SPC – Attribute Control Charts Chapter 6 - Part 2 SPC – Attribute Control Charts

Types of Control Charts Attribute charts Monitor fraction of defective units Monitor number of defects Difference between “defective unit” and a “defect?” A defective unit is a unit that is either defective. A defect is flaw on a given unit of a product. A unit can have many defects. A defective unit may be defined as, for example, a unit that has 3 or more defects.

Types of Control Charts Variables charts Monitors continuous quality characteristics. Continuous values (variables data) can theoretically assume an infinite number of values in some interval. Time Weight Ounces Diameter

Types of Control Control Chart Monitors Attribute control charts p chart Process fraction defective c chart number of defects u chart defects per unit Variables control charts X-bar chart Process mean R chart (Range Chart) Process variability

Use of p-Charts When observations can be placed into two categories. Good or bad Pass or fail Operate or doesn’t operate

p-chart A company that makes light bulbs wants to monitor the fraction of defective bulbs. The company decides to select a random sample of 100 bulbs in each day over a 5 day period Each of the 100 bulbs are tested to determine if they light up.

p-chart If a bulb does not light up, the bulb is defective. The company wants to Estimate the percentage of defective bulbs and Determine if the percentage of defective bulbs is increasing over time. A p chart is the appropriate tool for providing the company with this information.

Notation Sample size = n = 100 Number of samples (subgroups) = k = 5 X = number of defective bulbs in a sample p = sample fraction defective = ??? p-bar = estimated process fraction defective P = process fraction defective (unknown) p-bar is an estimate of P

Inspection Results

Compute p and p-bar

p-bar (Estimated Process Fraction Defective)

p-Chart Control Limits

p-Chart - Control Limits

Interpretation The estimated fraction of defective bulbs produced is .23. On Day 2, p was below the LCL. This means that a special cause occurred on that day to cause the process to go out of control. The special cause shifted the process fraction defective downward. This special cause was therefore favorable and should be ???

Interpretation After Day 2, the special cause lost its impact because on Day 4, the process appears to be back in control and at old fraction defective of .23. Until the special cause is identified and made part of the process, the process will be unstable and unpredictable. It is therefore impossible to obtain a statistical valid estimate of the process fraction defective because it can change from day to day.

Trend Within Control Limits Process fractions defective is shifting (trending) upward P = process fraction defective P P Sampling Distribution P P UCL LCL p-Chart

Applications Think of an application of a p-chart in: Sales Shipping department Law

Use of c-Charts When we are interested in monitoring number of defects on a given unit of product or service. Scratches, chips, dents on an airplane wing Errors on an invoice Pot holes on a 5-mile section of highway Complaints received per day Opportunity for a defect must be infinite. Probability of a defect on any one location or any one point in time must be small.

c-Chart c-chart notation: c = number of defects k = number of samples

c-Chart A car company wants to monitor the number of paint defects on a certain new model of one of its cars. Each day one car in inspected. The results after 5 days are shown on the next slide.

c-Chart

c-Chart - Mean

c-Chart – Control Limits

c-Chart – Control Limits

Conclusion Process shows upward trend. Even though trend is within the control limits, the process is out of control. Mean is shifting upward This is due to an unfavorable special cause. Must identify special cause and eliminate it from process. Who is responsible for finding and eliminating special cause?

Mini Case Think of an application of a c-chart bank.

u-Chart With a c chart, the sample size is one unit. A u-chart is like a c-chart, except that the sample size is greater than one unit. As a result, a u-chart tracks the number of defects per unit. A c-chart monitors the number of defects on one unit.

u-Chart A car company monitors the number of paint defects per car by taking a sample of 5 cars each day over the next 6 days. The results are shown on next side.

u-Chart

u-Chart

u-Chart

u-Chart

u-Chart

Conclusion The process appears stable. We can therefore get a statistically valid estimate the process mean number of defects per car. Our estimate of the mean number of paint defects per car is 10.5, the center line on the control chart. Thus, we expect each car to have, on average, 10.5 paint defects.

Conclusion Although the process is stable, the number of defects per car is too high. Deming calls this a stable process for the production of defective product. Important take away: A stable process (process in control) is not necessarily a good process because it can be in control at the wrong level. A stable process is predictable, but this doesn’t mean that what is being predicted is favorable.

Mini Case Who is responsible for improving this process? What is required to improve the process?

u-Chart vs. c-Chart If n = 1, u = c and Control limits of the two chart will therefore be the same.

Sample Size Control Chart When To Use Sample Size p-Chart Monitor the proportion of defectives in a process At least 50 c-Chart Monitor the number of defects 1 u-chart Monitor the number of defects per unit >1

In Practice You need 25 to 30 samples before computing initial control limits. When a special cause occurs, you should eliminate that sample and re-compute control limits if Special cause is identified Eliminated or made part of process To identify special causes, workers must keep log sheet, where they record any changes they make to the process.

Tracking Improvements UCL LCL Process not centered and not stable Process centered and stable Additional improvements made to the process