# Learning Objectives. Understand how to select the correct control chart for an application. Know how to fill out and maintain a control chart.

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1 CONTROL CHARTS

2 Learning Objectives Understand how to select the correct control chart for an application. Know how to fill out and maintain a control chart. Know how to interpret a control chart to determine the occurrence of special causes of variation.

3 How does it help? Control charts are useful to: determine the occurrence of of special cause situations. Utilize the opportunities presented by special cause situations to to identify and correct the occurrence of of the special causes..

4 IMPROVEMENT ROADMAP Uses of Control Charts Characterization Phase 1: Measurement Phase 2: Analysis Common Uses Control charts can be effectively used to determine special cause situations in the Measurement and Analysis phases Breakthrough Strategy Phase 3: Improvement Optimization Phase 4: Control

5 KEYS TO SUCCESS Use control charts on only a few critical output characteristics Ensure that you have the means to investigate any special cause

6 What is a Special Cause? Remember our earlier work with confidence intervals? Any occurrence which falls outside the confidence interval has a low probability of occurring by random chance and therefore is significantly different. If we can identify and correct the cause, we have an opportunity to significantly improve the stability of the process. Due to the amount of data involved, control charts have historically used 99% confidence for determining the occurrence of these special causes Special cause occurrence. Point Value +/- 3s = 99% Confidence Band X

7 What is a Control Chart? A control chart is simply a run chart with confidence intervals calculated and drawn in. These Statistical control limits form the trip wires which enable us to determine when a process characteristic is operating under the influence of a Special cause. +/- 3s = 99% Confidence Interval

8 So how do I construct a control chart? First things first: Select the metric to to be evaluated Select the right control chart for the metric Gather enough data to to calculate the control limits Plot the data on the chart Draw the control limits (UCL & LCL) onto the chart. Continue the run, investigating and correcting the cause of of any out of of control occurrence.

9 How do I select the correct chart? Variable What type of data do I have? Attribute What subgroup size is available? Counting defects or defectives? n > 10 1 < n < 10 n = 1 X-s Chart X-R Chart Note: A defective unit can have more than one defect. IMR Chart Defectives Constant Sample Size? yes no Defects Constant Opportunity? yes no np Chart p Chart c Chart u Chart

10 How do I calculate the control limits? X R Chart For the averages chart: CL = X UCL = X + A R 2 LCL = X A R 2 n D4 D3 A For the range chart: CL = R UCL LCL = D4 = D3 R R X = average of the subgroup averages R = average of the subgroup range values = a constant function of subgroup size (n) A 2 UCL = upper control limit LCL = lower control limit

11 How do I calculate the control limits? p and np Charts For varied sample size: For constant sample size: UCLp = P + 3 P ( 1 P) n ( ) UCL = np + 3 np np 1 P LCL p = P 3 P ( 1 P) n ( ) LCL = np 3 np np 1 P Note: P charts have an individually calculated control limit for each point plotted P = number of rejects in the subgroup/number inspected in subgroup P = total number of rejects/total number inspected n = number inspected in subgroup

12 How do I calculate the control limits? c and u Charts For varied opportunity (u): For constant opportunity (c): UCLu = U +3 U n UCL = C C +3 C LCL u = U 3 U n LCLC = C 3 C Note: U charts have an individually calculated control limit for each point plotted C = total number of nonconformities/total number of subgroups U = total number of nonconformities/total units evaluated n = number evaluated in subgroup

13 How do I interpret the charts? The process is said to be out of control if: One or more points fall outside of the control limits When you divide the chart into zones as shown and: 2 out of 3 points on the same side of the centerline in Zone A 4 out of 5 points on the same side of the centerline in Zone A or B 9 successive points on one side of the centerline 6 successive points successively increasing or decreasing 14 points successively alternating up and down 15 points in a row within Zone C (above and/or below centerline) Zone A Zone B Zone C Zone C Zone B Zone A Upper Control Limit (UCL) Centerline/Average Lower Control Limit (LCL)

14 What do I do when it s out of control? Time to Find and Fix the cause Look for patterns in in the data Analyze the out of of control occurrence Fishbone diagrams and Hypothesis tests are valuable discovery tools.

15 Learning Objectives Understand how to select the correct control chart for an application. Know how to fill out and maintain a control chart. Know how to interpret a control chart to determine out of control situations.

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