Using Control Charts to Keep an Eye on Variability Operations Management Dr. Ron Lembke

Goal of Control Charts  See if process is “in control” Process should show random values No trends or unlikely patterns  Visual representation much easier to interpret Tables of data – any patterns? Spot trends, unlikely patterns easily

NFL Control Chart?

Control Charts UCL LCL avg Values Sample Number

Definitions of Out of Control 1. No points outside control limits 2. Same number above & below center line 3. Points seem to fall randomly above and below center line 4. Most are near the center line, only a few are close to control limits 1. 8 Consecutive pts on one side of centerline 2. 2 of 3 points in outer third 3. 4 of 5 in outer two-thirds region

Control Charts NormalToo LowToo high 5 above, or belowRun of 5 Extreme variability

Control Charts UCL LCL avg 1σ1σ 2σ2σ 2σ2σ 1σ1σ

Control Charts 2 out of 3 in the outer third

Out of Control Point?  Is there an “assignable cause?” Or day-to-day variability?  If not usual variability, GET IT OUT Remove data point from data set, and recalculate control limits  If it is regular, day-to-day variability, LEAVE IT IN Include it when calculating control limits

Attributes vs. Variables Attributes:  Good / bad, works / doesn’t  count % bad (P chart)  count # defects / item (C chart) Variables:  measure length, weight, temperature (x-bar chart)  measure variability in length (R chart)

p Chart Control Limits # Defective Items in Sample i # Samples Sample i Size z = 2 for 95.5% limits z = 3 for 99.7% limits p = avg defect rate n = avg sample size s p = sample std dev

p Chart Example You’re manager of a 1,700 room hotel. For 7 days, you collect data on the readiness of all of the rooms that someone checked out of. Is the process in control (use z = 3)? © 1995 Corel Corp.

p Chart Hotel Data # RoomsNo. NotProportion DaynReady p 11, /1,300 =

p Chart Control Limits

p Chart Solution

Hotel Room Readiness P-Bar

R Chart  Type of variables control chart Interval or ratio scaled numerical data  Shows sample ranges over time Difference between smallest & largest values in inspection sample  Monitors variability in process  Example: Weigh samples of coffee & compute ranges of samples; Plot

Why do we need 2 charts? Consistent, but the average is in the wrong place UCL LCL UCL LCL X-Bar Chart R Chart The average works out ok, but way too much variability between points X-Bar Chart R Chart UCL LCL UCL LCL

You’re manager of a 500- room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control? Hotel Example

Hotel Data DayDelivery Time

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange Sample Mean =

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange Sample Range = LargestSmallest

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange

R Chart Control Limits Sample Range at Time i # Samples Table 10.3, p.433

Control Chart Limits, p.161

R Chart Control Limits

R Chart Solution

 X Chart Control Limits Sample Range at Time i # Samples Sample Mean at Time i

 X Chart Control Limits A 2 from Table 10-3

Control Chart Factors, p. 161

R &  X Chart Hotel Data Sample DayDelivery TimeMeanRange

 X Chart Control Limits

 X Chart Solution*

Summary  Overview of “In Control”  Attribute vs Continuous Control Charts  P Charts  X-bar and R charts