STATISTICS AND QUALITYThe P Chart

Statistical Quality Control (SQC)term used to describe the set of statistical tools used by quality professionals.

Statistical quality control can be divided into three broad categories:Descriptive Statistics - used to describe quality

characteristics and relationships. Included are statistics such as the mean, standard deviation, the range, and a measure of the distribution of data.

Statistical Process Control (SPC) - involves inspecting a random sample of the output from a process and deciding whether the process is producing products with characteristics that fall within a predetermined range. SPC answers the question of whether the process is functioning properly or not.

Statistical Quality Control Category (cont’d)

Acceptance Sampling - process of randomly inspecting a sample of goods and deciding whether to accept the entire lot based on the results. Acceptance sampling determines whether a batch of goods should be accepted or rejected.

Statistical Process Control Methods

Extends the use of descriptive statistics to monitor the quality of the product and process. There are common and assignable causes of variation in the production of every product. Using statistical process control we want to determine the amount of variation that is common or normal. Then we monitor the production process to make sure production stays within this normal range. To make sure that the process is in a state of control, and to monitor the production process, control charts are used.

SPC in TQMSPC

tool for identifying problems and make improvements

contributes to the TQM’s goal of continuous improvements

SOURCES OF VARIATION:

Common or Random causes of Variation – are based on random causes that we cannot identify. These types of variation are unavoidable and are due to slight differences in processing.

Assignable causes of Variation – variation observed that involves variations where the causes can be precisely identified and eliminated (i.e. poor quality in raw materials, an employee who needs more training, or a machine in need of repair).

VariabilityNon-Random

special causesdue to identifiable

factorscan be modified

through operator or management action

Randomcommon causesinherent in a

processcan be eliminated

only through improvements in the system

Copyright 2006 John Wiley & Sons, Inc.

Control Chartone of the most commonly used tool in

statistical process control for monitoring the production process

graph that shows whether a sample of data falls within the common or normal range of variation.

has upper and lower control limits that separate common from assignable causes of variation. The common range of variation is defined by the use of control chart limits.

Example of a Quality Control Chart for Cocoa Fizz

Control Charts contain:Center Line (CL) - is the mean, or average, of

the quality characteristic that is being measured.

Upper Control Limit (UCL) - the maximum acceptable variation from the mean for a process that is in a state of control.

Lower Control Limit (LCL) - the minimum acceptable variation from the mean for a process that is in a state of control.

Remember that in Control Charts:A point that plots within

the control limits indicates the process is in control

A point that plots outside the control limits is evidence that the process is out of control

There is a close connection between control charts and hypothesis testing

Quality MeasuresAttribute

a product characteristic that can be evaluated with a discrete response

good – bad; yes – no

Variablea product characteristic that is continuous

and can be measuredweight - length

Types of Control Charts:Control Chart for Variables - used to monitor

characteristics that can be measured and have a continuum of values, such as height, weight, or volume.

Mean (x- Bar) ChartsRange (R) Charts

Control Chart for Attributes - is used to monitor characteristics that have discrete values and can be counted. Often they can be evaluated with a simple yes or no decision. Examples include color, taste, or smell.

P- ChartsC- Charts

P- Chartused to measure the proportion that is defective

in a sample

The computation of the center line as well as the upper and lower control limits is similar to the computation for the other kinds of control charts. The center line is computed as the average proportion defective in the population, . This is obtained by taking a number of samples of observations at random and computing the average value of p across all samples.

p-ChartUCL = p + zp

LCL = p - zp

z = number of standard deviations from process averagep = sample proportion defective; an estimate of process averagep = standard deviation of sample proportion

n = sample size

p = p(1 - p)

n

p-Chart Example

20 samples of 100 pairs of jeans

NUMBER OF PROPORTIONSAMPLE DEFECTIVES DEFECTIVE

1 6 .06

2 0 .00

3 4 .04

: : :

: : :

20 18 .18

200

p-Chart Example (cont.)

UCL = p + z = 0.10 + 3p(1 - p)

n

0.10(1 - 0.10)

100

UCL = 0.190

LCL = 0.010

LCL = p - z = 0.10 - 3p(1 - p)

n

0.10(1 - 0.10)

100

= 200 / 20(100) = 0.10total defectives

total sample observationsp =

p-Chart Example (cont.)

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Pro

po

rtio

n d

efec

tive

Sample number2 4 6 8 10 12 14 16 18 20

UCL = 0.190

LCL = 0.010

p = 0.10

EXERCISE:Solve the given example using PH STAT or

any other Statistical Package.

References:Journal of Statistical SoftwareStatitCustomQC Overviewhttp://

www.statisticalsolutions.net/spc_basics.phpTHE BASICS OF STATISTICAL PROCESS

CONTROL & PROCESS BEHAVIOUR CHARTING A User’s

Guide to SPC by David HowardSPC Count VariableSTATISTICAL PROCESS CONTROL Chapter

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