Quality Management

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Control Chart

NP Chart

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(Ref: https://sixsigmastudyguide.com/attribute-chart-np-chart/)

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Part 1

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1. Choosing an np Chart.
2. What is np Chart.
3. From Lot 1 to Lot 20.
4. np Chart formula and calculations.

X-MR/i-MR Chart

X-bar R Chart

X-bar S Chart

U

Chart

C

Chart

P

Chart

NP

Chart

Subgroup

n = 1

eg: 20 Lots (20 Subgroups) and each Lot (Subgroup) has 1 Sample.

Subgroup

n = 2 to 9

eg: 20 Lots (20 Subgroups) and each Lot (Subgroups) has 2 to 9 Samples.

Subgroup

n > 10

eg: 20 Lots (20 Subgroups) and each Lot (Subgroup) has more than 10 Samples.

Sample Size

Variable

eg: 20 Lots (20 subgroups) and each Lot (Subgroup) uses different # of Samples.

Sample Size

Fixed

eg: 20 Lots (20 subgroups) and each Lot (Subgroup) uses same # of Samples.

Sample Size

Variable

eg: 20 Lots (20 subgroups) and each Lot (Subgroup) uses different # of Samples.

Sample Size

Fixed

eg: 20 Lots (20 subgroups) and each Lot (Subgroup) uses same # of Samples.

Subgroup size

eg: 10 Lots and each lot take 5 samples,

each Lot’s number contain 5 samples and that 5 sample is referred to as the Subgroup’s size.

Defects

eg: in a Subgorup of 5 Samples, found 8 kinds of Defects and we don’t know which Sample is Defective but within the 5 Samples found 8 kinds of Defects.

Defective

in Sample Size of 20, 5 are identified to be Defective meaning we exactly know among the 20, exactly which one is Defective.

Continuous Data

eg: measurements of each Sample can be 15.43mm, 18.99mm, 9.11mm.

Discrete Data

eg: defects/defectives or non-conformances counting like

1. in a Sample of 20 items found 5 Defective items.

2. in a Sample of 5 found 8 Defects.

Control Charts Selection

• Choosing an np Chart.
• What is np Chart.
• From Lot 1 to Lot 20.
• np Chart formula and calculations.

• “np Chart” is an Attribute Control Chart with data collected in subgroups that are the same size.
• “np Chart” is a Control Chart for Non-Conforming Units or Defectives. It is used to monitor the number of non-conforming or Defective items in the Measurement Process.
• It is therefore possible to use “np Chart” for both Quantitative and Qualitative Inspection Characteristics.
• This type of Chart is for Counting Items (with Yes/No data types).
• The expected sample size for all Lots should be the same for “np Chart” else when there are difference sample sizes then a “p Chart” is more suitable.

CL =

np = Total number of Defects

k = Number of Total Lots

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CL = np / k = Average Defects = Mean Defects (Average Defective Proportion)

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p bar = np / Sum of n (Sample sizes total)

• Choosing an np Chart.
• What is np Chart.
• From Lot 1 to Lot 20.
• np Chart formula and calculations.

CL =

CL =

CL =

Each Lot (Subgroup) has Sample of 200 items and 4 are found to be Defective

CL =

Each Lot (Subgroup)

Fixed Lot Size of 200

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

CL =

Not there are

20 Lots (20 Subgroups) and each Subgroup has

Sample of 200 units

CL =

• Choosing an np Chart.
• What is np Chart.
• From Lot 1 to Lot 20.
• np Chart formula and calculations.

CL =

np = Total number of Defects

k = Number of Total Lots

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CL = np / k = Average Defects = Mean Defects (Average Defective Proportion)

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p bar = np / Sum of n (Sample sizes total)

np is 105

Sum of Defects

k is 20

Total number of Lots

CL = Sum np / k

CL = 105 / 20

CL = 5.25

This is the Mid-Point (Mean) of the Control Chart

CL =

np is 105

Sum of Defects

Sum of n (Total Sample Qty)

p bar = Total Defects / Sum of n

p bar = 105 /4000

= 0.02625

CL =

CL =

with CL and p bar,

UCL and LCL of the NP Control Chart can be calculated

CL =

CL =