centerline; (3) More than 7 points rise or fall continuously; (4) Points rise or fall There are obvious periodic intervals; (5) More points are close to upper and lower control limits. If the above situation occurs, the cause should be promptly identified and the necessary measures taken.
The above method of controlling the length of the bag barrel has been successfully applied in the production process of the unit. Firstly, the bag length data is automatically measured by the detection device, and then the data is processed by the microcomputer. The standard deviation, average value, range, and process capability index values ​​can be calculated, and the histogram, mean value control chart and range control chart can be drawn. , It can also complete the alarm function of control maps and distribution defects. Yao Jiansong; Che Shiming; Yang Hao; Li Yuejin; Liang Guohe
Towel Set,Hand Towels ,Decorative Towels ,Luxury Towels
Towel & Handkerchief Co., Ltd. , http://www.nbtowels.com