PROCESS CAPABILITYBPT2423 – STATISTICAL PROCESS CONTROL

CHAPTER OUTLINE Estimation of Population σ from Sample Data Control Limits versus Specification Limits The 6σ Spread versus Specification Limits Calculating Process Capability Indices

LESSON OUTCOMES Understand the difference between

specification limits and control limits Learn to calculate and interpret the process

capability indices: Cp, Cr and Cpk

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 B

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) :

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 reality

CONTROL LIMIT vs SPEC. LIMIT

THE 6σ SPREAD vs SPEC. LIMITSThe spread of the individuals in a process, 6σ, is the measure used to compare the realities of production with the desires of the customers

Case I : 6σ < 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.

Case II : 6σ = USL - LSL

Case III : 6σ > 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 6σ SPREAD vs SPEC. LIMITS

CAPABILITY INDICESCapability Index, Cp

Cp > 1.00 : Case I situation exists. The greater this value, the betterCp = 1.00 : Case II situation exists. This is not optimal, but it is feasibleCp < 1.00 : Case III situation exists. Value of less than 1 are undesirable and reflect the process’s inability to meet the specification

CAPABILITY INDEX & 3 CASES

CAPABILITY INDICESCapability Ratio, Cr

Cr < 1.00 : Case ICr = 1.00 : Case IICr > 1.00 : Case III

Centering of the Process, Cpk

Where Z (min) is the smaller of :

MEANINGS OF Cpk MEASURES

Cpk = negative number

Cpk = zero

Cpk = between 0 and 1

Cpk = 1

Cpk > 1

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

RELATIONSHIP BETWEEN Cp AND Cpk

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

2. The Cp value does not reflect process centering3. When the process is centered Cp = Cpk

4. Cpk is always less than or equal to Cp

5. When Cp is greater than or equal to 1.0 and Cpk has a value of 1.00 or more, it indicates the process is producing product that conforms to specifications

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

7. A Cp value of less than 1.00 indicates that the process is not capable8. A Cpk value of zero indicates the process average is equal to one of the

specification limits9. A negative Cpk value indicates that the average is outside the specification limits

Cp AND Cpk FOR THE 3 CASES

EXERCISEHotels 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 Cp and Cpk

State of Process Control A 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 causes

When a process is under control, it is considered stable and the amount of future variation is predictable

Several benefits to a stable process: There is a rational basis for planning Quality levels are predictable When improvements are made, the effects of the

changes can be determined quickly and reliably

REVISE THE CHARTS

Control Chart Interpretation Correct interpretation of control charts is essential to

managing a process Understanding the sources and potential causes of

variation is critical to good management decisions Misinterpretation can lead to a variety of losses,

including: Blaming people for problems that they cannot control Spending time and money looking for problems that do not

exist Spending time and money on process adjustments or new

equipment that are not necessary Taking action where no action is warranted

REVISE THE CHARTS

There are two circumstances under which the control chart is revised and new limits calculated If a charts exhibits good control and any changes made to

improve the process are permanent When the new operating conditions become routine and no

out-of-control signals have been seen The revisions provide a better estimate of the population

standard deviation – a better understanding of the entire process can be gained

Control limits are also revised if pattern exist – provided that the patterns have been identified and eliminated

The new limits will reflect the changes and improvements made to the process – used to judge the process behavior in the future

REVISE THE CHARTS

Steps taken to revise the charts:1. Interpret the original chart2. Isolate the cause3. Take corrective action4. Revise 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 chart

The points removed will equal zero and the calculations will continue from there

REVISE THE CHARTS