Is This Capability Calculation Method Correct?

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    A washer manufacturing process has three critical parameters – ID (inner diameter), OD (outer diameter) and HD or hole diameter (there are 8 holes on the peripheral surface of washer)

    The specifications and tolerances of the product are as under :

    OD 25.00, – 0.00, + 0.05 mm
    ID 15.00, + 0.00, – 0.05 mm
    Out of Round i.e. ovality on OD as well as on ID = 0.03 mm max.
    Hole Dia. 3.00 ± 0.02 mm

    The diameters are measured with Dial Gauge Comparators which gives Minimum and Maximum values of diameters.

    The products are manufactured through 2 routes.

    First Route has 3 sequential steps in which OD, ID and holes are produced respectively on 3 machines.

    Second route also has 3 sequential steps but are carried out on single machine with a progressive tool.

    Question 1:
    To calculate process capability for OD and ID, shall I :
    a) Take average reading of all dia and then using upper and lower specification limit calculate Cp and Cpk.
    b) Then taking difference of max. and min. values calculate out of round value and using unilateral tolerance capability formula calculate Cpk

    Question 2:
    For Hole Dia. also shall I take average of averages of dia. of all 8 holes and calculate Cp and Cpk ? If yes, how variation in Hole Dia of individual holes will get captured?

    Question 3:
    Shall I report 3 Cp and 3 Cpk indicators of the process steps in case of First Route and the lowest of 3 Cp and Cpk for Route 2 ?


    Prabhu V


    Pls find the reply based on my understanding.

    Answer 1 :

    To calculate process capability for OD and ID:
    a) Pls set up a data collection plan for every day from the production and using both USL & LSL and can calculate both Cp & Cpk separately for OD & ID
    b) On ovality like above both Cp & Cpk can be calculated using LSL =0.00 mm and USL = 0.03 mm

    Answer 2:

    For HD (Hole Diameter)
    a) If HD is critical to quality then calculating the process capability for each hole of washer using LSL =2.98 mm and USL = 3.02 mm being required, instead of average hole diameter of the washer.
    b) As you have mentioned calculating the average of 8 hole’s diameter is hard to find where is the variation present if HD is CTQ parameter.

    Answer 3:
    a) From my understanding we can able to calculate Cp & Cpk values per CTQ parameter and it is useful for further study ( I am not sure about your understanding to study Cp & Cpk for machine wise)

    Pls do share your thoughts also.

    Prabhu V.



    My comments are as under :-

    – Hole dia is one of the critical characteristics.

    – I dont think calculating 8 separate Cpk for 8 different holes will be the right appraoch becasue a) all holes are being produced in one process step and my focus is to assess process capability. b)Once a piece is out, you cant ascertain hole position and therefore you cant compare changes in the same hole dimension from one piece to other.

    – I am not calculating Cp / Cpk for machines but for different processes as there are 2 separate process routes described in my initial query.


    Prabhu V


    Based on your original post and comments, please find the below.

    > Process capability study is necessary for in order to
    i) Measure the process involves only common cause of variation not special cause of variation and
    ii) Compare the variability with a proposed product tolerance.

    >Process capability index (Cp & Cpk) is the statistical measure of process capability (i.e the ability of a process to produce output within specification limits)

    >As HD is CTQ parameter as per initial query incase of any variation in individual HD it may be captured on some tools like multi-vari charts (capable of studying about Positional, Cyclical, Temporal variation).

    > Control charts are very much suitable for studying the process as you have mentioned that incase of two separate process were involved in the activity.



    Dear Neeraj Yadav,

    If you are done with the query on capability calculation, fine. Otherwise I will be pleased to offer the most right method considering the sequence of mfg. steps/operations described by you.

    Thanks for your attention.


    Chris Seider

    You must calculate separate process capability for each characteristic. Don’t do some average Cpk which is ridiculous. If you must calculate something, calculate a total ppm defective rate but see my question below.

    What problem are you trying to solve? If one set of holes is creating defects, then find the machine and specific machine components along with other X’s to fix the issue.



    @neerajyadav – What is your objective? (and if it’s answering a homework/test question, then go pound sand).

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