PROCESS CAPABILITY - PowerPoint Presentation

Slide1

PROCESS CAPABILITY

BPT2423 – STATISTICAL PROCESS CONTROLSlide2

CHAPTER OUTLINE

Estimation of Population σ

from Sample Data

Control Limits versus Specification Limits

The 6σ Spread versus Specification LimitsCalculating Process Capability IndicesSlide3

LESSON OUTCOMES

Understand the difference between specification limits and control limits

Learn to calculate and interpret the process capability indices: C

p

, Cr and C

pkSlide4

INTRODUCTION

Process capability refers to the ability of a process to produce products or provide services capable of meeting the specifications set by the customer or designer

Knowing the process capability gives insight into whether or not the process will be able to meet future demands place on it

Determining the process capability aids industry in meeting their customer demands – a customer may ask for part tolerances so fine that the machines are not capable of producing to that level of exactness

An undersized part A may not mate correctly with an oversized part BSlide5

ESTIMATION OF POPULATION σ

Sample values and their averages provide insight into the behavior of an entire population

ẋ becomes a more reliable estimate of µ as the sample size is increased

If the process can be assumed to be normal, the population standard deviation can be estimated from either the standard deviation associated with the sample standard deviation (s) or the range (R) :Slide6

CONTROL LIMIT vs SPEC. LIMIT

It is important to note that a process in statistical control will not necessarily meet specifications as established by the customer

There is a difference between a process conforming to specifications and a process performing within statistical control

Specifications

communicate what the customers expect, want or need from the process – considered the voice of the customer

Control limits

are

the voice of the process

– a prediction of the variation that the process will exhibit in the near future

Difference : specifications relay wishes and control limits tell of realitySlide7

CONTROL LIMIT vs SPEC. LIMITSlide8

THE 6σ

SPREAD vs SPEC. LIMITS

The spread of the individuals in a process, 6

σ

, is the measure used to compare the realities of production with the desires of the customers

Case I : 6

σ

< USL - LSL

This allows for more room for process shifts while staying within the specifications.

Notice that even if the process drifts out of control, the change must be dramatic before the parts are considered out of specification.Slide9

Case II : 6σ = USL - LSLCase III : 6

σ > USL - LSL

A shift in the process mean or an increase in the variation present in the process will creates an out of specification situation

Process is incapable of meeting the specification set by the customer. To correct this problem, management intervention will be necessary. The capability of the process cannot be improved without changing the existing process

THE 6

σ

SPREAD vs SPEC. LIMITSSlide10

CAPABILITY INDICES

Capability Index, C

p

Cp > 1.00 : Case I situation exists. The greater this value, the better

Cp = 1.00 : Case II situation exists. This is not optimal, but it is feasible

Cp < 1.00 : Case III situation exists. Value of less than 1

are undesirable

and reflect the process’s inability to meet the specificationSlide11

CAPABILITY INDEX & 3 CASESSlide12

CAPABILITY INDICES

Capability Ratio, C

r

Cr < 1.00 : Case I

Cr = 1.00 : Case II

Cr > 1.00 : Case III

Centering of the Process, C

pk

Where Z (min) is the smaller of :Slide13

MEANINGS OF C

pk

MEASURES

C

pk

= negative number

C

pk

= zero

C

pk

= between 0 and 1

C

pk

= 1

C

pk

> 1

Note : C

pk

is the ratio that reflects how the process is performing in relation to a nominal, center or target value.Slide14

RELATIONSHIP BETWEEN

C

p

AND

C

pk

When C

p

has a value of 1.0 or greater, the process is producing product capable of meeting specifications

The C

p

value does not reflect process centering

When the process is centered C

p

= C

pk

C

pk

is always less than or equal to C

p

When C

p

is greater than or equal to 1.0 and C

pk

has a value of 1.00 or more, it indicates the process is producing product that conforms to specifications

When C

pk

has a value less than 1.00, it indicates the process is producing product that does not conform to specifications

A C

p

value of less than 1.00 indicates that the process is not capable

A C

pk

value of zero indicates the process average is equal to one of the specification limits

A negative C

pk

value indicates that the average is outside the specification limitsSlide15

Cp

AND

C

pk

FOR THE 3 CASESSlide16

EXERCISE

Hotels use statistical information and control charts to track their performance on a variety of indicators. Recently a hotel manager has been asked whether or not his team is capable of maintaining scores between 8 and 10 (on a scale of 1 to 10) for “overall cleanliness of room”. The most recent data has a mean of 8.624, a standard deviation of 1.446 and n = 10. calculate and interpret C

p

and C

pkSlide17

State of Process ControlA process is considered to be in a state of control or under control when the performance of the process falls within the statistically calculated control limits and exhibits only chance / common causesWhen a process is under control, it is considered stable and the amount of future variation is predictableSeveral benefits to a stable process:There is a rational basis for planning

Quality levels are predictableWhen improvements are made, the effects of the changes can be determined quickly and reliably

REVISE THE CHARTSSlide18

Control Chart InterpretationCorrect interpretation of control charts is essential to managing a processUnderstanding the sources and potential causes of variation is critical to good management decisionsMisinterpretation can lead to a variety of losses, including:Blaming people for problems that they cannot controlSpending time and money looking for problems that do not exist

Spending time and money on process adjustments or new equipment that are not necessaryTaking action where no action is warranted

REVISE THE CHARTSSlide19

There are two circumstances under which the control chart is revised and new limits calculatedIf a charts exhibits good control and any changes made to improve the process are permanentWhen the new operating conditions become routine and no out-of-control signals have been seenThe revisions provide a better estimate of the population standard deviation – a better understanding of the entire process can be gainedControl limits are also revised if pattern exist

– provided that the patterns have been identified and eliminatedThe new limits will reflect the changes and improvements made to the process – used to judge the process behavior in the future

REVISE THE CHARTSSlide20

Steps taken to revise the charts:Interpret the original chartIsolate the causeTake corrective actionRevise the chart

It is necessary to remove any undesirable points or groups of points, the causes of which have been determined and corrected

If no cause can be found and corrected

, then the

points cannot be removed from the chartThe points removed will equal zero and the calculations will continue from there

REVISE THE CHARTS