Demerit Control Charts

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  • 1. Mark Smallwood Quality Management March 15, 2006 Demerit Control Charts A control chart is an important tool in statistical process control. Control charts provide a way to see whether a process is in control by being able to see if the process is within the set upper and lower limits. Control charts were created by Walter A. Shewart in the 1920’s and then picked up and used widely by W. Edward Demings. The demerit control chart was created by H.F. Dodge while working at Bell Laboratories as a means to chart products with more than one kind of possible defect. Some defects had very serious consequences on the performance of the product and some were not very serious. Dodge classified the various types of defects into four different categories. Conerly, et al described these different categories as follows: Class quot;Aquot; Defects-Very Serious. -Will render unit totally unfit for service. -Will surely cause operating failure of the unit in service which cannot be readily corrected on the job. -Liable to cause personal injury or property damage. Class quot;Bquot; Defects-Serious. -Will probably, but not surely cause Class quot;Aquot; operating failure of the unit in service. -Will surely cause trouble of a nature less serious than Class quot;Aquot; -Will surely cause increased maintenance or decreased life. Class quot;Cquot; Defects-Moderately Serious. -Will possibly cause operating failure of the unit in service. Likely to cause trouble of a nature less serious than operating failure. -Likely to cause increased maintenance or decreased life. -Major defects of appearance, finish, or workmanship. Class quot;Dquot; Defects-Not Serious. -Will not cause operating failure of the unit in service. -Minor defects of appearance, finish, or workmanship.
  • 2. The different types of defects first need to be classified as either A, B, C, or D. Once each defect is classified, a weight is given to each class depending on its severity. The most common weights used today are 100 for As, 50 for Bs, 10 for Cs, and 1 for Ds. Demerits are a defect of a product multiplied by its weight. Steps to Constructing a Demerit Control Chart 1. Calculate the number of demerits per sample. This is done by counting the number of A, B, C, and D defects and multiplying that number by the weight of each class. If there were 3 Class A defects then 3 would be multiplied by the Class A weight of 100 for a total of 300 demerits. Add up the total demerits for each class to get the number of demerits per inspection sample represented by d. This process is shown in the following formula: d = 100XA + 50XB + 10XC + XD, where XA is the number of Class A defects 2. Find the average number of demerits per unit, represented by u, by taking the number of demerits per sample, d, and dividing by the number of units in the sample, N. u=d/N 3. Find the average number of each class of defect per unit. For Class A, take the total number of Class A defects in the sample and divide by the number of units in the sample, N. Repeat for each class. A= XA / N 4. Calculate the standard deviation through the following formula. σ = SqRt ((1002 A + 502 B + 102 C + D)/N) -where A is the average number of Class A defects per unit -N is the number of units in the sample
  • 3. 5. Calculate the control limits through the following formulas. Center Line = = 100 A + 50 B + 10 C + D Upper Control Limit = + 3σ Lower Control Limit = - 3σ 6. Now that the center line and control limits have been calculated, a control chart can be constructed. Information from future inspections can be charted using these limits to monitor the performance of the process and to insure that the process is in control. Example The easiest way to learn to construct a demerit control chart is by following an example using real numbers. For this example, the following information will be used. Sample size = 1500 Class of Defects A B C D Number of Defects 2 5 12 13 First, calculate the total number of demerits in the sample using the formula from step 1. d = 100(2) + 50(5) + 10(12) + 13 = 583 Next, find the average number of demerits per unit. u = 583/1500 = .39 Next, find the average number of each class of defect per unit. A = 2/1500 = .0013 B = 5/1500 = .0033 C = 12/1500 = .008 D = 13/1500 = .009 Next, calculate the standard deviation. σ = SqRt ((1002(.0013) + 502(.0033) + 102(.008) + .009)/N) = .12 Next, calculate the control limits. Center Line = 100(.0013) + 50(.0033) + 10(.008) + .009 =.384 UCL = .384 + 3(.12) = .744 LCL = .384 – 3(.12) = .024
  • 4. Additional Information A large quantity of information can be found discussing control charts and the uses of control charts. However, compared to regular control charts, not much has been published describing the demerit control chart and the reasons for it. The best resources found are the articles cited in the bibliography of this paper. A demerit chart is a type of control chart, however, so a lot can be learned about them by reading what is available about control charts and seeing how a demerit chart can relate.
  • 5. Bibliography Conerly, Michael D.; Jones, L Allison,; Woodall, William H. “Exact properties of demerit control charts.” Journal of Quality Technology. Milwaukee: Apr 1999.Vol.31, Iss. 2; pg. 207, 10 pgs. Crossley, Mark L. “Weighted Pareto Control Charts Work” http://www.qualitydigest.com/mar05/departments/what_works.shtml. Dawson, Cree S.; McCallum, Jr ,Charles J.; Murphy, R. Bradford; Wolman, Eric. “Operations Research at Bell Laboratories through the 1970s: Part III.” Operations Research, Vol. 48, No. 4. (Jul. - Aug., 2000), pp. 517-526. Dodge, H. F. (1928). quot;A Method of Rating a Manufactured Productquot;. Bell System Technical Journal 7, pp. 350-368.