A-32AMitutoyo reserves the right to change any or all aspects of any product specication, including prices, designs and service content, without notice.A-32Specic examples of a process capability index (Cp) (bilateral tolerance)Note that Cp only represents the relationship between the tolerance limits and the process dispersion and does not consider the position of the process mean.Note: A process capability index that takes the difference between the process mean from the target process mean into consideration is generally called Cpk, which is the upper tolerance (USL minus the mean) divided by 3 (half of process capability) or the lower tolerance (the mean value minus LSL) divided by 3 , whichever is smaller.Control chartUsed to control the process by separating the process variation into that due to chance causes and that due to a malfunction. The control chart consists of one center line (CL) and the control limit lines rationally determined above and below it (UCL and LCL). It can be said that the process is in a state of statistical control if all points are within the upper and lower control limit lines without notable trends when the characteristic values that represent the process output are plotted. The control chart is a useful tool for controlling process output, and therefore quality.Chance causesThese causes of variation are of relatively low importance. Chance causes are technologically or economically impossible to eliminate even if they can be identied.X-R control chartA control chart used for process control that provides the most information on the process. The X-R control chart consists of the X control chart that uses the mean of each subgroup for control to monitor abnormal bias of the process mean and the R control chart that uses the range for control to monitor abnormal variation. Usually, both charts are used together.References- JIS Quality Control Handbook (Japanese Standards Association)Z 8101: 1981Z 8101-1: 1999Z 8101-2: 1999Z 9020: 1999Z 9021: 1998Note: This part of 'Quick Guide to Precision Measuring Instruments' (A-31 to A-32) has been written by Mitutoyo based on its own interpretation of the JIS Quality Control Handbook published by the Japanese Standards Association.How to read the control chartTypical trends of successive point position in the control chart that are considered undesirable are shown below. These trends are taken to mean that a ‘special cause’ is affecting the process output and that action from the process operator is required to remedy the situation. These determination rules only provide a guideline. Take the process-specic variation into consideration when actually making determination rules. Assuming that the upper and the lower control limits are 3 away from the center line, divide the control chart into six regions at intervals of 1 to apply the following rules. These rules are applicable to the X control chart and the X control chart. Note that these 'trend rules for action' were formulated assuming a normal distribution. Rules can be formulated to suit any other distribution.σ6σLSLUSLσ6σ8σLSLUSLσ6σ10σLSLUSLThe process capability is barely achieved as the 6 sigma process limits are coincident with the tolerance limits.Cp=1The process capability is the minimum value that can be generally accepted as it is no closer than 1 sigma to the tolerance limits.Cp=1.33The process capability is sufcient as it is no closer than 2 sigma to the tolerance limits.Cp=1.67Upper control limit (UCL)Center line (CL)Lower control limit (LCL)Subgroup number1 2 3 4 5 6 7UCLLCLXX+3X+2X+1X−1X−2X−31) There is a point beyond either of the control limit lines (±3 ).UCLLCLXX+3X+2X+1X−1X−2X−32) Nine consecutive points are to one side of the center line.UCLLCLXX+3X+2X+1X−1X−2X−33) Six points consecutively increase or decrease.UCLLCLXX+3X+2X+1X−1X−2X−34) 14 points alternately increase and decrease.UCLLCLXX+3X+2X+1X−1X−2X−35) Two of three consecutive points are over ±2 from the center line on either side.UCLLCLXX+3X+2X+1X−1X−2X−36) Four of ve consecutive points are over ±1 from the center line on either side.UCLLCLXX+3X+2X+1X−1X−2X−37) There are 15 consecutive points within ±1 from the center line.UCLLCLXX+3X+2X+1X−1X−2X−38) There are eight consecutive points over ±1 from the center line.A

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